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Smoothing inventory decision rules in seasonal supply chains
Accepted Manuscript
Smoothing inventory decision rules in seasonal supply chains Francesco Costantino , Giulio Di Gravio , Ahmed Shaban , Massimo Tronci PII: DOI: Reference:
S0957-4174(15)00609-0 10.1016/j.eswa.2015.08.052 ESWA 10266
To appear in:
Expert Systems With Applications
Received date: Revised date: Accepted date:
14 December 2014 29 August 2015 30 August 2015
Please cite this article as: Francesco Costantino , Giulio Di Gravio , Ahmed Shaban , Massimo Tronci , Smoothing inventory decision rules in seasonal supply chains, Expert Systems With Applications (2015), doi: 10.1016/j.eswa.2015.08.052
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Highlights
We study the value of smoothing replenishment rules in seasonal supply chains.
Simulation modeling is adopted to compare the traditional and smoothing OUT.
The impact of Holt-Winters parameters are studied under both replenishment rules.
Smoothing improves the ordering and inventory stability in seasonal supply chains.
Increasing the smoothing level reduces the bullwhip effect and inventory variance.
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Smoothing inventory decision rules in seasonal supply chains
Francesco Costantino1, Giulio Di Gravio1, Ahmed Shaban1,2,*, Massimo Tronci1
Department of Mechanical and Aerospace Engineering, University of Rome “La Sapienza”, Via Eudossiana, 18, 00184 Rome, Italy 2
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Department of Industrial Engineering, Faculty of Engineering, Fayoum University, 63514 Fayoum, Egypt [email protected], [email protected], [email protected], [email protected]
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Abstract
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A major cause of supply chain deficiencies is the bullwhip effect, which implies that demand variability amplifies as one moves upstream in supply chains. Smoothing inventory decision rules have been recognized as the most powerful approach to counteract the bullwhip effect. Although extensive studies have evaluated
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these smoothing rules with respect to several demand processes, focusing mainly the smoothing order-up-to (OUT) replenishment rule, less attention has been devoted to investigate their effectiveness in seasonal
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supply chains. This research addresses this gap by investigating the impact of the smoothing OUT on the seasonal supply chain performances. A simulation study has been conducted to evaluate and compare the smoothing OUT with the traditional OUT, both integrated with the Holt-Winters (HW) forecasting method,
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in a four-echelon supply chain experiences seasonal demand modified by random variation. The results show that the smoothing OUT replenishment rule is superior to the traditional OUT, in terms of the bullwhip effect, inventory variance ratio and average fill rate, especially when the seasonal cycle is small. In addition, the sensitivity analysis reveals that employing the smoothing replenishment rules reduces the impact of the demand parameters and the poor selection of the forecasting parameters on the ordering and inventory stability. Therefore, seasonal supply chain managers are strongly recommended to adopt the smoothing replenishment rules. Further managerial implications have been derived from the results.
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Keywords: Supply Chain; Seasonal Demand; Order-Up-To; Smoothing; Holt-Winters; Bullwhip Effect
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Corresponding author: Department of Mechanical and Aerospace Engineering, University of Rome “La Sapienza”, Via Eudossiana, 18, 00184 Rome, Italy. Tel: +39-3282777914, Fax: +39-0644585746 E-Mail: [email protected] E-Mail: [email protected]
Point-to-Point Responses to Reviewers
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Manuscript Number: ESWA-D-14-04437 Title: "Smoothing inventory decision rules in seasonal supply chains" Reviewer #1’s Comments
1) First of all, the paper's aims and scope match those of ESWA, so the topic is adequate for this journal.
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We thank the reviewer for appreciating our research, and for his valuable comments that have helped us to improve the earlier version of this manuscript considerably.
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2) The abstract in current form is superficial, and the abstract needs to rewrite to point out significance and impact of the paper.
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We thank the reviewer for this comment. We have improved the abstract structure and content with focusing specifically on the research problem statement, the research motivation and the contribution and the significance and impact of our research. The results, conclusions and managerial insights have also been rephrased to communicate our research insights in adequate manner. The abstract has almost been rewritten thoroughly and all changes in the revised abstract are highlighted in blue color.
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In particular, we have first described and discussed the bullwhip effect problem and its impacts as can be found in the first statement in the abstract. We have then introduced the motivation for conducting this research where smoothing replenishment rules have been suggested as an avoidance approach for the bullwhip effect but tested only for non-seasonal demand. Since previous research has been focusing on the impact of smoothing rules in non-seasonal supply chains, our research addresses this issue by investigating the impact of these rules in seasonal supply chains in terms of the bullwhip effect and inventory performance measures. In the revised abstract, we have also indicated the modeling approach adopted to conduct the quantitative analysis of the bullwhip effect in the seasonal supply chain model under traditional and smoothing replenishment rules. The main results of this study are summarized in the last
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part of the abstract where it has been found that smoothing inventory decision rules is superior to traditional rules in seasonal supply chains, providing further useful managerial insights. 3) The authors need to clearly demonstrate adequate understanding of the relevant literature. The authors need to include a good literature survey to show exactly what is novel about their approach. I would like a clear discussion on the current literature (2014-2015) versus the unique contribution of the paper.
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We thank the reviewer for this comment. We have upgraded the literature review in the revised manuscript according to the reviewer suggestion. The introduction section combines both the introduction and the literature review. We have also inserted a new table (Table 1) that summarizes the current literature relevant to the context of our contribution, incorporating many papers published recently in 2013-2015. The cited contributions in the table provide a clear idea on the scope of our study and a clear comparison between previous researches and our contribution in this research. The explanations of the results in this table are summarized throughout the introduction section which has been updated thoroughly and strengthened by recent references from ESWA and other high quality journals to satisfy the reviewers’ concerns.
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In particular, in the introduction section, we have started with explaining the bullwhip effect problem and its potential impacts in supply chains with providing a summary of the earlier researches that have addressed this subject (see, Paragraph 1). Next, we introduced the bullwhip effect operational causes and reviewed the modeling approaches adopted to quantify the bullwhip effect and its causes (see, Paragraph 2). In the third paragraph, we have focused on the impact of ordering policies (inventory decision rules) on the bullwhip effect with reviewing the previous related research. In this part, we have focused on the order-up-to (OUT) inventory replenishment policy which is used in our research as a benchmark since it is the most commonly used ordering policy in practice and in the bullwhip effect modeling research. In the fourth paragraph, we discussed and presented a modified version of the OUT replenishment rule, known as smoothing OUT, that can allow order smoothing and bullwhip effect avoidance. Then, we reviewed the previous related research from the context of the demand modeling, showing that there is a lack of studies devoted to investigating the bullwhip effect in seasonal supply chains (see, Paragraph 5). In Paragraphs 6-7, we reviewed the previous research, although limited, that attempted to quantify the bullwhip effect in seasonal supply chains (see, Paragraph 6), concluding also that limited studies (almost no studies other than Costantino et al. (2015a)) have been devoted to investigating the impact of smoothing replenishment rules in seasonal supply chains (see, Paragraph 7). The details of cited research in this paragraph are also summarized in Table 1. We have then discussed the motivation and contribution of this research as we aim at investigating the effect of smoothing inventory decision rules in seasonal supply chains (see, Paragraphs 7-8). Up to our knowledge, no studies other than Costantino et al. (2015a), which is published in ESWA, have attempted to explore the impact of smoothing replenishment rules in seasonal supply chains. Costantino et al. (2015a) proposed an inventory control system that relies on two control charts integrated with a set of simple decision rules to forecast future demand and adjust inventory position, whilst providing smoothing capability, to counteract the bullwhip effect. We alternatively propose the application of the smoothing OUT replenishment rule since it can easily be adapted from the traditional OUT which is commonly used in practice. We also consider a common forecasting method suitable for the seasonal demand (known as HoltPage 4 of 41
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Winters forecasting method) to integrate with the smoothing OUT, thus, all the modeling assumptions are consistent with real applications to a great extent to maximize the benefits that can be gained from this research. The main objective is to propose some robust tools that can be embedded in the decision support systems of the seasonal supply chains instead of the traditional ones.
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Finally, we explained the research contribution, methodology and organization (see, Paragraphs 8-9). Accordingly, we think that the literature relevant to the context of this paper is now covered satisfactorily in the revised paper. 4) In the conclusion section, the authors need to clearly discuss their theoretical contributions in Expert and Intelligent Systems compared to those in related papers in Expert and Intelligent Systems. Overall, contributions of the article are unclear and weak.
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We thank the reviewer for this comment. This research contributes theoretically to ESWA-related work through multiple dimensions. First, we have been motivated to submit this article to ESWA as we found some papers that are recently published in ESWA focusing on the same research problem (the impact of forecasting and inventory decision rules on the bullwhip effect) as per Jaipuria and Mahapatra (2014) and Costantino et al. (2015a) that are cited in this article. In Costantino et al. (2015a), the authors provided some directions for future research where one of these directions was to investigate the value of the smoothing inventory decision rules in seasonal supply chains as they provided some promising preliminary results and recommended further research. Therefore, we have extended the work of Costantino et al. (2015a) with evaluating the value of smoothing inventory decision rules in seasonal supply chain, focusing on the smoothing OUT replenishment policy. We have further integrated this inventory decision rule with the HW forecasting method to evaluate the impact of the forecasting parameters and their interaction with the inventory decision rules. We have aimed at providing some useful insights on the best integration of forecasting and inventory decision rules so that the mangers of seasonal supply chains can improve and adapt their current inventory decision support systems to improve ordering and inventory stability in their supply chains.
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To address the first part of the comment, in the revised manuscript, we have provided an explanation for the link between this research and ESWA-related work as can be found in both the introduction section (see, Paragraph 4, 7, 8) and the conclusion section (see, Paragraph 2). Therefore, this research is highly related to ESWA-related work and provides a good contribution that can be enhanced further as clarified in the future work directions in the conclusion section. To address the second part of the comment, we have further provided a comparison between our study and the current literature as can be found throughout the introduction section (see, Paragraph 7-8). We have further inserted a new table (Table 1) that summarizes the relevant literature, considering many recent contributions in 2013-2015. The cited contributions in the table provide a clear idea on the scope of our study and a clear comparison between previous researches and our contributions in this research. 5) It is required to provide some including remarks to further discuss the proposed methods, for example, what are the main advantages and limitations in comparison with existing methods? Page 5 of 41
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We thank the reviewer for this comment. We provided the advantages and limitation of this research as can be found in the discussion and implication section (see, Paragraph 1-5) and in the conclusions section (see, Paragraphs 2-3). In particular, in the discussion section, we have clarified the main strength and advantages of employing the smoothing replenishment rules in seasonal supply chains. The results of this paper shows that shifting from the traditional replenishment rules to the smoothing replenishment rules improves the ordering and inventory stability in seasonal supply chains, limiting potential bullwhip effect consequences. Furthermore, employing smoothing replenishment rules ameliorate the contribution of the forecasting and demand parameters to the bullwhip effect and inventory performances where it’s known that forecast updating is a major cause of the bullwhip effect and inventory instability. However, the results indicate that when the seasonal cycle is long, dampening order variability may amplify inventory instability at the most downstream echelons. This might limit the applications of smoothing replenishment rules especially when the supply chain is small (a few number of echelons) and facing a seasonal demand with long seasonal cycle. However, this issue can be overcome by enabling an incentive scheme to achieve coordination in seasonal supply chains. This specific explanation in integrated in the discussion and implications section (see, Paragraph 5). Other explanations for the advantages and limitations are provided in the conclusions section. Reviewer #2’s Comments
The topic is interesting, however, I would suggest the following comments for improvements:
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We thank the reviewer for appreciating our research, and for his valuable comments and suggestions that have helped us to improve the earlier version of this manuscript.
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Please give a frank account of the strengths and weaknesses of the proposed research method. This should include theoretical comparison to other smoothing decision rules.
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We thank the reviewer for this comment. To satisfy the reviewer’s comment, we have added a new paragraph discussing the strengths and weaknesses of the proposed research method in the discussion section (see, Paragraph 5). The strength of this research emerges from its uniqueness since the literature shows limited research that has attempted to evaluate the effectiveness of the smoothing replenishment rules in seasonal supply chains (see, Table 1). The results of this paper confirm that employing the smoothing replenishment rules (e.g., smoothing OUT) improves the ordering and inventory stability in seasonal supply chains. Another possible strength, concluded from the sensitivity analysis, is that employing the smoothing replenishment rules reduces the impact of the demand parameters and the poor selection of the forecasting parameters on the ordering and inventory stability. In this research, the smoothing OUT replenishment rule which is a modified version of the traditional OUT policy was considered to evaluate the impact of smoothing in seasonal supply chains. The traditional OUT, commonly used in practice, can simply be converted into smoothing OUT by adding two proportional controllers to the gaps of the net inventory and supply line (see, equation (11-12)). Therefore, the current seasonal supply chains that employ traditional OUT can largely benefit from the concepts and results presented in this study, to overcome the bullwhip effect. However, a possible weakness of the smoothing replenishment rules is that dampening the order variability has a negative impact on customer service due to an increased Page 6 of 41
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inventory variance. We have noticed that this trade-off between the bullwhip effect and inventory stability might happen at the most downstream echelons in seasonal supply chains when the seasonal cycle is long. Other issues are explained in the conclusions section.
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Second, I would like authors to add a paragraph in the introduction discussing the topic from an "expert systems" point of view. The journal aims in publishing paper in expert and intelligent systems; the introduction does not clearly place the paper in that area. We thank the reviewer for this comment. We have incorporated the required paragraphs in the introduction to clearly place the paper in the ESWA scope. The related discussions can be found in paragraphs 4 and 7.
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Specifically, the current manuscript addresses the bullwhip effect which implies information distortion in the sense of demand variability amplification as one moves upstream in the supply chain, causing severe inefficiencies such as excessive inventory, and high production and transportation costs. In traditional supply chains, each supply chain partner relies on the incoming information from the adjacent downstream echelon to make his forecasting and inventory planning which means that the upstream echelons receive distorted demand information. To achieve intelligent supply chain system, the first step should be allowing the upstream echelons to have accurate or less distorted information on the customer demand. Seasonal supply chains like other normal supply chains need to be equipped with robust inventory decision rules to counteract the bullwhip effect and avoid unwanted consequences. Previous supply chain research has been focusing on the non-seasonal supply chain and their efforts have proposed many avoidance approaches for the bullwhip effect such as the smoothing replenishment rules. This research attempts to evaluate the impact of these inventory decision rules in seasonal supply chains. The main objective is to propose and evaluate some robust tools that can be embedded in the decision support systems of the seasonal supply chains instead of the traditional ones. This explanation has been integrated to the introduction section in paragraph 4.
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To the best of our knowledge, no studies other than Costantino et al. (2015a) have attempted to explore or quantify the impact of smoothing replenishment rules in seasonal supply chains. Costantino et al. (2015a) contributed in ESWA with an inventory replenishment system that relies on two control charts integrated with a set of simple decision rules to forecast future demand and adjust inventory position, whilst providing smoothing capability, to counteract the bullwhip effect. Their preliminary results have shown that smoothing inventory decision rules (in general) can improve seasonal supply chain dynamics compared to traditional ordering policies, suggesting further analysis since their study was not devoted for the extensive analysis of seasonal supply chains. Motivated by these observations, this research attempts to confirm and extend the preliminary work of Costantino et al. (2015a) under different modeling assumptions in terms of the ordering and forecasting method. We mainly propose the application of the smoothing OUT replenishment rule to ameliorate the bullwhip effect in seasonal supply chain since it can easily be adapted from the traditional OUT replenishment system which is commonly used in practice. We further consider the Holt-Winters (HW) forecasting method (Triple Exponential Smoothing) to forecast future demand and update the inventory control parameters, as it is the most suitable forecasting method to forecast seasonal demand. These modeling assumptions are consistent with real applications and therefore the research
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insights will be meaningful to practitioners. This explanation is integrated in the introduction section in paragraph 7. Third, in your conclusion please clearly discuss your research contributions in expert and intelligent systems.
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We thank the reviewer or this comment. We have updated the conclusion section with inserting a new paragraph that explains the main contributions of this study to the ESWA-related work. In addition, other parts in the conclusion section have been updated. We have discussed the contributions of this research. We would like also to refer the reviewer to our replies under the comment # 4 of the first reviewer as he suggested the same improvements. All changes are highlighted with blue color.
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Smoothing inventory decision rules in seasonal supply chains
Abstract
A major cause of supply chain deficiencies is the bullwhip effect, which implies that demand variability
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amplifies as one moves upstream in supply chains. Smoothing inventory decision rules have been recognized as the most powerful approach to counteract the bullwhip effect. Although extensive studies have evaluated these smoothing rules with respect to several demand processes, focusing mainly the smoothing order-up-to
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(OUT) replenishment rule, less attention has been devoted to investigate their effectiveness in seasonal supply chains. This research addresses this gap by investigating the impact of the smoothing OUT on the
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seasonal supply chain performances. A simulation study has been conducted to evaluate and compare the smoothing OUT with the traditional OUT, both integrated with the Holt-Winters (HW) forecasting method, in a four-echelon supply chain experiences seasonal demand modified by random variation. The results show
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that the smoothing OUT replenishment rule is superior to the traditional OUT, in terms of the bullwhip effect, inventory variance ratio and average fill rate, especially when the seasonal cycle is small. In addition, the sensitivity analysis reveals that employing the smoothing replenishment rules reduces the impact of the
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demand parameters and the poor selection of the forecasting parameters on the ordering and inventory stability. Therefore, seasonal supply chain managers are strongly recommended to adopt the smoothing replenishment rules. Further managerial implications have been derived from the results.
Keywords: Supply Chain; Seasonal Demand; Order-Up-To; Smoothing; Holt-Winters; Bullwhip Effect
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1. Introduction A supply chain is an integrated system wherein a set of organizations/partners; e.g. suppliers, manufacturers, distributors, retailers and customers; are connected by material, financial and information flows in both upstream and downstream directions. A supply chain is a complex and dynamic system that should be designed and managed properly to match supply and demand at
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minimum cost. The lack of coordination among supply chain partners and the unavoidable uncertainty usually result in severe deficiencies in the supply chain. An example of such deficiency is the bullwhip effect which implies that orders variance amplifies as one moves upstream in the supply chain (see, Figure 1). Lee et al. (1997a, b) have indicated with providing some real examples from different industries that, even if the customer demand is stable and stationary, a supply chain
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will face the bullwhip effect for any case of misalignment between demand and supply. This can be attributed to the tendency of supply chain partners to update their forecasts and inventory control parameters in response to demand uncertainty which may subsequently lead to a propagation of distorted demand information across the supply chain (Disney and Lambrecht, 2008; Lee et al., 1997a, b). Forrester (1958) was almost the first to study the bullwhip effect through a set of
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simulation experiments utilizing system dynamics modeling, and concluded that the structure, policies and interactions within supply chains are the main drivers of demand variability amplification. Subsequent researchers developed simulation games to illustrate the bullwhip effect
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existence as well as its negative effects in supply chains (Sterman, 1989).
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Factory Orders Distributor Orders Wholesaler Orders
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Figure 1. An example of demand variability amplification in supply chain (Costantino et al., 2015a)
The bullwhip effect has attracted the attention of academics and practitioners because of its potential negative consequences in supply chains such as excessive inventory investment, poor customer service, lost revenues, misguided capacity plans, ineffective transportation, and missed production schedules (Chatfield et al., 2004; Lee et al., 1997a, b). Lee et al. (1997a, b) have Page 9 of 41
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identified five major operational causes of the bullwhip effect: demand signal processing, lead-time, order batching, price fluctuations and rationing and shortage gaming. Of our particular interest is the demand signal processing which includes the rational practice of adjusting the demand forecasts and accordingly adjusting the parameters of the inventory replenishment policies, where doing this rationale adjustments may cause under/over-reactions to short-term fluctuations in demand,
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inducing the bullwhip effect (Costantino et al., 2015a, b, c; Dejonckheere et al., 2004). Extensive research has been devoted to quantify the impact of the demand signal processing and the other bullwhip effect causes, utilizing several modeling approaches (Chatfield, 2013): statistical modeling (Chen et al., 2000a, b; Cho and Lee, 2013), simulation modeling (Chatfield et al., 2004; Chatfield, 2013; Costantino et al. 2014a, b, c) and control theoretic modeling (Dejonckheere et al. 2003; Dejonckheere et al., 2004; Jakšič and Rusjan, 2008). The summary of the relevant literature is
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presented in Table 1 showing clearly this classification.
Previous research has emphasized the importance of selecting accurate forecasting methods and proper ordering policies (inventory decision rules) in order to counteract the bullwhip effect in supply chains (Costantino et al., 2015b; Costas et al., 2015; Dejonckheere et al., 2004; Jaipuria and
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Mahapatra, 2014; Shaban et al., 2015; Wright and Yuan, 2008). The majority of the bullwhip effect studies have been considering the order-up-to inventory policies in their models motivated by its
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common use in practice (Chen et al., 2000a, b; Costas et al., 2015; Dejonckheere et al., 2004). Most previous studies have shown that the bullwhip effect is guaranteed when the order-up-to inventory policy (OUT) is employed in supply chains irrespective of the forecasting method integrated
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with it and without making any assumptions about the demand process (Bayraktar et al., 2008; Dejonckheere et al., 2003, 2004). Costas et al. (2015) have recently confirmed the same conclusions
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for the OUT inventory control policy and proposed the Goldratt’s Theory of Constraints to reduce
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the bullwhip effect.
The bullwhip effect implies information distortion in the sense of demand variability amplification as one moves upstream in the supply chain, causing severe inefficiencies such as high production and transportation costs. In traditional supply chains, each supply chain partner relies on the incoming orders from the adjacent downstream echelon to make his forecasting and inventory planning which means that the upstream echelons receive distorted demand information. To achieve intelligent supply chain system, the first step should be allowing the upstream echelons to have accurate information (or less distorted information) on the customer demand. Most importantly, Page 10 of 41
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smoothing replenishment rules have been recognized as the most powerful approaches to avoid/eliminate the bullwhip effect. Many researchers have been attempting to evaluate their dynamic performance compared to other traditional ordering policies, under various operational conditions. The available smoothing replenishment rules have been developed mainly based on the periodic review order-up-to policy by incorporating smoothing terms in the OUT replenishment rule
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where their rationale is to avoid the over/under-reaction to short-run fluctuation in demand and thus limiting the bullwhip effect (Costantino et al., 2015a; Dejonckheere et al., 2003, 2004). In traditional OUT, the replenishment order decision is generated to recover the entire gaps between the target and current levels of net inventory (safety stock) and supply line inventory, while in smoothing OUT only a fraction of each gap is recovered (controlled by the smoothing terms/parameters), where the target levels are dynamically updated according to demand forecast in
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every review period. However, some researches have shown that dampening the bullwhip effect might increase inventory instability causing low service level (Costantino et al., 2015a; Disney and Lambrecht, 2008; Jaipuria and Mahapatra, 2014). In Table 1, we provide further details on the previous research related to the context of this paper, focusing on the modeling aspects and the
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scope of study.
The majority of the bullwhip studies have assumed that the demand process is non-seasonal and
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stationary process, e.g., modeling it as autoregressive moving average (ARMA) and its variants (Cho and Lee, 2012, 2013; Costantino et al., 2013b; Wang and Disney, 2015). In particular, most of the previous studies have quantified the bullwhip effect in supply chains facing customer demand
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follows the autoregressive AR and ARMA demand processes; and employing the traditional OUT policy with different forecasting systems such as moving average (MA), exponential smoothing
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(ES), and mean squared error optimal forecasting (MMSE) methods (Chandra and Grabis, 2005; Chen et al., 2000a, b; Costantino et al., 2015a, b; Disney et al., 2006; Hussain et al., 2012; Ma et al.,
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2013; Zhang, 2004). Many other studies have adopted the normality assumption for modeling the external demand in similar supply chain models (Chatfield, 2013; Chatfield et al., 2004; Costantino et al., 2013a, b; Costas et al., 2015; Dejonckheere et al., 2004). The same conclusions are valid for the previous studies on the smoothing replenishment rules where previous studies have been considering step demand (Ciancimino et al., 2012; Dejonckheere et al., 2004) or other common non-seasonal demand process such as normal and autoregressive (Costantino et al., 2015b; Dejonckheere et al., 2004). In general, there is a lack of studies that have been devoted to study the bullwhip effect in seasonal supply chains, either for traditional OUT or for smoothing OUT Page 11 of 41
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inventory decision rules (Bayraktar et al., 2008; Cho and Lee, 2012; Costantino et al., 2015a). This can easily be seen in Table 1 that summarizes the relevant literature according to some categories, modeling technique, inventory control policy, forecasting method, demand model, performance metrics and scope of study. This table is adapted from Costantino et al. (2015b) but with
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incorporating the proper changes to support the context of this research.
The seasonality phenomenon of demand is a common occurrence in many supply chains where it is common that a supply chain faces demand process contain a seasonal cycle repeats itself after a regular period of time (Wei, 1990). The seasonality may stem from multiple factors such as weather, which affects many business and economic activities like clothing and food industries (Cho and Lee, 2013; Chopra and Meindl, 2004; Wei, 1990). The seasonality can potentially cause
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mismatching supply with demand in supply chains and thus might result in the bullwhip effect (Cho and Lee, 2012, 2013). Cho and Lee (2012) have quantified statistically the bullwhip effect in a twoechelon supply chain employs traditional OUT policy and experiences a seasonal autoregressivemoving average process (SARMA (1, 0) X (0,1)s) showing that the lead-time must be smaller than the seasonal cycle to mitigate the bullwhip effect. They have further evaluated the bullwhip effect in
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this supply chain model under different information sharing scenarios (Cho and Lee, 2013). Bayraktar et al. (2008) have analyzed the impact of exponential smoothing forecasts (Holt-Winters)
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within the traditional OUT on the bullwhip effect for a single electronic supply chain experiences seasonal demand. They have concluded that although high seasonality would reduce the forecast accuracy, it has a significant effect on the reduction of bullwhip effect; providing further
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conclusions regarding the impact of the forecasting parameters on the bullwhip effect. Costantino et al. (2013b) have quantified the impact of demand seasonality parameters, forecasting and safety
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stock parameters and their interactions on the bullwhip effect and inventory stability, in a fourechelon supply chain employs the traditional OUT policy, through a simulation study. Nagaraja et
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al. (2015) have quantified statistically the bullwhip effect in a supply chain employs OUT and faces SARMA(p, q) × (P, Q)s demand process, showing that the bullwhip effect can be mitigated considerably by reducing the lead-time in relation to the seasonal lag value. The previous studies on the bullwhip effect in seasonal supply chains, although limited, have been considering the traditional OUT policy without investigating the smoothing replenishment rules that have been found to be a powerful solution for avoiding the bullwhip effect.
Seasonal supply chains like other normal supply chains need to be equipped with robust inventory Page 12 of 41
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decision rules to counteract the bullwhip effect and avoid unwanted consequences. Previous supply chain research has been focusing on the non-seasonal supply chain and their efforts have reached to many avoidance approaches for the bullwhip effect such as the smoothing replenishment rules (Costantino et al., 2015a; Dejonckheere et al., 2003, 2004). This research attempts to evaluate and predict the impact of the smoothing inventory decision rules in seasonal supply chains. The main
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objective is to propose some robust tools that can be embedded in the decision support systems of the seasonal supply chains instead of the traditional ones. Up to our knowledge, no studies other than Costantino et al. (2015a) have attempted to explore or quantify the impact of smoothing replenishment rules in seasonal supply chains. Costantino et al. (2015a) contributed in ESWA with a real-time SPC inventory replenishment system that relies on two control charts integrated with a set of simple decision rules to forecast future demand and adjust inventory position, whilst
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providing smoothing capability, to counteract the bullwhip effect. Their preliminary results have shown that smoothing inventory decision rules (in general) can improve seasonal supply chain dynamics compared to traditional ordering policies, suggesting further analysis since their study was not devoted for the extensive analysis of seasonal supply chains. Motivated by these observations, this research attempts to confirm and extend the preliminary work of Costantino et al.
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(2015a) under different modeling assumptions with respect to the ordering policy and forecasting method. We mainly propose the application of the smoothing OUT replenishment rule to ameliorate
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the bullwhip effect in seasonal supply chain since it can easily be adapted from the traditional OUT which is commonly used in practice, and the smoothing OUT is well recognized in literature as well. We further consider the Holt-Winters (HW) forecasting method (Triple Exponential
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Smoothing) to forecast future demand and update the inventory control parameters, as it is the most suitable forecasting method to forecast seasonal demand. Therefore, this research considers
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modeling assumptions that are consistent with real applications and therefore the research insights
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will be meaningful to practitioners.
Simulation is the most appropriate modeling approach to investigate the performances of complex systems like multi-echelon supply chains (Chatfield, 2013; Chatfield et al., 2004; Costantino et al., 2015a, b). Therefore, in this research, a simulation study is conducted to evaluate and compare the smoothing OUT with the traditional OUT, both integrated with the Holt-Winters (HW) forecasting method, in a four-echelon supply chain experiences seasonal demand modified by random variation. We further evaluate the impact of the HW forecasting parameters under the traditional and smoothing replenishment rules to understand the impact of these parameters and their interaction Page 13 of 41
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with the different replenishment rules. The seasonal supply chain performance is evaluated in terms of the bullwhip effect ratio, inventory variance ratio and average fill rate (service level). The results show that the smoothing OUT improves the ordering and inventory stability in the seasonal supply chain. The results also show that increasing the order smoothing level improves the ordering and inventory stability in the seasonal supply chain. The sensitivity analysis confirms that employing
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the smoothing replenishment rules reduces the impact of both the seasonal demand parameters and the poor selection of the forecasting parameters on the ordering and inventory stability. The results provide some useful managerial insights that can be utilized by supply chain managers of seasonal supply chains to re-engineer their decision support systems, and they can further utilize these insights to develop expert systems to handle the operational and behavioral causes of the bullwhip effect. The results of this study provide further useful managerial implications on controlling the
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ordering and inventory stability in seasonal supply chains.
The paper is organized as follows. Section 2 introduces the modeling methodology: supply chain model, ordering policy, forecasting method, seasonal demand model, and performance measures. Section 3 introduces the simulation model and validation results. Section 4 presents the simulation
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results and sensitivity analysis, and the discussion and implications are presented in Section 5. The
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conclusions and future research are provided in Section 6.
Table 1: Related research (Costantino et al., 2015b)
al.
Statistical, Simulation
CE
Chen et (2000a, b)
Inventory control
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Modeling technique
Traditional OUT
Forecasting method
MA, ES
Control theoretic
Traditional OUT, Smoothing OUT
MA, ES, demand signaling
Chatfield et al. (2004)
Simulation
Traditional OUT
MA
Dejonckheere et al. (2004)
Control theoretic, Simulation
Traditional OUT, Smoothing OUT
MA, ES, demand signaling
Zhang (2004)
Statistical
Traditional OUT
MA, ES, MMSE
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Dejonckheere et al. (2003)
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Demand model
AR
Sinusoidal , Real data, i.i.d. normally distributed demand, Step i.i.d. normally distributed demand i.i.d. normally distributed demand
AR
Performance measures
Bullwhip ratio
effect
Bullwhip ratio
effect
Bullwhip ratio
effect
Bullwhip ratio
effect
Bullwhip ratio
effect
Scope of study Measuring the impact of leadtime, forecast parameter and information sharing on the bullwhip effect, in supply chain employs the traditional OUT. Comparing the bullwhip effect under different forecasting methods within traditional OUT. Quantifying the impact of smoothing OUT on the bullwhip effect Quantifying the impact of lead-time variation, information sharing and quality on the bullwhip effect Quantifying the impact of forecasting, information sharing and order smoothing on the bullwhip effect Measuring the impact of lead time and demand pattern parameter on the bullwhip under different forecasting methods
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Chandra and Grabis (2005)
Disney et (2006)
al.
MA, ES, Naïve, Autoregress ive
AR
Bullwhip ratio, Inventory
Traditional OUT, Smoothing OUT
ES
i.i.d. normally distributed demand, AR, MA, ARMA
Bullwhip effect ratio, Inventory Variance, Fill rate
Seasonal
Bullwhip ratio
Simulation
Traditional OUT, MRP
Control theoretic
effect Avg.
Bayraktar et al. (2008)
Simulation
Traditional OUT
Triple exponential smoothing (HW forecasting method)
Kelepouris al. (2008)
Simulation
Traditional OUT
ES
Real data
Bullwhip effect ratio, Fill rate
Wright and Yuan (2008)
Simulation
Smoothing OUT
MA, Holt’s and Brown’s methods
Local trends modified by i.i.d
Bullwhip effect ratio, Root mean square, Inv. costs
Ciancimino al. (2012)
Simulation
Smoothing OUT
ES
Step demand
Bullwhip effect ratio, Inventory variance, Fill rate
Simulation
Traditional OUT
ES, MMSE
AR
Bullwhip effect ratio, Inventory variance
Statistical
Traditional OUT
Cho and Lee (2012)
Cho and Lee (2013)
Statistical
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Ma et al. (2013)
Statistical
et
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Costantino al. (2013b)
Costantino al. (2014c)
et
Jaipuria and Mahapatra (2014)
Costantino et al. (2014b, d)
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MMSE
Traditional OUT
Traditional OUT
MMSE
MA, ES, MMSE
Seasonal demand SARMA (1, 0) X (0,1)s Seasonal demand SARMA (1, 0) X (0,1)s Price sensitive demand with AR i.i.d. normally distributed demand, Seasonal modified by i.i.d i.i.d. normally distributed demand
Quantifying the bullwhip effect and inventory variance under a generalized OUT policy for different demand patterns Measuring the impact of seasonality, lead-time and HW forecasting parameters, and their interactions on the bullwhip effect in E-SC employs traditional OUT Investigating the impact of lead time, exponential smoothing parameter and safety stock on the bullwhip effect in simulated real supply chain Evaluating the impact of improved forecasting and inventory control parameters on the bullwhip effect and inventory costs Analyzing the operational response of a synchronized supply chain employs the smoothing OUT. Analyzing the bullwhip effect ratio and inventory variance under different forecasting methods within traditional OUT.
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Hussain et al. (2012)
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et
PT
et
effect
Analyzing the bullwhip effect under traditional OUT and MRP approach with different forecasting methods
Bullwhip ratio
effect
Quantifying the bullwhip effect in a seasonal supply chain employs the traditional OUT
Order variance, Avg. inventory, inventory variance, inventory cost
Analyzing the value of information sharing in seasonal supply chain employs the traditional OUT
Bullwhip effect ratio, Inventory variance
Analyzing the bullwhip effect ratio and inventory variance under different forecasting methods integrated with traditional OUT.
Bullwhip effect ratio, Inventory variance, Fill rate
Exploring the bullwhip effect and inventory variance in a seasonal supply chain employs traditional OUT.
Bullwhip effect ratio, Inventory variance, Fill rate
Analyzing the value of information sharing and inventory control coordination on supply chain performances
Simulation
Traditional OUT
MA
Simulation
Traditional OUT
MA
AI, Simulation
Traditional OUT
ARIMA, DWT-ANN
Real data, literature data
Mean square error, bullwhip effect ratio, Inventory variance
Analyzing the value of improved forecasting on order and inventory variances
MA, SPCForecasting
i.i.d. normally distributed demand, AR
Bullwhip effect ratio, Inventory variance, Fill rate
Developing inventory control systems based on control charts to improve supply chain dynamics
Simulation
Traditional OUT, SPC
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Demand patterns of different frequencie s, Real data i.i.d. normally distributed demand, AR, seasonal
Investigating the bullwhip effect under damped trend used within traditional OUT and comparing it to other forecasting methods.
Control theoretic
Traditional OUT
MA, ES, Naïve, Damped trend
Costantino et al. (2015a, b)
Simulation
Traditional OUT, smoothing OUT, SPC
MA, ES, SPCForecasting
Costas et (2015)
Multi-agent simulation
Traditional OUT, Theory of Constraints (TOC)
MA
i.i.d. normally distributed demand
Bullwhip effect ratio, Inventory variance
Mitigating the bullwhip effect with Goldratt’s Theory of Constraints (TOC)
Statistical
Traditional OUT
MMSE
Seasonal demand SARMA (p, q) × (P, Q)s
Bullwhip ratio
Quantifying the bullwhip effect in supply chains with seasonal demand components and use traditional OUT.
Nagaraja et al. (2015)
Bullwhip effect ratio, Inventory variance, Fill rate
Developing forecasting and inventory control systems based on control charts to counteract the bullwhip effect
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al.
effect
effect
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Li et al. (2014)
Bullwhip ratio
2. Modeling Methodology 2.1 Supply Chain Model
In this research, we model and simulate a multi-echelon supply chain that consists of a customer, a
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retailer, a wholesaler, a distributor, a factory, and an external supplier (see, Figure 2). This is a wellknown supply chain model, known as the Beer Game model, and has been utilized in many
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previous bullwhip effect investigations (Chatfield, 2013; Chatfield et al., 2004; Ciancimino et al., 2012; Costantino et al., 2014a, b, c, d; Costantino et al., 2015a, b). Figure 2 depicts a visual representation of the supply chain structure in which, at any period, each echelon i receives orders
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from its downstream partner i 1 , satisfies these orders from his own stock and then issues his orders with echelon i 1 . The retailer observes and satisfies the customer demand Dt and places
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orders with the wholesaler where the retailer is the only partner in the supply chain that has direct
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access to the actual customer demand.
Customer
Retailer
Wholesaler
Distributor
Factory
External Supplier
Information flow Product flow
Figure 2. A multi-echelon supply chain
The supply chain model presents the following assumptions (Ciancimino et al., 2012; Costantino et
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al., 2015a, b; Sterman, 1989; Wright and Yuan, 2008):
the factory has unlimited capacity to produce any quantity ordered by the distributor;
the stocking capacity at any echelon is unlimited;
the unfulfilled orders, due to out of stock, at any echelon are not lost while they become
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backlogged orders, to satisfy as soon as the inventory recovers;
the transportation capacity between adjacent echelons is unlimited;
the ordering and delivery lead-times are deterministic and fixed across the supply;
the replenishment orders are always positive or equal to zero, cancelations are not allowed
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(no returns).
The regulation of information and material flows in the above supply chain model is controlled based on the mathematical model represented by the difference equations (1-6). The equations define the basic state variables at each echelon i that are updated in each period t based on a specific sequence of events; where i 1, ..., 4 ; i.e., i 1 stands for the retailer and i 4 stands for
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the factory, and we also refer to the customer as echelon i 0 (Costantino et al., 2014c, 2015a, b).
(1)
1 SRti Min IOti Bti1; Iti1 SRtiLd
(2)
1 Iti I ti1 SRtiLd SRti
(3)
Bti Bti1 IOti SRti
(4)
NIti Iti Bti
(5)
IPt i NI ti SLit
(6)
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CE
PT
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1 SLit SLit 1 Oti1 SRtiLd
In each period t , each echelon i receives an amount of shipment SRtiL1i shipped by the upstream d
echelon i 1 at time t Lid , where Lid expresses the delivery lead-time. Thus, the initial inventory level I ti1 is increased by the shipment SRtiL1i and at the same time decreases by the amount of SRti d
released down to the echelon i 1 (see, equation (3)). The amount SRti to ship to echelon i 1 depends on the minimum of the initial inventory I ti1 added to the incoming shipment SRtiL1i , and d
i t
i t 1
the incoming order IO added to the initial backlogged order B Page 17 of 41
(see, equation (2)) where at the
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retailer (echelon i 1 ), the incoming order at time t is the observed customer demand at this time ( IOti 1 Dt ). Thus, the net inventory NI ti presented in equation (5) is equal to the difference between the available inventory level I ti (see, equation (3)) and the backlog level Bti (see, equation (4)) at time t . The inventory position of echelon i at time t in equation (6) is the accumulation of the amount in supply line SLit in equation (1) and the net inventory level in equation (5). The
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replenishment order Oti of each echelon i 1 at time t is controlled and issued based on the generalized order-up-to inventory policy. 2.2 Smoothing Order-Up-To Inventory Policy
The periodic review order-up-to inventory policy, known also as (R, S), is common in the literature
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of supply chain dynamics because of its popularity in practice (Disney and Lambrecht, 2008). This type of replenishment policies is common in practice as in retailing that tends to replenish inventories frequently (e.g. daily, weekly, etc.). A generalized variant of this policy is used here to allow order smoothing through avoiding the over/under-reaction to demand and inventory variations. In the traditional OUT policy, at the end of each review period ( R ), where it is assumed
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that R 1 in this model, a non-negative replenishment order Oti is placed whenever the inventory position IPt i is lower than a specific target inventory or base stock level Sti (see, equation (7)). In
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other words, the entire gap between the target and actual levels of inventory position are taken into account in the placed order. The traditional order-up-to policy can be represented mathematically as
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PT
in equations (7-8).
Oti Max Sti IPt i , 0
(7)
Sti LDˆ ti SSti
(8)
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The base stock level Sti is dynamically updated in each time period based on the expected demand over the total lead-time (review period and delivery lead-time, Lid R ) plus a safety stock component (see, equation (8)). The Holt-Winters forecasting technique is adopted to estimate the expected demand ( Dˆ ti ) since it the most suitable forecasting method for predicting seasonal demand (Bayraktar et al., 2008). Following the relevant literature, we have considered the safety stock that is required to account for demand variation by extending the lead-time with the safety stock paramter Ki as shown in equation (9) (Costantino et al. 2015a, b; Dejonckheere et al., 2004). Page 18 of 41
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(9)
Sti ( Lid R K i ) Dˆ ti
In the traditional order-up-to policy, the order can be divided into: a demand forecast, a net inventory error term and a supply line inventory error term, but both the errors terms are completely taken into account in the placed order (see, equation, (10)). Some researchers have proposed some ways that can increase the flexibility of OUT to allow order smoothing in which the decision maker
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does not recover the entire errors in one time period. Specifically, in the smoothing OUT inventory decision rule, a fraction of each error term is recovered in each review period to dampen the ordering variability. Equation (11) represents the generalized order-up-to policy which can allow order smoothing with setting Tn 1 and Ts 1 .
Lid Dˆ ti SLit K i Dˆ ti NI ti Tn Ts
(10)
(11)
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Oti Dˆ ti
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Oti ( Lid R K i ) Dˆ ti NI ti SLit Oti Dˆ ti Lid Dˆ ti K i Dˆ ti NI ti SLit Oti Dˆ ti Lid Dˆ ti SLit K i Dˆ ti NI ti
In equation (11), the term Lid Dˆ ti represents the target amount in supply line/pipeline ( TSLit ), and
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K i Dˆ ti denotes the target net inventory/safety stock ( TNI ti ); and Tn and Ts are two proportional
controllers (smoothing parameters) for regulating the recovery of the errors of net inventory and
PT
supply line over time, respectively. For simplicity, we consider Tn Ts and thus the replenishment rule can be written in a general form in equation (12), in which, setting Tn 1 turns the replenishment rule into a traditional order-up-to policy that doesn’t allow order smoothing
AC
CE
(Ciancimino et al., 2012; Costantino et al., 2015a; Dejonckheere et al., 2003, 2004).
TNI ti TSLit IPt i Oti Max Dˆ ti , 0 Tn
(12)
2.3 Holt-Winters Forecasting The demand forecast at each echelon in the supply chain model ( Dˆ ti ) is estimated based on the HoltWinters forecasting method (Triple Exponential Smoothing) which is suitable for demand patterns with trend and seasonal components. The Holt-Winters (HW) method comprises the forecast equation and Page 19 of 41
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three smoothing equations for level component lti , trend component bti , and seasonal component
ti , including the smoothing parameters , and , respectively (Chopra and Meindl, 2004; Montgomery et al., 2008). In each period t , the three smoothing components are updated according to the following equations (13-15):
(13)
bti lti lti1 1 bti1
(14)
ti IOti lti 1 ti s
(15) (16)
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Ft i m lti mbti ti m s
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lti IOti ti s 1 lti1 bti1
where:
, and are the HW forecast smoothing parameters,
lti is the estimated level of incoming order to echelon i at time t ,
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bti is the estimated trend of incoming order to echelon i at time t ,
ti is the estimated seasonality of incoming order to echelon i at time t ,
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s is the number of periods in a seasonal cycle,
Ft i m is the forecasted demand at m periods ahead, where m 1, ..., s .
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In each period t , the demand forecast at m periods ahead ( Ft i m ) can be estimated based on equation (16). However, in this model, it is only required to dynamically estimate the next period’s demand (the
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one-period ahead demand forecast, Dˆ ti ) where Dˆ ti Ft i1 lti bti Sti1 s , to calculate the target levels of supply line inventory and net inventory (see, equations (11-12)). To apply the HW method, it is
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required to have at least two complete seasonal cycles of demand/incoming order data to obtain the initial values of the forecast components ( l0i , b0i and 0i ) that can be calculated using the formulas in equations (17-19). This can be managed in the simulation model by selecting a proper warm-up period.
l0i
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1 s IOij s j 1
(17)
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i
b0i
i
1 s IOs j IO j s s j 1
0i IO ij l0i ,
(18)
j 1, ..., s
(19)
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2.4 Seasonal Demand Model The external demand ( Dt ) faced by the retailer is generated to have a seasonal component and modified with random variation, according to the formula in equation (20). This demand generator is adapted from Zhao and Xie (2002) and Costantino et al. (2013b, 2015a) and consists of constant demand ( base ), trend component ( slope ), seasonal component (sinusoidal function with
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parameters season and SeasonCycle ), and noise component ( ). In this study, the trend component is neglected with setting slope 0 , and the base will be set relatively high to season and in the simulation experiments to avoid the generation of negative demand, to satisfy the nonnegativity condition of customer demand.
(20)
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2 Dt base slope t season sin t N 0, 2 SeasonCycle 2.5 Performance Measures
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The objective of this study is to investigate the impact of the smoothing replenishment rules in seasonal supply chain in terms of the demand variability amplification and the corresponding
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inventory performances. Therefore, three performance measures are considered: bullwhip effect ratio (i.e., order variance ratio), inventory variance ratio, and average fill rate (i.e., service level).
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The bullwhip effect ratio ( BWEi ), known also as order variance ratio, has been widely used in the literature of supply chain dynamics to quantify the amplification of order variability across the supply chain (Ciancimino et al., 2012; Costantino et al., 2014c; Disney and Lambrecht, 2008). The
BWEi as shown in equation (21) represents the ratio of orders variance at echelon i ( O2i ) relative to the demand variance ( D2 ) where BWEi 1 results in bullwhip effect; BWEi 1 results in order smoothing; and BWEi 1 results in a “pass-on-orders” (Disney and Lambrecht, 2008).
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BWEi
O2i
(21)
D2
The second performance measure is the inventory variance ratio which was proposed by Disney and Towill (2003) to measure the degree of inventory stability since it quantifies the fluctuations in net
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2 inventory ( NI ) relative to the demand variance ( D2 ) as presented in equation (22). An increased i
inventory variance ratio indicates higher inventory instability that would result in higher holding and backlog levels, lower service level and subsequently higher inventory costs (Disney and Lambrecht, 2008). Therefore, dampening both the bullwhip effect ratio and the inventory variance ratio across the supply chain reflects improved operational performance of the supply chain (i.e.,
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improved ordering and inventory stability).
InvRi
2 NI i
D2
(22)
The average fill rate ( AFRi ) quantifies the percentage of items supplied immediately by echelon i
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from stock at hand to satisfy the incoming order (Costantino et al., 2014c, 2015a; Zipkin, 2000). The fill rate ( FRti ) is computed every time there is a positive incoming order (i.e., when IOti 0 ) as
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shown in equation (23), where SRti stands for the shipment released by echelon i at time t , Bti1 stands for the initial backlog at echelon i at time t , and IOti is the incoming order to echelon i at
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time t . The effective computational time ( Teff ) is equivalent to the summation of all periods with IOti 0 ; hence Teff T where T is the total computational time. The fill rate time series can then
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be used to calculate the average fill rate ( AFRi ), which implies the average service level, as
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indicated in equation (24).
SRti Bti1 100 FRti IOti 0
AFRi
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if SRti Bti1 0 i t
i t 1
if SR B Teff t 1
FRti
Teff
(23)
0
(24)
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3. Simulation Model Validation Simulation modeling is the most suitable tool to characterize the performance of complex and dynamic systems like multi-echelon supply chains. It provides the ability to model a multi-echelon supply chain in a single, connected and cohesive model, so that the limitations of simple models in representing larger systems are avoided (Chatfield, 2013; Costantino et al., 2015a, b, c). The
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simulation model logic is presented in Figure 3 in which the parameters to adjust in each simulation run are indicated as well. The simulation model used for this study has been developed using
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CE
PT
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Simul8 and has been validated by comparing its output with previous leading research.
Figure 3. Simulation model flowchart
The available results in previous research are obtained for traditional OUT with simple exponential smoothing method (ES) (Chen et al., 2000; Dejonckheere et al., 2004) and smoothing OUT with ES (Dejonckheere et al., 2004) under normal demand. Therefore, we adjust the settings of our Page 23 of 41
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simulation model by turning the HW forecasting system into ES (with setting 0 and 0 ). Specifically, we have compared the simulation model results with the control engineering results of Dejonckheere et al. (2004), and the statistical results of Chen et al. (2014b) who derived a closed form expressions for the bullwhip effect ratio (see, equation (25)). For this validation, we consider the same simulation settings in Dejonckheere et al. (2004) for conducting direct comparisons with
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them. Therefore, for each ordering policy, the simulation model was run for 20 replications of a replication length of 5200 periods each and with a warm-up period of 200 periods. The customer demand in Dejonckheere et al. (2004) is assumed to follow the normal distribution with a mean of 100 and a standard deviation of 10 and therefore the parameters of the above seasonal demand model are set to: base 100 , season 0 , and 10 , to generate the same data set of the normal
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demand.
The HW method has been turned into a single ES using the following initial settings: b0i 0 and
0i 0 ; and its smoothing parameters are set to: 0.1 , 0 and 0 where the value of is selected according to Dejonckheere et al. (2004). The lead-time, review period, and safety stock
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parameter are set to: Lid 2 , R 1 , and Ki 2 , where Lid R K i 5, i . We applied these values in equation (25) to get the bullwhip effect ratio at each echelon i based on Chen et al.
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(2000b), where i 1,..., m (echelon index) and m 4 , i 0.1, i and Li Lid R Ki in which the safety stock parameter is included.
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O2i
i
(25)
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D2
m 2 L2 2 1 2 Li i i i i 1 2 i
The results presented in Table 2 indicate that the simulation model is working as intended where the
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difference between the simulation output and the previous research results are not significant. Furthermore, the results confirm the significance of the smoothing inventory rules in the supply chain when the demand is normal. It can be observed that increasing the smoothing level from
Tn 1 to Tn 4 decreases the bullwhip effect considerably across the supply chain. The bullwhip
effect ratio is almost eliminated at all echelons other than the factory that produces a very low bullwhip effect when Tn 4 ( BWE 1.361 ) compared to BWE 25.96 when Tn 1 .
Table 2. Simulation model validation results Page 24 of 41
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Classical OUT (Tn=1) SIM. Model
Dejonckheere et al. (2004)
Chen et al. (2000b)
SIM. Model
Dejonckheere et al. (2004)
Retailer
2.27
2.26
2.26
0.421
0.423
Wholesaler
5.18
5.16
5.06
0.479
0.4828
Distributor
11.83
11.84
11.39
0.765
0.773
Factory
25.96
27.22
25.63
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BWE
Smoothing OUT (Tn=4)
4. Simulation Results and Analysis 4.1 The Effect of Smoothing
1.361
1.376
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The impact of the smoothing OUT replenishment rule ( Tn 1 ) is evaluated and compared to the traditional OUT ordering rule ( Tn 1 ) under two levels of seasonality (low and high) combined with two levels of seasonal cycle (low and high). The design of this simulation experiment is adopted to evaluate the effect of order smoothing under a wide range of the seasonal demand parameters. We consider the following designs of the generalized OUT replenishment rule to also
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investigate the effect of the smoothing parameter level on the seasonal supply chain performances:
Tn 1 , Tn Lid , Tn Lid 1 and Tn 2 Lid . These four designs based on the lead-time have been
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proposed in some previous studies that have attempted to investigate the impact of smoothing OUT replenishment rules in supply chains but under non-seasonal demand like step and normal demand
PT
(Ciancimino et al., 2012; Dejonckheere et al., 2004). For this comparison, the forecasting parameters are set to: 0.1 , 0 and 0.1 . In each scenario, following the same logic in the
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flowchart in Figure 3, the simulation model is run for 20 replications, with a replication length of 1200 periods and a warm-up-period of 200 periods. The other parameters of the supply chain
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model are set to: b0i 0 , s SeasonCycle , Ki 1 , and Lid 2 .
The results of a single simulation run, showing the impact of shifting from the traditional OUT ( Tn 1 ) to the smoothing OUT ( Tn 1 ) on the orders and inventory variations over time (last 200 periods), are presented in Figures 4-5. The results in these figures indicate that the ordering and inventory stability across the supply chain becomes higher under the smoothing OUT compared to the traditional OUT. The ordering variability increases in the upstream direction under the classical OUT where the factory’s orders shows the highest variability as can be observed in Figure 4a. Page 25 of 41
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However, the ordering variability decreases in the upstream direction under the smoothing OUT where the factory’s orders variability is the lowest (see, Figure 4b). The same conclusions are valid for the inventory level variation as it increases in the upstream direction under the classical OUT (see, Figure 5a) while decreases in the same direction under the smoothing OUT (see, Figure 5b).
100
(a) Classical OUT (Tn=1)
Order quantity
80 70 60 50 40 30 20 10 0 1
21
41
61
Customer Demand
81
100
121
Wholesaler Order
70 60 50 40 30 20 10 0 1
21
41
61
81
Retailer Order
161
101
121
Wholesaler Order
141
181
Factory Order
161
Distributor Order
181
Factory Order
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Customer Demand
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80
141
Distributor Order
(b) Smoothing OUT (Tn=2Ld=4)
90
Order quantity
101
Retailer Order
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90
Figure 4. The order rate variation over time under different smoothing levels when Season=10 and
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SeasonCycle=7
(a) Classical OUT (Tn=1)
150 125 75
PT
Inventory level
100 50 25 0 -25 -75 -100 1
CE
-50
21
41
61
Retailer Inventory
101
121
141
Distributor Inventory
161
181
Factory Inventory
(b) Smoothing OUT (Tn=2Ld=4)
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150
81
Wholesaler Inventory
125
Inventory level
100
75 50 25
0
-25 -50 -75
-100 1
21
41
Retailer Inventory
61
81
Wholesaler Inventory
101
121
Distributor Inventory
141
161
181
Factory Inventory
Figure 5. The inventory level variation over time under different smoothing levels when Season=10 and SeasonCycle=7 Page 26 of 41
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4.1.1
Bullwhip Effect Analysis
The bullwhip effect ratio results ( BWEi ), based on the average of 20 simulation runs, are presented in Figure 6a and show that shifting from the traditional OUT to the smoothing OUT has a significant impact on the ordering stability in the supply chain, regardless of the combination of the
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seasonal parameters. Furthermore, the results show that any increase in the smoothing level Tn leads to a decrease in the bullwhip effect ratio across the supply chain (at all echelons) whatever the demand parameters. For example, when Season 5 and SeasonCycle 7 , increasing the smoothing level from Tn 1 to Tn 4 reduces the bullwhip effect magnitude across the supply chain, e.g., from 1.88 to 0.30 at the retailer (respectively) and from 12.40 to 0.43 at the factory. In
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other words, the bullwhip effect is eliminated by increasing the smoothing level to Tn 4 .
The results in Figure 6a also indicate that the seasonal cycle has a significant contribution to the bullwhip effect magnitude where longer seasonal cycle increases the bullwhip effect while high seasonal level leads to a lower bullwhip effect. However, the results show that the selection of high smoothing level can mitigate the effect of the seasonal cycle and therefore smoothing replenishment
Inventory Performance Measures
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4.1.2
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rules are recommended for the seasonal supply chains with longer seasonal cycles.
The results of inventory variance ratio exhibited in Figure 6b show a similar behavior to the
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bullwhip effect results in Figure 6a. It can be seen that increasing the smoothing level leads to a higher inventory stability (lower inventory variance ratio) across the supply chain whatever the
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demand parameters. However, it can be noticed that as the seasonal cycle increases, higher smoothing level increases the inventory ratio at the retailer to some extent whilst improving the
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inventory stability at the upstream echelons. The results also show that the inventory variance ratio is less sensitive to the seasonal level while it is highly sensitive to the seasonal cycle regardless of the smoothing level. However, this sensitivity decreases as the smoothing level increases. For instance, when Season 5 , as the seasonal cycle increases from SeasonCycle 7 to SeasonCycle 14 , the inventory variance ratio increases considerably at all echelons regardless of the smoothing level, e.g., increases from 5.47 to 7.06 at the retailer and from 34.72 to 50.09 at the factory under Tn 1 , while increases from 3.49 to 8.72 at the retailer and from 4.56 to 7.58 at the factory under Tn 4 . The results further show that the Page 27 of 41
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inventory variance ratio at the retailer increases as the smoothing level increases only when the seasonal cycle is long.
The average fill rate results in Figure 6c confirm the findings for the
inventory variance ratio where increasing the smoothing level leads to a higher average fill rate across the supply chain. Therefore, the inventory stability is improved in seasonal the supply chain
16.0
(a) Bullwhip effect ratio
14.0 12.0 10.0
BWE
8.0 6.0 4.0
0.0 Retailer Wholesaler Distributor Factory
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=5, SeasonCycle=7) 1.88 0.78 0.44 0.30 3.55 0.71 0.29 0.18 6.72 0.76 0.31 0.21 12.40 0.95 0.43 0.31
70.0
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2.0 Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=10, SeasonCycle=7) 1.82 0.80 0.42 0.27 3.34 0.67 0.21 0.11 5.99 0.61 0.16 0.09 10.13 0.61 0.18 0.12
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=5, SeasonCycle=14) 1.95 1.17 0.82 0.60 3.91 1.63 0.86 0.49 7.65 2.38 0.95 0.45 14.32 3.53 1.13 0.51
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=10, SeasonCycle=14) 1.87 1.37 0.98 0.72 3.57 1.99 1.02 0.54 6.65 2.92 1.07 0.43 11.62 4.32 1.15 0.38
(b) Inventory variance ratio
60.0
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50.0 40.0 InvR
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when shifting from the traditional OUT to the smoothing OUT.
30.0
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20.0 10.0 0.0
PT
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=5, SeasonCycle=7) Retailer 5.47 4.39 3.76 3.49 Wholesaler 9.75 4.54 2.95 2.47 Distributor 16.98 5.39 3.44 3.01 Factory 34.72 7.31 5.04 4.56
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=5, SeasonCycle=14) 7.06 8.72 8.97 8.72 14.13 13.04 9.92 7.40 29.97 20.50 11.38 6.94 50.09 29.75 13.48 7.58
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=10, SeasonCycle=14) 8.25 10.64 11.11 10.71 19.59 15.37 11.95 8.53 43.13 27.86 13.12 6.86 59.83 37.05 14.18 5.98
(c) Average fill rate
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120.0
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=10, SeasonCycle=7) 5.68 4.62 3.64 3.17 9.05 4.08 2.01 1.38 14.55 3.90 1.63 1.22 36.09 4.24 1.99 1.70
100.0 80.0
AFR%
AC
60.0 40.0
20.0 0.0
Retailer Wholesaler Distributor Factory
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=5, SeasonCycle=7) 100.0 100.0 100.0 100.0 99.9 100.0 100.0 100.0 98.8 100.0 100.0 100.0 95.6 99.9 100.0 100.0
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=10, SeasonCycle=7) 99.7 99.9 100.0 100.0 97.2 99.9 100.0 100.0 91.0 99.8 100.0 100.0 82.4 99.7 100.0 100.0
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=5, SeasonCycle=14) 100.0 100.0 100.0 100.0 99.5 99.8 100.0 100.0 95.8 98.7 99.8 100.0 93.1 97.1 99.6 100.0
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=10, SeasonCycle=14) 97.4 97.2 97.4 97.7 81.9 90.6 96.5 98.7 71.6 80.4 95.4 99.2 75.6 82.3 95.0 99.3
Figure 6. The impact of order smoothing on supply chain performances under different seasonal parameters Page 28 of 41
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The above results confirm that shifting from the traditional OUT to the smoothing OUT can improve the ordering and inventory stability in the seasonal supply chains. It has further been found that increasing the smoothing level leads to lower bullwhip effect, lower inventory variance and higher average service level across the supply chain. These conclusions have been proven in
CR IP T
previous research for non-seasonal demand, and we confirm and extend these conclusions to the seasonal demand as well. 4.2 The Impact of Forecasting Parameters
The above analysis has been conducted to investigate the impact of the smoothing replenishment rule on the supply chain performances under different combinations of the seasonal demand
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parameters, considering specific settings for the forecasting and other operational parameters. In this section, we extend the analysis to investigate the impact of the HW’s parameters on the supply chain performances, considering three levels of combined with three levels of ; and each combination is evaluated under two levels of smoothing. The experimental ranges of and are selected based on earlier research (Bayraktar et al., 2008) while the values of Tn are selected based
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on the above results. The comparisons are conducted under the four demand patterns used above to understand the interaction between the forecasting parameters, smoothing level and demand
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parameters. The other parameters are set to: Lid 2 , 0 , and Ki 1 for the different simulation experiments.
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The results in Figures 7-9 indicate that the smoothing OUT replenishment rule is superior to the traditional OUT replenishment rule under the different combinations of the seasonal demand
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parameters, regardless of the forecasting parameters. It can be further seen that all performance measures are highly sensitive to while less sensitive to where smaller values of leads to lower bullwhip effect, lower inventory variance ratio, and higher average fill rate, regardless of the
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demand parameters. However, larger values of leads to a higher ordering and inventory instability, especially at the most upstream echelons, under the traditional OUT policy ( Tn 1 ). These bullwhip effect results confirm the previous findings of Bayraktar et al. (2008) that investigated the impact of the HW parameters in a seasonal supply chain employs the traditional OUT ordering policy. They have shown that smaller values of are best suited to mitigate the bullwhip effect, however, their study have not considered the impact of the forecasting parameters on the inventory stability. The results in this research extend their findings and further confirm the Page 29 of 41
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value of the smoothing replenishment rules in the seasonal supply chain, confirming the preliminary results of Costantino et al. (2015a). It can be observed that all performances measures become less sensitive to either forecasting paramter when the smoothing level is high ( Tn 4 ). Therefore, the smoothing replenishment rule helps to alleviate the contribution of the improper selection of the
(a) Season=5, SeasonCycle=7
80.0 70.0 60.0
BWE
50.0 40.0 30.0 20.0 10.0
Retailer Wholesaler Distributor Factory
γ=0.05
γ=0.1 α=0.05
γ=0.2
1.39 2.04 3.01 4.35
1.37 1.87 2.57 3.54
1.38 1.90 2.62 3.66
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 1.89 1.88 1.89 3.71 3.55 3.60 7.14 6.72 6.84 13.03 12.40 12.70
γ=0.05
γ=0.1 α=0.2
3.19 10.29 28.31 62.40
3.21 10.28 28.38 62.35
70.0 60.0
BWE
50.0 40.0
20.0 10.0 γ=0.1 α=0.05
γ=0.2
1.27 1.75 2.46 3.42
1.32 1.75 2.31 3.07
1.33 1.78 2.39 3.21
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 1.75 1.82 1.85 3.24 3.34 3.41 5.86 5.99 6.15 9.90 10.13 10.42
γ=0.05
ED
γ=0.05
γ=0.1 α=0.05
γ=0.2
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 0.29 0.30 0.30 0.19 0.18 0.18 0.23 0.21 0.21 0.34 0.31 0.31
0.20 0.11 0.12 0.14
0.19 0.10 0.09 0.11
0.20 0.10 0.10 0.12
γ=0.05
γ=0.1 α=0.2
γ=0.2
0.55 0.47 0.63 1.13
0.57 0.49 0.63 1.10
0.57 0.49 0.64 1.12
3.01 8.80 20.00 35.62
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
3.14 9.22 20.59 35.99
3.17 9.34 20.77 36.22
0.17 0.06 0.06 0.07
0.17 0.05 0.04 0.04
0.17 0.05 0.04 0.04
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 0.26 0.27 0.27 0.11 0.11 0.11 0.11 0.09 0.09 0.15 0.12 0.12
γ=0.05
γ=0.1 α=0.2
γ=0.2
0.53 0.33 0.31 0.47
0.56 0.37 0.33 0.46
0.56 0.38 0.34 0.47
γ=0.05
γ=0.1 α=0.2
γ=0.2
1.09 1.50 2.13 3.17
1.10 1.57 2.36 3.71
1.12 1.64 2.56 4.12
(c) Season=5, SeasonCycle=14
PT
80.0 70.0 60.0 50.0 40.0
CE
BWE
3.23 10.36 28.59 62.72
M
30.0
Retailer Wholesaler Distributor Factory
γ=0.05
(b) Season=10, SeasonCycle=7
80.0
0.0
γ=0.2
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0.0
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forecasting parameters to the ordering and inventory instability in supply chains.
30.0 20.0 10.0
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0.0
Retailer Wholesaler Distributor Factory
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γ=0.05
γ=0.1 α=0.05
γ=0.2
1.82 3.81 6.74 10.50
1.46 2.19 3.27 4.80
1.42 2.02 2.87 4.09
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 2.30 1.95 1.92 5.80 3.91 3.71 12.03 7.65 7.15 21.90 14.32 13.46
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
3.46 12.20 33.18 74.49
3.13 9.91 27.56 63.30
3.11 9.68 26.97 62.31
0.44 0.32 0.31 0.35
0.40 0.22 0.17 0.17
0.40 0.23 0.17 0.15
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 0.63 0.60 0.61 0.54 0.49 0.51 0.54 0.45 0.49 0.65 0.51 0.54
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(d) Season=10, SeasonCycle=14
80.0 70.0 60.0 50.0
BWE
40.0 30.0 20.0 10.0
Retailer Wholesaler Distributor Factory
γ=0.05
γ=0.1 α=0.05
γ=0.2
1.49 2.61 4.30 6.58
1.39 1.99 2.84 4.04
1.40 1.95 2.72 3.80
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 1.92 1.87 1.89 4.14 3.57 3.57 8.13 6.65 6.61 14.35 11.62 11.53
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
2.93 8.86 21.22 40.42
2.95 8.49 19.77 36.91
2.99 8.58 19.84 36.87
0.48 0.29 0.26 0.30
0.46 0.23 0.13 0.10
0.47 0.25 0.14 0.09
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 0.71 0.72 0.73 0.54 0.54 0.59 0.45 0.43 0.50 0.48 0.38 0.45
γ=0.05
γ=0.1 α=0.2
γ=0.2
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0.0
1.27 1.72 2.32 3.20
1.34 1.93 2.84 4.22
1.38 2.07 3.16 4.86
Figure 7. The main and interaction effects of the forecasting parameters and smoothing level on the bullwhip effect (a) Season=5, SeasonCycle=7
300.0
InvR
200.0 150.0 100.0 50.0
Retailer Wholesaler Distributor Factory
γ=0.05
γ=0.1 α=0.05
γ=0.2
4.49 6.04 8.37 12.22
4.68 6.24 8.32 11.32
4.71 6.33 8.51 11.67
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 5.27 5.47 5.51 9.38 9.75 9.86 16.62 16.98 17.22 34.36 34.72 35.56
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
6.74 18.07 48.70 164.97
6.95 18.59 49.96 170.09
6.98 18.71 50.48 171.71
3.20 1.78 1.87 2.34
3.23 1.79 1.82 2.24
3.24 1.80 1.84 2.26
M
0.0
AN US
250.0
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 3.45 3.49 3.50 2.43 2.47 2.49 3.01 3.01 3.04 4.62 4.56 4.59
γ=0.05
γ=0.1 α=0.2
γ=0.2
4.07 4.02 6.11 11.00
4.13 4.14 6.22 11.01
4.14 4.17 6.27 11.11
γ=0.05
γ=0.1 α=0.2
γ=0.2
3.94 2.68 2.81 4.37
4.04 2.89 3.00 4.42
4.05 2.94 3.07 4.49
γ=0.05
γ=0.1 α=0.2
γ=0.2
9.39 13.76 21.78 32.02
10.57 15.80 25.96 39.05
10.99 16.72 28.22 43.11
(b) Season=10, SeasonCycle=7
300.0
ED
250.0
InvR
200.0 150.0
PT
100.0 50.0 0.0
γ=0.1 α=0.05
γ=0.2
4.88 6.13 7.97 12.33
5.14 6.53 8.21 11.86
5.18 6.63 8.41 12.37
CE
Retailer Wholesaler Distributor Factory
γ=0.05
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 5.46 5.68 5.71 8.62 9.05 9.15 13.97 14.55 14.80 34.25 36.09 37.19
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
6.10 15.42 42.58 109.29
6.21 16.29 44.86 111.92
6.23 16.52 45.46 112.51
2.76 0.88 0.77 0.96
2.81 0.90 0.71 0.83
2.81 0.92 0.72 0.84
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 3.11 3.17 3.18 1.31 1.38 1.40 1.25 1.22 1.24 1.83 1.70 1.72
(c) Season=5, SeasonCycle=14
300.0
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250.0
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200.0 150.0 100.0 50.0
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γ=0.05
γ=0.1 α=0.05
γ=0.2
5.29 8.91 16.39 27.29
6.04 8.57 12.49 17.75
6.36 8.92 12.64 17.39
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 6.26 7.06 7.41 14.12 14.13 14.67 33.53 29.97 30.81 62.63 50.09 50.30
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
9.01 34.13 109.95 244.82
9.82 36.27 111.69 233.36
10.11 37.68 114.93 235.81
6.72 3.99 3.31 3.74
7.60 4.39 3.11 2.97
7.95 4.71 3.37 3.10
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 7.71 8.72 9.09 6.46 7.40 7.92 6.29 6.94 7.61 7.45 7.58 8.29
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(d) Season=10, SeasonCycle=14
300.0 250.0
InvR
200.0 150.0 100.0 50.0
Retailer Wholesaler Distributor Factory
γ=0.05
γ=0.1 α=0.05
γ=0.2
6.23 10.62 19.85 27.68
7.44 10.72 16.49 20.56
7.98 11.33 17.14 20.82
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 7.37 8.25 8.63 18.25 19.59 20.46 43.34 43.13 45.10 64.86 59.83 61.51
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
13.21 35.79 107.03 186.77
14.75 38.29 112.22 189.72
15.31 39.66 115.52 192.79
7.83 3.95 2.66 2.71
9.22 4.68 2.52 1.76
9.72 5.17 2.95 1.97
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 9.20 10.71 11.24 7.03 8.53 9.31 5.72 6.86 7.93 5.38 5.98 7.12
γ=0.05
γ=0.1 α=0.2
γ=0.2
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0.0
11.12 15.35 24.93 33.92
12.31 17.10 31.08 45.26
12.63 17.71 34.24 51.42
Figure 8. The main and interaction effects of the forecasting parameters and smoothing level on the inventory variance ratio
100.0 90.0 80.0
AFR%
70.0 60.0 50.0 40.0 30.0 20.0 10.0 γ=0.05
γ=0.1 α=0.05
γ=0.2
Retailer 100.00 Wholesaler 99.99 Distributor 99.91 Factory 99.60
100.00 99.99 99.95 99.77
100.00 99.99 99.94 99.76
90.0 80.0 60.0
20.0 10.0
γ=0.05
γ=0.1 α=0.05
γ=0.2
99.90 99.55 98.53 96.66
99.87 99.46 98.51 96.84
99.86 99.42 98.37 96.53
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AFR%
70.0
30.0
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γ=0.05
γ=0.1 α=0.2
γ=0.2
99.98 98.01 88.56 80.31
99.98 97.84 87.78 79.29
99.98 97.78 87.65 79.25
γ=0.05
γ=0.1 α=0.05
γ=0.2
100.00 100.00 100.00 100.00
100.00 100.00 100.00 100.00
100.00 100.00 100.00 100.00
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 99.99 99.99 99.99
γ=0.05
γ=0.1 α=0.2
γ=0.2
100.00 100.00 99.91 99.59
100.00 100.00 99.90 99.58
100.00 100.00 99.90 99.57
γ=0.05
γ=0.05
γ=0.1 α=0.2
γ=0.2
99.95 99.97 99.87 99.50
99.95 99.96 99.85 99.48
99.94 99.96 99.84 99.46
ED
100.0
40.0
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 100.00 100.00 100.00 99.89 99.89 99.88 98.88 98.84 98.80 95.84 95.63 95.45
(b) Season=10, SeasonCycle=7
110.0
50.0
γ=0.05
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0.0
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(a) Season=5, SeasonCycle=7
110.0
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 99.73 99.67 99.66 97.67 97.24 97.12 92.05 91.05 90.67 83.71 82.35 81.79
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
98.97 88.74 75.94 71.04
98.80 87.66 75.11 70.43
98.76 87.50 74.96 70.43
99.99 100.00 100.00 100.00
99.99 100.00 100.00 100.00
99.99 100.00 100.00 100.00
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 99.98 99.98 99.98 100.00 100.00 100.00 100.00 100.00 100.00 99.98 99.99 99.99
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(c) Season=5, SeasonCycle=14
110.0 100.0 90.0 80.0
AFR%
70.0 60.0 50.0 40.0 30.0 20.0 10.0 γ=0.05
γ=0.1 α=0.05
γ=0.2
Retailer 100.00 Wholesaler 99.88 Distributor 98.90 Factory 97.83
100.00 99.98 99.79 99.26
100.00 99.98 99.80 99.31
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 99.99 100.00 99.99 99.29 99.50 99.48 95.11 95.80 95.49 92.33 93.11 92.87
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
99.45 90.40 77.31 77.71
99.35 88.50 75.11 76.44
99.32 87.48 74.09 75.88
99.99 100.00 99.99 99.98
99.99 100.00 100.00 100.00
99.99 100.00 100.00 100.00
(d) Season=10, SeasonCycle=14
110.0 100.0 90.0 80.0 70.0
50.0 40.0 30.0 20.0 10.0 0.0
Retailer Wholesaler Distributor Factory
γ=0.05
γ=0.1 α=0.05
γ=0.2
99.47 96.35 90.66 90.84
99.38 97.24 92.58 92.27
99.24 96.85 91.94 91.86
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 97.91 97.45 97.05 84.56 81.88 80.27 73.21 71.56 70.21 76.56 75.60 74.75
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 99.99 99.98 99.98 100.00 99.99 99.99 99.98 99.99 99.98 99.92 99.95 99.92
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AFR%
60.0
γ=0.05
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
86.36 70.34 60.51 66.76
83.26 66.98 57.60 64.39
81.87 65.70 56.56 63.67
99.10 99.93 99.82 99.71
98.57 99.91 99.99 100.00
98.33 99.87 99.99 100.00
γ=0.05
γ=0.1 α=0.2
γ=0.2
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0.0
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 98.47 97.69 97.35 99.25 98.73 98.42 99.27 99.18 98.88 99.22 99.27 98.97
99.97 99.63 97.88 96.08
99.96 99.48 96.99 94.61
99.95 99.37 96.44 93.78
γ=0.05
γ=0.1 α=0.2
γ=0.2
96.64 90.98 83.28 83.91
95.28 87.36 76.56 78.41
94.69 85.55 73.22 75.77
Figure 9. The main and interaction effects of the forecasting parameters and smoothing level on the
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average fill rate
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5. Discussion and Implications
Previous research has confirmed the effectiveness of the smoothing replenishment rules in supply
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chains under non-seasonal demand. They have shown that shifting from the traditional replenishment rules to the smoothing replenishment rules can mitigate and eliminate the bullwhip
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effect but it has been shown that dampening the bullwhip effect might affect the inventory stability. In particular, increasing the order smoothing level may increase the inventory instability causing a
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lower average fill rate. The present study has attempted to extend the previous researches by investigating the value of smoothing inventory decision rules in seasonal supply chains. The seasonality phenomenon of demand is a common occurrence in many supply chains where it may stem from factors such as weather, which affects many business and economic activities like clothing and food industries. The seasonality can potentially cause mismatch between supply and demand in supply chains.
This paper has attempted to evaluate the impact of smoothing replenishment rules in a seasonal Page 33 of 41
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supply chain in which the demand pattern has seasonal components modified by random variation. A simulation study has been conducted to evaluate the performance of a four-echelon supply chain facing a seasonal demand and employs a generalized order-up-to inventory policy (with smoothing capability) integrated with Holt-Winters forecasting method (Triple Exponential Smoothing). The supply chain performance has been evaluated under the different ordering policies in terms of
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bullwhip effect ratio, inventory variance ratio and average fill rate. The results have shown that shifting from the traditional OUT to the smoothing OUT improves the ordering and inventory stability in the seasonal supply chain. It has further been shown that increasing the smoothing level leads to lower bullwhip effect, lower inventory variance ratio, and higher average fill rate. This conclusion has been confirmed under the various combinations of the seasonal parameters.
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In this research, we have also quantified the contribution of the seasonal demand parameters to the bullwhip effect and inventory performance measures, under the traditional and smoothing replenishment rules. The results reveal that longer seasonal cycle increases the bullwhip effect while high seasonal level leads to a lower bullwhip effect. However, it has been found that the adoption of the smoothing OUT with selecting high smoothing level can mitigate the contribution
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of the seasonal cycle to the bullwhip effect and therefore high smoothing levels is recommended for seasonal supply chains with longer seasonal cycles to counteract the bullwhip effect. The results
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have also shown that the inventory variance ratio is less sensitive to the seasonal level while it is highly sensitive to the seasonal cycle regardless of the replenishment rule. However, this sensitivity decreases considerably as the smoothing level increases. In general, smoothing replenishment rules
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can improve the ordering and inventory stability in the seasonal supply chains.
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Demand forecast updating has been recognized as a major cause of the bullwhip effect and inventory instability in supply chains. Therefore, we have quantified the impact of the smoothing
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parameters of the HW method on the bullwhip effect and inventory performances under the different ordering policies. The results have shown that the smoothing parameter of the level component ( ) has the major contribution to the bullwhip effect and inventory performances. It has been found that the value of should always be set to low level since any increase in this parameter leads to higher bullwhip effect and inventory instability. The smoothing parameter of the seasonal component ( ) has been found to be of less contribution to the performance measures. The results have also shown that the sensitivity of all performance measures to the smoothing parameters of the forecasting method is reduced under the smoothing OUT compared to the Page 34 of 41
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traditional OUT. In other words, the contribution of the forecasting parameters to the bullwhip effect and inventory instability becomes lower under the smoothing OUT.
The strength of this research emerges from its uniqueness since the literature shows limited research that has attempted to evaluate the effectiveness of the smoothing replenishment rules in seasonal
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supply chains (see, Table 1). The results of this paper confirm that employing the smoothing replenishment rules (e.g., smoothing OUT) improves the ordering and inventory stability in seasonal supply chains. Another possible strength, concluded from the sensitivity analysis, is that employing the smoothing replenishment rules reduces the impact of the demand parameters and the poor selection of the forecasting parameters on the ordering and inventory stability. In this research, the smoothing OUT replenishment rule which is a modified version of the traditional OUT policy
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was considered to evaluate the impact of smoothing in seasonal supply chains. The traditional OUT, which is commonly used in practice, can simply be converted into smoothing OUT by adding two proportional controllers to the gaps of the net inventory and supply line (see, equation (11-12)). Therefore, the current seasonal supply chains that employ traditional OUT can largely benefit from the concepts and results presented in this study, to counteract the bullwhip effect. However, a
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possible weakness of the smoothing replenishment rules is that dampening the order variability has a negative impact on customer service due to an increased inventory variance. We have noticed that
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this trade-off between the bullwhip effect and inventory stability might happen at the most downstream echelons in seasonal supply chains when the seasonal cycle is long. This might limit the applications of smoothing replenishment rules especially when the inventory cost is an issue and
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that the supply chain consists of a few number of echelons and facing a seasonal demand with high seasonal cycle. However, this issue can be managed by enabling incentive schemes between
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upstream and downstream echelons to achieve coordination in seasonal supply chains.
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6. Conclusions
Smoothing inventory decision rules have been proposed as a mitigation/avoidance solution for the bullwhip effect. However, most of the previous studies have evaluated the impact of smoothing replenishment rules under non-seasonal and stationary demand processes. This paper has attempted to fill this research gap by evaluating the impact of smoothing replenishment rules in a multiechelon supply chain facing a seasonal demand modified by a random variation. A simulation study has been conducted to study the supply chain performances under the traditional and smoothing
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OUT replenishment rules, both integrated with the Holt-Winters forecasting method. The results have shown that shifting from the traditional replenishment rule to the smoothing one leads to a higher ordering and inventory stability across the supply chain. It has further been found that increasing the smoothing level leads to lower bullwhip effect, lower inventory variance ratio and higher average fill rate across the supply chain. The impact of the forecasting parameters has also
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been investigated showing that smaller value of the smoothing parameter of the level component are best suited to improve the ordering and inventory stability in the seasonal supply chain, especially under the traditional OUT policy. Most importantly, it has been found that employing the smoothing replenishment rules limiting the impact of the demand parameters and the improper selection of the forecasting parameters on the ordering and inventory stability. Therefore, it can be
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concluded that the smoothing replenishment rules have a great value in seasonal supply chains.
This research contributes towards advancing the knowledge in the areas of forecasting and inventory control in seasonal supply chains as it provides useful insights to improve the ordering and inventory stability in such supply chains. This research has extended the previous contribution of Costantino et al. (2015a) in ESWA in which they provided an evidence of the value of order
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smoothing in seasonal supply chains. Costantino et al. (2015a) have proposed a real-time SPC inventory replenishment system that relies on control chart system to forecast demand and adjust
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inventory position whilst providing smoothing capability to counteract the bullwhip effect. In this research, alternatively, we have proposed the application of the smoothing OUT replenishment rule in seasonal supply chains, and compared to traditional OUT. The results have shown the
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effectiveness of applying smoothing replenishment rules (e.g., smoothing OUT) in seasonal supply chain, confirming the preliminary results of Costantino et al. (2015a). The results have further
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confirmed that the proper selection of the forecasting parameters is essential to improve the ordering and inventory stability in seasonal supply chains. The research relied on the smoothing
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OUT which is a modified version of the traditional OUT (commonly used in practice) and relied on the HW forecasting method which is commonly used to forecast seasonal demand, to be consistent with real applications. The results thus provide useful managerial insights that can be utilized by supply chain managers of seasonal supply chains to re-engineer their decision support systems, and they can further utilize these insights to develop expert systems.
The previous research on the bullwhip effect can be classified into two broad categories, i.e. theoretical and empirical research (Costantino et al., 2015b), where both categories have been Page 36 of 41
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utilized to prove the bullwhip existence, to understand and identify its causes, and to evaluate proposed mitigation/avoidance approaches. The above conclusions and implications have been obtained based on a simulation study which follows the first category of the bullwhip effect research. This modeling approach has already been shared by many other researchers to investigate the bullwhip effect under various settings (Chatfield, 2013; Costantino et al., 2015a, b). However, in
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order to further validate the effectiveness of smoothing replenishment rules in seasonal supply chains, the study should be extended to real applications or the same study can be repeated with real data from industry but this is not always convenient. Nevertheless, the simulation model used for the analysis that resulted in the above promising conclusions has been validated with previous leading research in the literature and thus the obtained conclusions are valid and can be useful for both academics and practitioners. Another limitation is that the current simulation study has
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neglected the impact of the lead-time and its interaction with seasonal cycle where some earlier researches have highlighted the significance of this relationship through analytical modeling studies (Cho and Lee, 2012, 2013).
The present study can be extended further to investigate the impact of both information sharing and
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smoothing replenishment rules on the performances of seasonal supply chains. The future work can also consider the main and interaction effects of the important operational parameters such as lead-
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time, forecasting parameters, smoothing level, and information sharing. This goal can be achieved through a similar simulation study supported by experimental design approach. The future research should also study the value of smoothing replenishment rules under a wider range of the seasonal
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Smoothing inventory decision rules in seasonal supply chains Francesco Costantino , Giulio Di Gravio , Ahmed Shaban , Massimo Tronci PII: DOI: Reference:
S0957-4174(15)00609-0 10.1016/j.eswa.2015.08.052 ESWA 10266
To appear in:
Expert Systems With Applications
Received date: Revised date: Accepted date:
14 December 2014 29 August 2015 30 August 2015
Please cite this article as: Francesco Costantino , Giulio Di Gravio , Ahmed Shaban , Massimo Tronci , Smoothing inventory decision rules in seasonal supply chains, Expert Systems With Applications (2015), doi: 10.1016/j.eswa.2015.08.052
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Highlights
We study the value of smoothing replenishment rules in seasonal supply chains.
Simulation modeling is adopted to compare the traditional and smoothing OUT.
The impact of Holt-Winters parameters are studied under both replenishment rules.
Smoothing improves the ordering and inventory stability in seasonal supply chains.
Increasing the smoothing level reduces the bullwhip effect and inventory variance.
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Smoothing inventory decision rules in seasonal supply chains
Francesco Costantino1, Giulio Di Gravio1, Ahmed Shaban1,2,*, Massimo Tronci1
Department of Mechanical and Aerospace Engineering, University of Rome “La Sapienza”, Via Eudossiana, 18, 00184 Rome, Italy 2
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Department of Industrial Engineering, Faculty of Engineering, Fayoum University, 63514 Fayoum, Egypt [email protected], [email protected], [email protected], [email protected]
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Abstract
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A major cause of supply chain deficiencies is the bullwhip effect, which implies that demand variability amplifies as one moves upstream in supply chains. Smoothing inventory decision rules have been recognized as the most powerful approach to counteract the bullwhip effect. Although extensive studies have evaluated
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these smoothing rules with respect to several demand processes, focusing mainly the smoothing order-up-to (OUT) replenishment rule, less attention has been devoted to investigate their effectiveness in seasonal
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supply chains. This research addresses this gap by investigating the impact of the smoothing OUT on the seasonal supply chain performances. A simulation study has been conducted to evaluate and compare the smoothing OUT with the traditional OUT, both integrated with the Holt-Winters (HW) forecasting method,
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in a four-echelon supply chain experiences seasonal demand modified by random variation. The results show that the smoothing OUT replenishment rule is superior to the traditional OUT, in terms of the bullwhip effect, inventory variance ratio and average fill rate, especially when the seasonal cycle is small. In addition, the sensitivity analysis reveals that employing the smoothing replenishment rules reduces the impact of the demand parameters and the poor selection of the forecasting parameters on the ordering and inventory stability. Therefore, seasonal supply chain managers are strongly recommended to adopt the smoothing replenishment rules. Further managerial implications have been derived from the results.
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Keywords: Supply Chain; Seasonal Demand; Order-Up-To; Smoothing; Holt-Winters; Bullwhip Effect
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Corresponding author: Department of Mechanical and Aerospace Engineering, University of Rome “La Sapienza”, Via Eudossiana, 18, 00184 Rome, Italy. Tel: +39-3282777914, Fax: +39-0644585746 E-Mail: [email protected] E-Mail: [email protected]
Point-to-Point Responses to Reviewers
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Manuscript Number: ESWA-D-14-04437 Title: "Smoothing inventory decision rules in seasonal supply chains" Reviewer #1’s Comments
1) First of all, the paper's aims and scope match those of ESWA, so the topic is adequate for this journal.
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We thank the reviewer for appreciating our research, and for his valuable comments that have helped us to improve the earlier version of this manuscript considerably.
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2) The abstract in current form is superficial, and the abstract needs to rewrite to point out significance and impact of the paper.
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We thank the reviewer for this comment. We have improved the abstract structure and content with focusing specifically on the research problem statement, the research motivation and the contribution and the significance and impact of our research. The results, conclusions and managerial insights have also been rephrased to communicate our research insights in adequate manner. The abstract has almost been rewritten thoroughly and all changes in the revised abstract are highlighted in blue color.
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In particular, we have first described and discussed the bullwhip effect problem and its impacts as can be found in the first statement in the abstract. We have then introduced the motivation for conducting this research where smoothing replenishment rules have been suggested as an avoidance approach for the bullwhip effect but tested only for non-seasonal demand. Since previous research has been focusing on the impact of smoothing rules in non-seasonal supply chains, our research addresses this issue by investigating the impact of these rules in seasonal supply chains in terms of the bullwhip effect and inventory performance measures. In the revised abstract, we have also indicated the modeling approach adopted to conduct the quantitative analysis of the bullwhip effect in the seasonal supply chain model under traditional and smoothing replenishment rules. The main results of this study are summarized in the last
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part of the abstract where it has been found that smoothing inventory decision rules is superior to traditional rules in seasonal supply chains, providing further useful managerial insights. 3) The authors need to clearly demonstrate adequate understanding of the relevant literature. The authors need to include a good literature survey to show exactly what is novel about their approach. I would like a clear discussion on the current literature (2014-2015) versus the unique contribution of the paper.
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We thank the reviewer for this comment. We have upgraded the literature review in the revised manuscript according to the reviewer suggestion. The introduction section combines both the introduction and the literature review. We have also inserted a new table (Table 1) that summarizes the current literature relevant to the context of our contribution, incorporating many papers published recently in 2013-2015. The cited contributions in the table provide a clear idea on the scope of our study and a clear comparison between previous researches and our contribution in this research. The explanations of the results in this table are summarized throughout the introduction section which has been updated thoroughly and strengthened by recent references from ESWA and other high quality journals to satisfy the reviewers’ concerns.
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In particular, in the introduction section, we have started with explaining the bullwhip effect problem and its potential impacts in supply chains with providing a summary of the earlier researches that have addressed this subject (see, Paragraph 1). Next, we introduced the bullwhip effect operational causes and reviewed the modeling approaches adopted to quantify the bullwhip effect and its causes (see, Paragraph 2). In the third paragraph, we have focused on the impact of ordering policies (inventory decision rules) on the bullwhip effect with reviewing the previous related research. In this part, we have focused on the order-up-to (OUT) inventory replenishment policy which is used in our research as a benchmark since it is the most commonly used ordering policy in practice and in the bullwhip effect modeling research. In the fourth paragraph, we discussed and presented a modified version of the OUT replenishment rule, known as smoothing OUT, that can allow order smoothing and bullwhip effect avoidance. Then, we reviewed the previous related research from the context of the demand modeling, showing that there is a lack of studies devoted to investigating the bullwhip effect in seasonal supply chains (see, Paragraph 5). In Paragraphs 6-7, we reviewed the previous research, although limited, that attempted to quantify the bullwhip effect in seasonal supply chains (see, Paragraph 6), concluding also that limited studies (almost no studies other than Costantino et al. (2015a)) have been devoted to investigating the impact of smoothing replenishment rules in seasonal supply chains (see, Paragraph 7). The details of cited research in this paragraph are also summarized in Table 1. We have then discussed the motivation and contribution of this research as we aim at investigating the effect of smoothing inventory decision rules in seasonal supply chains (see, Paragraphs 7-8). Up to our knowledge, no studies other than Costantino et al. (2015a), which is published in ESWA, have attempted to explore the impact of smoothing replenishment rules in seasonal supply chains. Costantino et al. (2015a) proposed an inventory control system that relies on two control charts integrated with a set of simple decision rules to forecast future demand and adjust inventory position, whilst providing smoothing capability, to counteract the bullwhip effect. We alternatively propose the application of the smoothing OUT replenishment rule since it can easily be adapted from the traditional OUT which is commonly used in practice. We also consider a common forecasting method suitable for the seasonal demand (known as HoltPage 4 of 41
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Winters forecasting method) to integrate with the smoothing OUT, thus, all the modeling assumptions are consistent with real applications to a great extent to maximize the benefits that can be gained from this research. The main objective is to propose some robust tools that can be embedded in the decision support systems of the seasonal supply chains instead of the traditional ones.
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Finally, we explained the research contribution, methodology and organization (see, Paragraphs 8-9). Accordingly, we think that the literature relevant to the context of this paper is now covered satisfactorily in the revised paper. 4) In the conclusion section, the authors need to clearly discuss their theoretical contributions in Expert and Intelligent Systems compared to those in related papers in Expert and Intelligent Systems. Overall, contributions of the article are unclear and weak.
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We thank the reviewer for this comment. This research contributes theoretically to ESWA-related work through multiple dimensions. First, we have been motivated to submit this article to ESWA as we found some papers that are recently published in ESWA focusing on the same research problem (the impact of forecasting and inventory decision rules on the bullwhip effect) as per Jaipuria and Mahapatra (2014) and Costantino et al. (2015a) that are cited in this article. In Costantino et al. (2015a), the authors provided some directions for future research where one of these directions was to investigate the value of the smoothing inventory decision rules in seasonal supply chains as they provided some promising preliminary results and recommended further research. Therefore, we have extended the work of Costantino et al. (2015a) with evaluating the value of smoothing inventory decision rules in seasonal supply chain, focusing on the smoothing OUT replenishment policy. We have further integrated this inventory decision rule with the HW forecasting method to evaluate the impact of the forecasting parameters and their interaction with the inventory decision rules. We have aimed at providing some useful insights on the best integration of forecasting and inventory decision rules so that the mangers of seasonal supply chains can improve and adapt their current inventory decision support systems to improve ordering and inventory stability in their supply chains.
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To address the first part of the comment, in the revised manuscript, we have provided an explanation for the link between this research and ESWA-related work as can be found in both the introduction section (see, Paragraph 4, 7, 8) and the conclusion section (see, Paragraph 2). Therefore, this research is highly related to ESWA-related work and provides a good contribution that can be enhanced further as clarified in the future work directions in the conclusion section. To address the second part of the comment, we have further provided a comparison between our study and the current literature as can be found throughout the introduction section (see, Paragraph 7-8). We have further inserted a new table (Table 1) that summarizes the relevant literature, considering many recent contributions in 2013-2015. The cited contributions in the table provide a clear idea on the scope of our study and a clear comparison between previous researches and our contributions in this research. 5) It is required to provide some including remarks to further discuss the proposed methods, for example, what are the main advantages and limitations in comparison with existing methods? Page 5 of 41
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We thank the reviewer for this comment. We provided the advantages and limitation of this research as can be found in the discussion and implication section (see, Paragraph 1-5) and in the conclusions section (see, Paragraphs 2-3). In particular, in the discussion section, we have clarified the main strength and advantages of employing the smoothing replenishment rules in seasonal supply chains. The results of this paper shows that shifting from the traditional replenishment rules to the smoothing replenishment rules improves the ordering and inventory stability in seasonal supply chains, limiting potential bullwhip effect consequences. Furthermore, employing smoothing replenishment rules ameliorate the contribution of the forecasting and demand parameters to the bullwhip effect and inventory performances where it’s known that forecast updating is a major cause of the bullwhip effect and inventory instability. However, the results indicate that when the seasonal cycle is long, dampening order variability may amplify inventory instability at the most downstream echelons. This might limit the applications of smoothing replenishment rules especially when the supply chain is small (a few number of echelons) and facing a seasonal demand with long seasonal cycle. However, this issue can be overcome by enabling an incentive scheme to achieve coordination in seasonal supply chains. This specific explanation in integrated in the discussion and implications section (see, Paragraph 5). Other explanations for the advantages and limitations are provided in the conclusions section. Reviewer #2’s Comments
The topic is interesting, however, I would suggest the following comments for improvements:
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We thank the reviewer for appreciating our research, and for his valuable comments and suggestions that have helped us to improve the earlier version of this manuscript.
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Please give a frank account of the strengths and weaknesses of the proposed research method. This should include theoretical comparison to other smoothing decision rules.
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We thank the reviewer for this comment. To satisfy the reviewer’s comment, we have added a new paragraph discussing the strengths and weaknesses of the proposed research method in the discussion section (see, Paragraph 5). The strength of this research emerges from its uniqueness since the literature shows limited research that has attempted to evaluate the effectiveness of the smoothing replenishment rules in seasonal supply chains (see, Table 1). The results of this paper confirm that employing the smoothing replenishment rules (e.g., smoothing OUT) improves the ordering and inventory stability in seasonal supply chains. Another possible strength, concluded from the sensitivity analysis, is that employing the smoothing replenishment rules reduces the impact of the demand parameters and the poor selection of the forecasting parameters on the ordering and inventory stability. In this research, the smoothing OUT replenishment rule which is a modified version of the traditional OUT policy was considered to evaluate the impact of smoothing in seasonal supply chains. The traditional OUT, commonly used in practice, can simply be converted into smoothing OUT by adding two proportional controllers to the gaps of the net inventory and supply line (see, equation (11-12)). Therefore, the current seasonal supply chains that employ traditional OUT can largely benefit from the concepts and results presented in this study, to overcome the bullwhip effect. However, a possible weakness of the smoothing replenishment rules is that dampening the order variability has a negative impact on customer service due to an increased Page 6 of 41
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inventory variance. We have noticed that this trade-off between the bullwhip effect and inventory stability might happen at the most downstream echelons in seasonal supply chains when the seasonal cycle is long. Other issues are explained in the conclusions section.
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Second, I would like authors to add a paragraph in the introduction discussing the topic from an "expert systems" point of view. The journal aims in publishing paper in expert and intelligent systems; the introduction does not clearly place the paper in that area. We thank the reviewer for this comment. We have incorporated the required paragraphs in the introduction to clearly place the paper in the ESWA scope. The related discussions can be found in paragraphs 4 and 7.
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Specifically, the current manuscript addresses the bullwhip effect which implies information distortion in the sense of demand variability amplification as one moves upstream in the supply chain, causing severe inefficiencies such as excessive inventory, and high production and transportation costs. In traditional supply chains, each supply chain partner relies on the incoming information from the adjacent downstream echelon to make his forecasting and inventory planning which means that the upstream echelons receive distorted demand information. To achieve intelligent supply chain system, the first step should be allowing the upstream echelons to have accurate or less distorted information on the customer demand. Seasonal supply chains like other normal supply chains need to be equipped with robust inventory decision rules to counteract the bullwhip effect and avoid unwanted consequences. Previous supply chain research has been focusing on the non-seasonal supply chain and their efforts have proposed many avoidance approaches for the bullwhip effect such as the smoothing replenishment rules. This research attempts to evaluate the impact of these inventory decision rules in seasonal supply chains. The main objective is to propose and evaluate some robust tools that can be embedded in the decision support systems of the seasonal supply chains instead of the traditional ones. This explanation has been integrated to the introduction section in paragraph 4.
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To the best of our knowledge, no studies other than Costantino et al. (2015a) have attempted to explore or quantify the impact of smoothing replenishment rules in seasonal supply chains. Costantino et al. (2015a) contributed in ESWA with an inventory replenishment system that relies on two control charts integrated with a set of simple decision rules to forecast future demand and adjust inventory position, whilst providing smoothing capability, to counteract the bullwhip effect. Their preliminary results have shown that smoothing inventory decision rules (in general) can improve seasonal supply chain dynamics compared to traditional ordering policies, suggesting further analysis since their study was not devoted for the extensive analysis of seasonal supply chains. Motivated by these observations, this research attempts to confirm and extend the preliminary work of Costantino et al. (2015a) under different modeling assumptions in terms of the ordering and forecasting method. We mainly propose the application of the smoothing OUT replenishment rule to ameliorate the bullwhip effect in seasonal supply chain since it can easily be adapted from the traditional OUT replenishment system which is commonly used in practice. We further consider the Holt-Winters (HW) forecasting method (Triple Exponential Smoothing) to forecast future demand and update the inventory control parameters, as it is the most suitable forecasting method to forecast seasonal demand. These modeling assumptions are consistent with real applications and therefore the research
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insights will be meaningful to practitioners. This explanation is integrated in the introduction section in paragraph 7. Third, in your conclusion please clearly discuss your research contributions in expert and intelligent systems.
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We thank the reviewer or this comment. We have updated the conclusion section with inserting a new paragraph that explains the main contributions of this study to the ESWA-related work. In addition, other parts in the conclusion section have been updated. We have discussed the contributions of this research. We would like also to refer the reviewer to our replies under the comment # 4 of the first reviewer as he suggested the same improvements. All changes are highlighted with blue color.
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Smoothing inventory decision rules in seasonal supply chains
Abstract
A major cause of supply chain deficiencies is the bullwhip effect, which implies that demand variability
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amplifies as one moves upstream in supply chains. Smoothing inventory decision rules have been recognized as the most powerful approach to counteract the bullwhip effect. Although extensive studies have evaluated these smoothing rules with respect to several demand processes, focusing mainly the smoothing order-up-to
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(OUT) replenishment rule, less attention has been devoted to investigate their effectiveness in seasonal supply chains. This research addresses this gap by investigating the impact of the smoothing OUT on the
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seasonal supply chain performances. A simulation study has been conducted to evaluate and compare the smoothing OUT with the traditional OUT, both integrated with the Holt-Winters (HW) forecasting method, in a four-echelon supply chain experiences seasonal demand modified by random variation. The results show
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that the smoothing OUT replenishment rule is superior to the traditional OUT, in terms of the bullwhip effect, inventory variance ratio and average fill rate, especially when the seasonal cycle is small. In addition, the sensitivity analysis reveals that employing the smoothing replenishment rules reduces the impact of the
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demand parameters and the poor selection of the forecasting parameters on the ordering and inventory stability. Therefore, seasonal supply chain managers are strongly recommended to adopt the smoothing replenishment rules. Further managerial implications have been derived from the results.
Keywords: Supply Chain; Seasonal Demand; Order-Up-To; Smoothing; Holt-Winters; Bullwhip Effect
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1. Introduction A supply chain is an integrated system wherein a set of organizations/partners; e.g. suppliers, manufacturers, distributors, retailers and customers; are connected by material, financial and information flows in both upstream and downstream directions. A supply chain is a complex and dynamic system that should be designed and managed properly to match supply and demand at
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minimum cost. The lack of coordination among supply chain partners and the unavoidable uncertainty usually result in severe deficiencies in the supply chain. An example of such deficiency is the bullwhip effect which implies that orders variance amplifies as one moves upstream in the supply chain (see, Figure 1). Lee et al. (1997a, b) have indicated with providing some real examples from different industries that, even if the customer demand is stable and stationary, a supply chain
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will face the bullwhip effect for any case of misalignment between demand and supply. This can be attributed to the tendency of supply chain partners to update their forecasts and inventory control parameters in response to demand uncertainty which may subsequently lead to a propagation of distorted demand information across the supply chain (Disney and Lambrecht, 2008; Lee et al., 1997a, b). Forrester (1958) was almost the first to study the bullwhip effect through a set of
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simulation experiments utilizing system dynamics modeling, and concluded that the structure, policies and interactions within supply chains are the main drivers of demand variability amplification. Subsequent researchers developed simulation games to illustrate the bullwhip effect
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existence as well as its negative effects in supply chains (Sterman, 1989).
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60 50
Factory Orders Distributor Orders Wholesaler Orders
Retailer Orders
Customer Demand
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Order quantity
70
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90
40 30 20
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10
0
Figure 1. An example of demand variability amplification in supply chain (Costantino et al., 2015a)
The bullwhip effect has attracted the attention of academics and practitioners because of its potential negative consequences in supply chains such as excessive inventory investment, poor customer service, lost revenues, misguided capacity plans, ineffective transportation, and missed production schedules (Chatfield et al., 2004; Lee et al., 1997a, b). Lee et al. (1997a, b) have Page 9 of 41
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identified five major operational causes of the bullwhip effect: demand signal processing, lead-time, order batching, price fluctuations and rationing and shortage gaming. Of our particular interest is the demand signal processing which includes the rational practice of adjusting the demand forecasts and accordingly adjusting the parameters of the inventory replenishment policies, where doing this rationale adjustments may cause under/over-reactions to short-term fluctuations in demand,
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inducing the bullwhip effect (Costantino et al., 2015a, b, c; Dejonckheere et al., 2004). Extensive research has been devoted to quantify the impact of the demand signal processing and the other bullwhip effect causes, utilizing several modeling approaches (Chatfield, 2013): statistical modeling (Chen et al., 2000a, b; Cho and Lee, 2013), simulation modeling (Chatfield et al., 2004; Chatfield, 2013; Costantino et al. 2014a, b, c) and control theoretic modeling (Dejonckheere et al. 2003; Dejonckheere et al., 2004; Jakšič and Rusjan, 2008). The summary of the relevant literature is
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presented in Table 1 showing clearly this classification.
Previous research has emphasized the importance of selecting accurate forecasting methods and proper ordering policies (inventory decision rules) in order to counteract the bullwhip effect in supply chains (Costantino et al., 2015b; Costas et al., 2015; Dejonckheere et al., 2004; Jaipuria and
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Mahapatra, 2014; Shaban et al., 2015; Wright and Yuan, 2008). The majority of the bullwhip effect studies have been considering the order-up-to inventory policies in their models motivated by its
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common use in practice (Chen et al., 2000a, b; Costas et al., 2015; Dejonckheere et al., 2004). Most previous studies have shown that the bullwhip effect is guaranteed when the order-up-to inventory policy (OUT) is employed in supply chains irrespective of the forecasting method integrated
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with it and without making any assumptions about the demand process (Bayraktar et al., 2008; Dejonckheere et al., 2003, 2004). Costas et al. (2015) have recently confirmed the same conclusions
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for the OUT inventory control policy and proposed the Goldratt’s Theory of Constraints to reduce
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the bullwhip effect.
The bullwhip effect implies information distortion in the sense of demand variability amplification as one moves upstream in the supply chain, causing severe inefficiencies such as high production and transportation costs. In traditional supply chains, each supply chain partner relies on the incoming orders from the adjacent downstream echelon to make his forecasting and inventory planning which means that the upstream echelons receive distorted demand information. To achieve intelligent supply chain system, the first step should be allowing the upstream echelons to have accurate information (or less distorted information) on the customer demand. Most importantly, Page 10 of 41
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smoothing replenishment rules have been recognized as the most powerful approaches to avoid/eliminate the bullwhip effect. Many researchers have been attempting to evaluate their dynamic performance compared to other traditional ordering policies, under various operational conditions. The available smoothing replenishment rules have been developed mainly based on the periodic review order-up-to policy by incorporating smoothing terms in the OUT replenishment rule
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where their rationale is to avoid the over/under-reaction to short-run fluctuation in demand and thus limiting the bullwhip effect (Costantino et al., 2015a; Dejonckheere et al., 2003, 2004). In traditional OUT, the replenishment order decision is generated to recover the entire gaps between the target and current levels of net inventory (safety stock) and supply line inventory, while in smoothing OUT only a fraction of each gap is recovered (controlled by the smoothing terms/parameters), where the target levels are dynamically updated according to demand forecast in
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every review period. However, some researches have shown that dampening the bullwhip effect might increase inventory instability causing low service level (Costantino et al., 2015a; Disney and Lambrecht, 2008; Jaipuria and Mahapatra, 2014). In Table 1, we provide further details on the previous research related to the context of this paper, focusing on the modeling aspects and the
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scope of study.
The majority of the bullwhip studies have assumed that the demand process is non-seasonal and
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stationary process, e.g., modeling it as autoregressive moving average (ARMA) and its variants (Cho and Lee, 2012, 2013; Costantino et al., 2013b; Wang and Disney, 2015). In particular, most of the previous studies have quantified the bullwhip effect in supply chains facing customer demand
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follows the autoregressive AR and ARMA demand processes; and employing the traditional OUT policy with different forecasting systems such as moving average (MA), exponential smoothing
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(ES), and mean squared error optimal forecasting (MMSE) methods (Chandra and Grabis, 2005; Chen et al., 2000a, b; Costantino et al., 2015a, b; Disney et al., 2006; Hussain et al., 2012; Ma et al.,
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2013; Zhang, 2004). Many other studies have adopted the normality assumption for modeling the external demand in similar supply chain models (Chatfield, 2013; Chatfield et al., 2004; Costantino et al., 2013a, b; Costas et al., 2015; Dejonckheere et al., 2004). The same conclusions are valid for the previous studies on the smoothing replenishment rules where previous studies have been considering step demand (Ciancimino et al., 2012; Dejonckheere et al., 2004) or other common non-seasonal demand process such as normal and autoregressive (Costantino et al., 2015b; Dejonckheere et al., 2004). In general, there is a lack of studies that have been devoted to study the bullwhip effect in seasonal supply chains, either for traditional OUT or for smoothing OUT Page 11 of 41
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inventory decision rules (Bayraktar et al., 2008; Cho and Lee, 2012; Costantino et al., 2015a). This can easily be seen in Table 1 that summarizes the relevant literature according to some categories, modeling technique, inventory control policy, forecasting method, demand model, performance metrics and scope of study. This table is adapted from Costantino et al. (2015b) but with
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incorporating the proper changes to support the context of this research.
The seasonality phenomenon of demand is a common occurrence in many supply chains where it is common that a supply chain faces demand process contain a seasonal cycle repeats itself after a regular period of time (Wei, 1990). The seasonality may stem from multiple factors such as weather, which affects many business and economic activities like clothing and food industries (Cho and Lee, 2013; Chopra and Meindl, 2004; Wei, 1990). The seasonality can potentially cause
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mismatching supply with demand in supply chains and thus might result in the bullwhip effect (Cho and Lee, 2012, 2013). Cho and Lee (2012) have quantified statistically the bullwhip effect in a twoechelon supply chain employs traditional OUT policy and experiences a seasonal autoregressivemoving average process (SARMA (1, 0) X (0,1)s) showing that the lead-time must be smaller than the seasonal cycle to mitigate the bullwhip effect. They have further evaluated the bullwhip effect in
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this supply chain model under different information sharing scenarios (Cho and Lee, 2013). Bayraktar et al. (2008) have analyzed the impact of exponential smoothing forecasts (Holt-Winters)
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within the traditional OUT on the bullwhip effect for a single electronic supply chain experiences seasonal demand. They have concluded that although high seasonality would reduce the forecast accuracy, it has a significant effect on the reduction of bullwhip effect; providing further
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conclusions regarding the impact of the forecasting parameters on the bullwhip effect. Costantino et al. (2013b) have quantified the impact of demand seasonality parameters, forecasting and safety
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stock parameters and their interactions on the bullwhip effect and inventory stability, in a fourechelon supply chain employs the traditional OUT policy, through a simulation study. Nagaraja et
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al. (2015) have quantified statistically the bullwhip effect in a supply chain employs OUT and faces SARMA(p, q) × (P, Q)s demand process, showing that the bullwhip effect can be mitigated considerably by reducing the lead-time in relation to the seasonal lag value. The previous studies on the bullwhip effect in seasonal supply chains, although limited, have been considering the traditional OUT policy without investigating the smoothing replenishment rules that have been found to be a powerful solution for avoiding the bullwhip effect.
Seasonal supply chains like other normal supply chains need to be equipped with robust inventory Page 12 of 41
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decision rules to counteract the bullwhip effect and avoid unwanted consequences. Previous supply chain research has been focusing on the non-seasonal supply chain and their efforts have reached to many avoidance approaches for the bullwhip effect such as the smoothing replenishment rules (Costantino et al., 2015a; Dejonckheere et al., 2003, 2004). This research attempts to evaluate and predict the impact of the smoothing inventory decision rules in seasonal supply chains. The main
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objective is to propose some robust tools that can be embedded in the decision support systems of the seasonal supply chains instead of the traditional ones. Up to our knowledge, no studies other than Costantino et al. (2015a) have attempted to explore or quantify the impact of smoothing replenishment rules in seasonal supply chains. Costantino et al. (2015a) contributed in ESWA with a real-time SPC inventory replenishment system that relies on two control charts integrated with a set of simple decision rules to forecast future demand and adjust inventory position, whilst
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providing smoothing capability, to counteract the bullwhip effect. Their preliminary results have shown that smoothing inventory decision rules (in general) can improve seasonal supply chain dynamics compared to traditional ordering policies, suggesting further analysis since their study was not devoted for the extensive analysis of seasonal supply chains. Motivated by these observations, this research attempts to confirm and extend the preliminary work of Costantino et al.
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(2015a) under different modeling assumptions with respect to the ordering policy and forecasting method. We mainly propose the application of the smoothing OUT replenishment rule to ameliorate
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the bullwhip effect in seasonal supply chain since it can easily be adapted from the traditional OUT which is commonly used in practice, and the smoothing OUT is well recognized in literature as well. We further consider the Holt-Winters (HW) forecasting method (Triple Exponential
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Smoothing) to forecast future demand and update the inventory control parameters, as it is the most suitable forecasting method to forecast seasonal demand. Therefore, this research considers
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modeling assumptions that are consistent with real applications and therefore the research insights
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will be meaningful to practitioners.
Simulation is the most appropriate modeling approach to investigate the performances of complex systems like multi-echelon supply chains (Chatfield, 2013; Chatfield et al., 2004; Costantino et al., 2015a, b). Therefore, in this research, a simulation study is conducted to evaluate and compare the smoothing OUT with the traditional OUT, both integrated with the Holt-Winters (HW) forecasting method, in a four-echelon supply chain experiences seasonal demand modified by random variation. We further evaluate the impact of the HW forecasting parameters under the traditional and smoothing replenishment rules to understand the impact of these parameters and their interaction Page 13 of 41
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with the different replenishment rules. The seasonal supply chain performance is evaluated in terms of the bullwhip effect ratio, inventory variance ratio and average fill rate (service level). The results show that the smoothing OUT improves the ordering and inventory stability in the seasonal supply chain. The results also show that increasing the order smoothing level improves the ordering and inventory stability in the seasonal supply chain. The sensitivity analysis confirms that employing
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the smoothing replenishment rules reduces the impact of both the seasonal demand parameters and the poor selection of the forecasting parameters on the ordering and inventory stability. The results provide some useful managerial insights that can be utilized by supply chain managers of seasonal supply chains to re-engineer their decision support systems, and they can further utilize these insights to develop expert systems to handle the operational and behavioral causes of the bullwhip effect. The results of this study provide further useful managerial implications on controlling the
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ordering and inventory stability in seasonal supply chains.
The paper is organized as follows. Section 2 introduces the modeling methodology: supply chain model, ordering policy, forecasting method, seasonal demand model, and performance measures. Section 3 introduces the simulation model and validation results. Section 4 presents the simulation
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results and sensitivity analysis, and the discussion and implications are presented in Section 5. The
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conclusions and future research are provided in Section 6.
Table 1: Related research (Costantino et al., 2015b)
al.
Statistical, Simulation
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Chen et (2000a, b)
Inventory control
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Modeling technique
Traditional OUT
Forecasting method
MA, ES
Control theoretic
Traditional OUT, Smoothing OUT
MA, ES, demand signaling
Chatfield et al. (2004)
Simulation
Traditional OUT
MA
Dejonckheere et al. (2004)
Control theoretic, Simulation
Traditional OUT, Smoothing OUT
MA, ES, demand signaling
Zhang (2004)
Statistical
Traditional OUT
MA, ES, MMSE
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Dejonckheere et al. (2003)
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Demand model
AR
Sinusoidal , Real data, i.i.d. normally distributed demand, Step i.i.d. normally distributed demand i.i.d. normally distributed demand
AR
Performance measures
Bullwhip ratio
effect
Bullwhip ratio
effect
Bullwhip ratio
effect
Bullwhip ratio
effect
Bullwhip ratio
effect
Scope of study Measuring the impact of leadtime, forecast parameter and information sharing on the bullwhip effect, in supply chain employs the traditional OUT. Comparing the bullwhip effect under different forecasting methods within traditional OUT. Quantifying the impact of smoothing OUT on the bullwhip effect Quantifying the impact of lead-time variation, information sharing and quality on the bullwhip effect Quantifying the impact of forecasting, information sharing and order smoothing on the bullwhip effect Measuring the impact of lead time and demand pattern parameter on the bullwhip under different forecasting methods
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Chandra and Grabis (2005)
Disney et (2006)
al.
MA, ES, Naïve, Autoregress ive
AR
Bullwhip ratio, Inventory
Traditional OUT, Smoothing OUT
ES
i.i.d. normally distributed demand, AR, MA, ARMA
Bullwhip effect ratio, Inventory Variance, Fill rate
Seasonal
Bullwhip ratio
Simulation
Traditional OUT, MRP
Control theoretic
effect Avg.
Bayraktar et al. (2008)
Simulation
Traditional OUT
Triple exponential smoothing (HW forecasting method)
Kelepouris al. (2008)
Simulation
Traditional OUT
ES
Real data
Bullwhip effect ratio, Fill rate
Wright and Yuan (2008)
Simulation
Smoothing OUT
MA, Holt’s and Brown’s methods
Local trends modified by i.i.d
Bullwhip effect ratio, Root mean square, Inv. costs
Ciancimino al. (2012)
Simulation
Smoothing OUT
ES
Step demand
Bullwhip effect ratio, Inventory variance, Fill rate
Simulation
Traditional OUT
ES, MMSE
AR
Bullwhip effect ratio, Inventory variance
Statistical
Traditional OUT
Cho and Lee (2012)
Cho and Lee (2013)
Statistical
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Ma et al. (2013)
Statistical
et
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Costantino al. (2013b)
Costantino al. (2014c)
et
Jaipuria and Mahapatra (2014)
Costantino et al. (2014b, d)
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MMSE
Traditional OUT
Traditional OUT
MMSE
MA, ES, MMSE
Seasonal demand SARMA (1, 0) X (0,1)s Seasonal demand SARMA (1, 0) X (0,1)s Price sensitive demand with AR i.i.d. normally distributed demand, Seasonal modified by i.i.d i.i.d. normally distributed demand
Quantifying the bullwhip effect and inventory variance under a generalized OUT policy for different demand patterns Measuring the impact of seasonality, lead-time and HW forecasting parameters, and their interactions on the bullwhip effect in E-SC employs traditional OUT Investigating the impact of lead time, exponential smoothing parameter and safety stock on the bullwhip effect in simulated real supply chain Evaluating the impact of improved forecasting and inventory control parameters on the bullwhip effect and inventory costs Analyzing the operational response of a synchronized supply chain employs the smoothing OUT. Analyzing the bullwhip effect ratio and inventory variance under different forecasting methods within traditional OUT.
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Hussain et al. (2012)
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et
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et
effect
Analyzing the bullwhip effect under traditional OUT and MRP approach with different forecasting methods
Bullwhip ratio
effect
Quantifying the bullwhip effect in a seasonal supply chain employs the traditional OUT
Order variance, Avg. inventory, inventory variance, inventory cost
Analyzing the value of information sharing in seasonal supply chain employs the traditional OUT
Bullwhip effect ratio, Inventory variance
Analyzing the bullwhip effect ratio and inventory variance under different forecasting methods integrated with traditional OUT.
Bullwhip effect ratio, Inventory variance, Fill rate
Exploring the bullwhip effect and inventory variance in a seasonal supply chain employs traditional OUT.
Bullwhip effect ratio, Inventory variance, Fill rate
Analyzing the value of information sharing and inventory control coordination on supply chain performances
Simulation
Traditional OUT
MA
Simulation
Traditional OUT
MA
AI, Simulation
Traditional OUT
ARIMA, DWT-ANN
Real data, literature data
Mean square error, bullwhip effect ratio, Inventory variance
Analyzing the value of improved forecasting on order and inventory variances
MA, SPCForecasting
i.i.d. normally distributed demand, AR
Bullwhip effect ratio, Inventory variance, Fill rate
Developing inventory control systems based on control charts to improve supply chain dynamics
Simulation
Traditional OUT, SPC
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Demand patterns of different frequencie s, Real data i.i.d. normally distributed demand, AR, seasonal
Investigating the bullwhip effect under damped trend used within traditional OUT and comparing it to other forecasting methods.
Control theoretic
Traditional OUT
MA, ES, Naïve, Damped trend
Costantino et al. (2015a, b)
Simulation
Traditional OUT, smoothing OUT, SPC
MA, ES, SPCForecasting
Costas et (2015)
Multi-agent simulation
Traditional OUT, Theory of Constraints (TOC)
MA
i.i.d. normally distributed demand
Bullwhip effect ratio, Inventory variance
Mitigating the bullwhip effect with Goldratt’s Theory of Constraints (TOC)
Statistical
Traditional OUT
MMSE
Seasonal demand SARMA (p, q) × (P, Q)s
Bullwhip ratio
Quantifying the bullwhip effect in supply chains with seasonal demand components and use traditional OUT.
Nagaraja et al. (2015)
Bullwhip effect ratio, Inventory variance, Fill rate
Developing forecasting and inventory control systems based on control charts to counteract the bullwhip effect
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al.
effect
effect
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Li et al. (2014)
Bullwhip ratio
2. Modeling Methodology 2.1 Supply Chain Model
In this research, we model and simulate a multi-echelon supply chain that consists of a customer, a
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retailer, a wholesaler, a distributor, a factory, and an external supplier (see, Figure 2). This is a wellknown supply chain model, known as the Beer Game model, and has been utilized in many
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previous bullwhip effect investigations (Chatfield, 2013; Chatfield et al., 2004; Ciancimino et al., 2012; Costantino et al., 2014a, b, c, d; Costantino et al., 2015a, b). Figure 2 depicts a visual representation of the supply chain structure in which, at any period, each echelon i receives orders
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from its downstream partner i 1 , satisfies these orders from his own stock and then issues his orders with echelon i 1 . The retailer observes and satisfies the customer demand Dt and places
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orders with the wholesaler where the retailer is the only partner in the supply chain that has direct
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access to the actual customer demand.
Customer
Retailer
Wholesaler
Distributor
Factory
External Supplier
Information flow Product flow
Figure 2. A multi-echelon supply chain
The supply chain model presents the following assumptions (Ciancimino et al., 2012; Costantino et
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al., 2015a, b; Sterman, 1989; Wright and Yuan, 2008):
the factory has unlimited capacity to produce any quantity ordered by the distributor;
the stocking capacity at any echelon is unlimited;
the unfulfilled orders, due to out of stock, at any echelon are not lost while they become
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backlogged orders, to satisfy as soon as the inventory recovers;
the transportation capacity between adjacent echelons is unlimited;
the ordering and delivery lead-times are deterministic and fixed across the supply;
the replenishment orders are always positive or equal to zero, cancelations are not allowed
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(no returns).
The regulation of information and material flows in the above supply chain model is controlled based on the mathematical model represented by the difference equations (1-6). The equations define the basic state variables at each echelon i that are updated in each period t based on a specific sequence of events; where i 1, ..., 4 ; i.e., i 1 stands for the retailer and i 4 stands for
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the factory, and we also refer to the customer as echelon i 0 (Costantino et al., 2014c, 2015a, b).
(1)
1 SRti Min IOti Bti1; Iti1 SRtiLd
(2)
1 Iti I ti1 SRtiLd SRti
(3)
Bti Bti1 IOti SRti
(4)
NIti Iti Bti
(5)
IPt i NI ti SLit
(6)
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1 SLit SLit 1 Oti1 SRtiLd
In each period t , each echelon i receives an amount of shipment SRtiL1i shipped by the upstream d
echelon i 1 at time t Lid , where Lid expresses the delivery lead-time. Thus, the initial inventory level I ti1 is increased by the shipment SRtiL1i and at the same time decreases by the amount of SRti d
released down to the echelon i 1 (see, equation (3)). The amount SRti to ship to echelon i 1 depends on the minimum of the initial inventory I ti1 added to the incoming shipment SRtiL1i , and d
i t
i t 1
the incoming order IO added to the initial backlogged order B Page 17 of 41
(see, equation (2)) where at the
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retailer (echelon i 1 ), the incoming order at time t is the observed customer demand at this time ( IOti 1 Dt ). Thus, the net inventory NI ti presented in equation (5) is equal to the difference between the available inventory level I ti (see, equation (3)) and the backlog level Bti (see, equation (4)) at time t . The inventory position of echelon i at time t in equation (6) is the accumulation of the amount in supply line SLit in equation (1) and the net inventory level in equation (5). The
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replenishment order Oti of each echelon i 1 at time t is controlled and issued based on the generalized order-up-to inventory policy. 2.2 Smoothing Order-Up-To Inventory Policy
The periodic review order-up-to inventory policy, known also as (R, S), is common in the literature
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of supply chain dynamics because of its popularity in practice (Disney and Lambrecht, 2008). This type of replenishment policies is common in practice as in retailing that tends to replenish inventories frequently (e.g. daily, weekly, etc.). A generalized variant of this policy is used here to allow order smoothing through avoiding the over/under-reaction to demand and inventory variations. In the traditional OUT policy, at the end of each review period ( R ), where it is assumed
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that R 1 in this model, a non-negative replenishment order Oti is placed whenever the inventory position IPt i is lower than a specific target inventory or base stock level Sti (see, equation (7)). In
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other words, the entire gap between the target and actual levels of inventory position are taken into account in the placed order. The traditional order-up-to policy can be represented mathematically as
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in equations (7-8).
Oti Max Sti IPt i , 0
(7)
Sti LDˆ ti SSti
(8)
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The base stock level Sti is dynamically updated in each time period based on the expected demand over the total lead-time (review period and delivery lead-time, Lid R ) plus a safety stock component (see, equation (8)). The Holt-Winters forecasting technique is adopted to estimate the expected demand ( Dˆ ti ) since it the most suitable forecasting method for predicting seasonal demand (Bayraktar et al., 2008). Following the relevant literature, we have considered the safety stock that is required to account for demand variation by extending the lead-time with the safety stock paramter Ki as shown in equation (9) (Costantino et al. 2015a, b; Dejonckheere et al., 2004). Page 18 of 41
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(9)
Sti ( Lid R K i ) Dˆ ti
In the traditional order-up-to policy, the order can be divided into: a demand forecast, a net inventory error term and a supply line inventory error term, but both the errors terms are completely taken into account in the placed order (see, equation, (10)). Some researchers have proposed some ways that can increase the flexibility of OUT to allow order smoothing in which the decision maker
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does not recover the entire errors in one time period. Specifically, in the smoothing OUT inventory decision rule, a fraction of each error term is recovered in each review period to dampen the ordering variability. Equation (11) represents the generalized order-up-to policy which can allow order smoothing with setting Tn 1 and Ts 1 .
Lid Dˆ ti SLit K i Dˆ ti NI ti Tn Ts
(10)
(11)
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Oti Dˆ ti
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Oti ( Lid R K i ) Dˆ ti NI ti SLit Oti Dˆ ti Lid Dˆ ti K i Dˆ ti NI ti SLit Oti Dˆ ti Lid Dˆ ti SLit K i Dˆ ti NI ti
In equation (11), the term Lid Dˆ ti represents the target amount in supply line/pipeline ( TSLit ), and
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K i Dˆ ti denotes the target net inventory/safety stock ( TNI ti ); and Tn and Ts are two proportional
controllers (smoothing parameters) for regulating the recovery of the errors of net inventory and
PT
supply line over time, respectively. For simplicity, we consider Tn Ts and thus the replenishment rule can be written in a general form in equation (12), in which, setting Tn 1 turns the replenishment rule into a traditional order-up-to policy that doesn’t allow order smoothing
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(Ciancimino et al., 2012; Costantino et al., 2015a; Dejonckheere et al., 2003, 2004).
TNI ti TSLit IPt i Oti Max Dˆ ti , 0 Tn
(12)
2.3 Holt-Winters Forecasting The demand forecast at each echelon in the supply chain model ( Dˆ ti ) is estimated based on the HoltWinters forecasting method (Triple Exponential Smoothing) which is suitable for demand patterns with trend and seasonal components. The Holt-Winters (HW) method comprises the forecast equation and Page 19 of 41
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three smoothing equations for level component lti , trend component bti , and seasonal component
ti , including the smoothing parameters , and , respectively (Chopra and Meindl, 2004; Montgomery et al., 2008). In each period t , the three smoothing components are updated according to the following equations (13-15):
(13)
bti lti lti1 1 bti1
(14)
ti IOti lti 1 ti s
(15) (16)
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Ft i m lti mbti ti m s
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lti IOti ti s 1 lti1 bti1
where:
, and are the HW forecast smoothing parameters,
lti is the estimated level of incoming order to echelon i at time t ,
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bti is the estimated trend of incoming order to echelon i at time t ,
ti is the estimated seasonality of incoming order to echelon i at time t ,
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s is the number of periods in a seasonal cycle,
Ft i m is the forecasted demand at m periods ahead, where m 1, ..., s .
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In each period t , the demand forecast at m periods ahead ( Ft i m ) can be estimated based on equation (16). However, in this model, it is only required to dynamically estimate the next period’s demand (the
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one-period ahead demand forecast, Dˆ ti ) where Dˆ ti Ft i1 lti bti Sti1 s , to calculate the target levels of supply line inventory and net inventory (see, equations (11-12)). To apply the HW method, it is
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required to have at least two complete seasonal cycles of demand/incoming order data to obtain the initial values of the forecast components ( l0i , b0i and 0i ) that can be calculated using the formulas in equations (17-19). This can be managed in the simulation model by selecting a proper warm-up period.
l0i
Page 20 of 41
1 s IOij s j 1
(17)
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i
b0i
i
1 s IOs j IO j s s j 1
0i IO ij l0i ,
(18)
j 1, ..., s
(19)
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2.4 Seasonal Demand Model The external demand ( Dt ) faced by the retailer is generated to have a seasonal component and modified with random variation, according to the formula in equation (20). This demand generator is adapted from Zhao and Xie (2002) and Costantino et al. (2013b, 2015a) and consists of constant demand ( base ), trend component ( slope ), seasonal component (sinusoidal function with
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parameters season and SeasonCycle ), and noise component ( ). In this study, the trend component is neglected with setting slope 0 , and the base will be set relatively high to season and in the simulation experiments to avoid the generation of negative demand, to satisfy the nonnegativity condition of customer demand.
(20)
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2 Dt base slope t season sin t N 0, 2 SeasonCycle 2.5 Performance Measures
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The objective of this study is to investigate the impact of the smoothing replenishment rules in seasonal supply chain in terms of the demand variability amplification and the corresponding
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inventory performances. Therefore, three performance measures are considered: bullwhip effect ratio (i.e., order variance ratio), inventory variance ratio, and average fill rate (i.e., service level).
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The bullwhip effect ratio ( BWEi ), known also as order variance ratio, has been widely used in the literature of supply chain dynamics to quantify the amplification of order variability across the supply chain (Ciancimino et al., 2012; Costantino et al., 2014c; Disney and Lambrecht, 2008). The
BWEi as shown in equation (21) represents the ratio of orders variance at echelon i ( O2i ) relative to the demand variance ( D2 ) where BWEi 1 results in bullwhip effect; BWEi 1 results in order smoothing; and BWEi 1 results in a “pass-on-orders” (Disney and Lambrecht, 2008).
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BWEi
O2i
(21)
D2
The second performance measure is the inventory variance ratio which was proposed by Disney and Towill (2003) to measure the degree of inventory stability since it quantifies the fluctuations in net
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2 inventory ( NI ) relative to the demand variance ( D2 ) as presented in equation (22). An increased i
inventory variance ratio indicates higher inventory instability that would result in higher holding and backlog levels, lower service level and subsequently higher inventory costs (Disney and Lambrecht, 2008). Therefore, dampening both the bullwhip effect ratio and the inventory variance ratio across the supply chain reflects improved operational performance of the supply chain (i.e.,
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improved ordering and inventory stability).
InvRi
2 NI i
D2
(22)
The average fill rate ( AFRi ) quantifies the percentage of items supplied immediately by echelon i
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from stock at hand to satisfy the incoming order (Costantino et al., 2014c, 2015a; Zipkin, 2000). The fill rate ( FRti ) is computed every time there is a positive incoming order (i.e., when IOti 0 ) as
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shown in equation (23), where SRti stands for the shipment released by echelon i at time t , Bti1 stands for the initial backlog at echelon i at time t , and IOti is the incoming order to echelon i at
PT
time t . The effective computational time ( Teff ) is equivalent to the summation of all periods with IOti 0 ; hence Teff T where T is the total computational time. The fill rate time series can then
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be used to calculate the average fill rate ( AFRi ), which implies the average service level, as
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indicated in equation (24).
SRti Bti1 100 FRti IOti 0
AFRi
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if SRti Bti1 0 i t
i t 1
if SR B Teff t 1
FRti
Teff
(23)
0
(24)
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3. Simulation Model Validation Simulation modeling is the most suitable tool to characterize the performance of complex and dynamic systems like multi-echelon supply chains. It provides the ability to model a multi-echelon supply chain in a single, connected and cohesive model, so that the limitations of simple models in representing larger systems are avoided (Chatfield, 2013; Costantino et al., 2015a, b, c). The
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simulation model logic is presented in Figure 3 in which the parameters to adjust in each simulation run are indicated as well. The simulation model used for this study has been developed using
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CE
PT
ED
M
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Simul8 and has been validated by comparing its output with previous leading research.
Figure 3. Simulation model flowchart
The available results in previous research are obtained for traditional OUT with simple exponential smoothing method (ES) (Chen et al., 2000; Dejonckheere et al., 2004) and smoothing OUT with ES (Dejonckheere et al., 2004) under normal demand. Therefore, we adjust the settings of our Page 23 of 41
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simulation model by turning the HW forecasting system into ES (with setting 0 and 0 ). Specifically, we have compared the simulation model results with the control engineering results of Dejonckheere et al. (2004), and the statistical results of Chen et al. (2014b) who derived a closed form expressions for the bullwhip effect ratio (see, equation (25)). For this validation, we consider the same simulation settings in Dejonckheere et al. (2004) for conducting direct comparisons with
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them. Therefore, for each ordering policy, the simulation model was run for 20 replications of a replication length of 5200 periods each and with a warm-up period of 200 periods. The customer demand in Dejonckheere et al. (2004) is assumed to follow the normal distribution with a mean of 100 and a standard deviation of 10 and therefore the parameters of the above seasonal demand model are set to: base 100 , season 0 , and 10 , to generate the same data set of the normal
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demand.
The HW method has been turned into a single ES using the following initial settings: b0i 0 and
0i 0 ; and its smoothing parameters are set to: 0.1 , 0 and 0 where the value of is selected according to Dejonckheere et al. (2004). The lead-time, review period, and safety stock
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parameter are set to: Lid 2 , R 1 , and Ki 2 , where Lid R K i 5, i . We applied these values in equation (25) to get the bullwhip effect ratio at each echelon i based on Chen et al.
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(2000b), where i 1,..., m (echelon index) and m 4 , i 0.1, i and Li Lid R Ki in which the safety stock parameter is included.
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O2i
i
(25)
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D2
m 2 L2 2 1 2 Li i i i i 1 2 i
The results presented in Table 2 indicate that the simulation model is working as intended where the
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difference between the simulation output and the previous research results are not significant. Furthermore, the results confirm the significance of the smoothing inventory rules in the supply chain when the demand is normal. It can be observed that increasing the smoothing level from
Tn 1 to Tn 4 decreases the bullwhip effect considerably across the supply chain. The bullwhip
effect ratio is almost eliminated at all echelons other than the factory that produces a very low bullwhip effect when Tn 4 ( BWE 1.361 ) compared to BWE 25.96 when Tn 1 .
Table 2. Simulation model validation results Page 24 of 41
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Classical OUT (Tn=1) SIM. Model
Dejonckheere et al. (2004)
Chen et al. (2000b)
SIM. Model
Dejonckheere et al. (2004)
Retailer
2.27
2.26
2.26
0.421
0.423
Wholesaler
5.18
5.16
5.06
0.479
0.4828
Distributor
11.83
11.84
11.39
0.765
0.773
Factory
25.96
27.22
25.63
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BWE
Smoothing OUT (Tn=4)
4. Simulation Results and Analysis 4.1 The Effect of Smoothing
1.361
1.376
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The impact of the smoothing OUT replenishment rule ( Tn 1 ) is evaluated and compared to the traditional OUT ordering rule ( Tn 1 ) under two levels of seasonality (low and high) combined with two levels of seasonal cycle (low and high). The design of this simulation experiment is adopted to evaluate the effect of order smoothing under a wide range of the seasonal demand parameters. We consider the following designs of the generalized OUT replenishment rule to also
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investigate the effect of the smoothing parameter level on the seasonal supply chain performances:
Tn 1 , Tn Lid , Tn Lid 1 and Tn 2 Lid . These four designs based on the lead-time have been
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proposed in some previous studies that have attempted to investigate the impact of smoothing OUT replenishment rules in supply chains but under non-seasonal demand like step and normal demand
PT
(Ciancimino et al., 2012; Dejonckheere et al., 2004). For this comparison, the forecasting parameters are set to: 0.1 , 0 and 0.1 . In each scenario, following the same logic in the
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flowchart in Figure 3, the simulation model is run for 20 replications, with a replication length of 1200 periods and a warm-up-period of 200 periods. The other parameters of the supply chain
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model are set to: b0i 0 , s SeasonCycle , Ki 1 , and Lid 2 .
The results of a single simulation run, showing the impact of shifting from the traditional OUT ( Tn 1 ) to the smoothing OUT ( Tn 1 ) on the orders and inventory variations over time (last 200 periods), are presented in Figures 4-5. The results in these figures indicate that the ordering and inventory stability across the supply chain becomes higher under the smoothing OUT compared to the traditional OUT. The ordering variability increases in the upstream direction under the classical OUT where the factory’s orders shows the highest variability as can be observed in Figure 4a. Page 25 of 41
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However, the ordering variability decreases in the upstream direction under the smoothing OUT where the factory’s orders variability is the lowest (see, Figure 4b). The same conclusions are valid for the inventory level variation as it increases in the upstream direction under the classical OUT (see, Figure 5a) while decreases in the same direction under the smoothing OUT (see, Figure 5b).
100
(a) Classical OUT (Tn=1)
Order quantity
80 70 60 50 40 30 20 10 0 1
21
41
61
Customer Demand
81
100
121
Wholesaler Order
70 60 50 40 30 20 10 0 1
21
41
61
81
Retailer Order
161
101
121
Wholesaler Order
141
181
Factory Order
161
Distributor Order
181
Factory Order
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Customer Demand
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80
141
Distributor Order
(b) Smoothing OUT (Tn=2Ld=4)
90
Order quantity
101
Retailer Order
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90
Figure 4. The order rate variation over time under different smoothing levels when Season=10 and
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SeasonCycle=7
(a) Classical OUT (Tn=1)
150 125 75
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Inventory level
100 50 25 0 -25 -75 -100 1
CE
-50
21
41
61
Retailer Inventory
101
121
141
Distributor Inventory
161
181
Factory Inventory
(b) Smoothing OUT (Tn=2Ld=4)
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150
81
Wholesaler Inventory
125
Inventory level
100
75 50 25
0
-25 -50 -75
-100 1
21
41
Retailer Inventory
61
81
Wholesaler Inventory
101
121
Distributor Inventory
141
161
181
Factory Inventory
Figure 5. The inventory level variation over time under different smoothing levels when Season=10 and SeasonCycle=7 Page 26 of 41
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4.1.1
Bullwhip Effect Analysis
The bullwhip effect ratio results ( BWEi ), based on the average of 20 simulation runs, are presented in Figure 6a and show that shifting from the traditional OUT to the smoothing OUT has a significant impact on the ordering stability in the supply chain, regardless of the combination of the
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seasonal parameters. Furthermore, the results show that any increase in the smoothing level Tn leads to a decrease in the bullwhip effect ratio across the supply chain (at all echelons) whatever the demand parameters. For example, when Season 5 and SeasonCycle 7 , increasing the smoothing level from Tn 1 to Tn 4 reduces the bullwhip effect magnitude across the supply chain, e.g., from 1.88 to 0.30 at the retailer (respectively) and from 12.40 to 0.43 at the factory. In
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other words, the bullwhip effect is eliminated by increasing the smoothing level to Tn 4 .
The results in Figure 6a also indicate that the seasonal cycle has a significant contribution to the bullwhip effect magnitude where longer seasonal cycle increases the bullwhip effect while high seasonal level leads to a lower bullwhip effect. However, the results show that the selection of high smoothing level can mitigate the effect of the seasonal cycle and therefore smoothing replenishment
Inventory Performance Measures
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4.1.2
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rules are recommended for the seasonal supply chains with longer seasonal cycles.
The results of inventory variance ratio exhibited in Figure 6b show a similar behavior to the
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bullwhip effect results in Figure 6a. It can be seen that increasing the smoothing level leads to a higher inventory stability (lower inventory variance ratio) across the supply chain whatever the
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demand parameters. However, it can be noticed that as the seasonal cycle increases, higher smoothing level increases the inventory ratio at the retailer to some extent whilst improving the
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inventory stability at the upstream echelons. The results also show that the inventory variance ratio is less sensitive to the seasonal level while it is highly sensitive to the seasonal cycle regardless of the smoothing level. However, this sensitivity decreases as the smoothing level increases. For instance, when Season 5 , as the seasonal cycle increases from SeasonCycle 7 to SeasonCycle 14 , the inventory variance ratio increases considerably at all echelons regardless of the smoothing level, e.g., increases from 5.47 to 7.06 at the retailer and from 34.72 to 50.09 at the factory under Tn 1 , while increases from 3.49 to 8.72 at the retailer and from 4.56 to 7.58 at the factory under Tn 4 . The results further show that the Page 27 of 41
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inventory variance ratio at the retailer increases as the smoothing level increases only when the seasonal cycle is long.
The average fill rate results in Figure 6c confirm the findings for the
inventory variance ratio where increasing the smoothing level leads to a higher average fill rate across the supply chain. Therefore, the inventory stability is improved in seasonal the supply chain
16.0
(a) Bullwhip effect ratio
14.0 12.0 10.0
BWE
8.0 6.0 4.0
0.0 Retailer Wholesaler Distributor Factory
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=5, SeasonCycle=7) 1.88 0.78 0.44 0.30 3.55 0.71 0.29 0.18 6.72 0.76 0.31 0.21 12.40 0.95 0.43 0.31
70.0
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2.0 Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=10, SeasonCycle=7) 1.82 0.80 0.42 0.27 3.34 0.67 0.21 0.11 5.99 0.61 0.16 0.09 10.13 0.61 0.18 0.12
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=5, SeasonCycle=14) 1.95 1.17 0.82 0.60 3.91 1.63 0.86 0.49 7.65 2.38 0.95 0.45 14.32 3.53 1.13 0.51
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=10, SeasonCycle=14) 1.87 1.37 0.98 0.72 3.57 1.99 1.02 0.54 6.65 2.92 1.07 0.43 11.62 4.32 1.15 0.38
(b) Inventory variance ratio
60.0
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50.0 40.0 InvR
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when shifting from the traditional OUT to the smoothing OUT.
30.0
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20.0 10.0 0.0
PT
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=5, SeasonCycle=7) Retailer 5.47 4.39 3.76 3.49 Wholesaler 9.75 4.54 2.95 2.47 Distributor 16.98 5.39 3.44 3.01 Factory 34.72 7.31 5.04 4.56
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=5, SeasonCycle=14) 7.06 8.72 8.97 8.72 14.13 13.04 9.92 7.40 29.97 20.50 11.38 6.94 50.09 29.75 13.48 7.58
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=10, SeasonCycle=14) 8.25 10.64 11.11 10.71 19.59 15.37 11.95 8.53 43.13 27.86 13.12 6.86 59.83 37.05 14.18 5.98
(c) Average fill rate
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120.0
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=10, SeasonCycle=7) 5.68 4.62 3.64 3.17 9.05 4.08 2.01 1.38 14.55 3.90 1.63 1.22 36.09 4.24 1.99 1.70
100.0 80.0
AFR%
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60.0 40.0
20.0 0.0
Retailer Wholesaler Distributor Factory
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=5, SeasonCycle=7) 100.0 100.0 100.0 100.0 99.9 100.0 100.0 100.0 98.8 100.0 100.0 100.0 95.6 99.9 100.0 100.0
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=10, SeasonCycle=7) 99.7 99.9 100.0 100.0 97.2 99.9 100.0 100.0 91.0 99.8 100.0 100.0 82.4 99.7 100.0 100.0
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=5, SeasonCycle=14) 100.0 100.0 100.0 100.0 99.5 99.8 100.0 100.0 95.8 98.7 99.8 100.0 93.1 97.1 99.6 100.0
Tn=1.0 Tn=2 Tn=3 Tn=4 (Season=10, SeasonCycle=14) 97.4 97.2 97.4 97.7 81.9 90.6 96.5 98.7 71.6 80.4 95.4 99.2 75.6 82.3 95.0 99.3
Figure 6. The impact of order smoothing on supply chain performances under different seasonal parameters Page 28 of 41
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The above results confirm that shifting from the traditional OUT to the smoothing OUT can improve the ordering and inventory stability in the seasonal supply chains. It has further been found that increasing the smoothing level leads to lower bullwhip effect, lower inventory variance and higher average service level across the supply chain. These conclusions have been proven in
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previous research for non-seasonal demand, and we confirm and extend these conclusions to the seasonal demand as well. 4.2 The Impact of Forecasting Parameters
The above analysis has been conducted to investigate the impact of the smoothing replenishment rule on the supply chain performances under different combinations of the seasonal demand
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parameters, considering specific settings for the forecasting and other operational parameters. In this section, we extend the analysis to investigate the impact of the HW’s parameters on the supply chain performances, considering three levels of combined with three levels of ; and each combination is evaluated under two levels of smoothing. The experimental ranges of and are selected based on earlier research (Bayraktar et al., 2008) while the values of Tn are selected based
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on the above results. The comparisons are conducted under the four demand patterns used above to understand the interaction between the forecasting parameters, smoothing level and demand
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parameters. The other parameters are set to: Lid 2 , 0 , and Ki 1 for the different simulation experiments.
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The results in Figures 7-9 indicate that the smoothing OUT replenishment rule is superior to the traditional OUT replenishment rule under the different combinations of the seasonal demand
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parameters, regardless of the forecasting parameters. It can be further seen that all performance measures are highly sensitive to while less sensitive to where smaller values of leads to lower bullwhip effect, lower inventory variance ratio, and higher average fill rate, regardless of the
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demand parameters. However, larger values of leads to a higher ordering and inventory instability, especially at the most upstream echelons, under the traditional OUT policy ( Tn 1 ). These bullwhip effect results confirm the previous findings of Bayraktar et al. (2008) that investigated the impact of the HW parameters in a seasonal supply chain employs the traditional OUT ordering policy. They have shown that smaller values of are best suited to mitigate the bullwhip effect, however, their study have not considered the impact of the forecasting parameters on the inventory stability. The results in this research extend their findings and further confirm the Page 29 of 41
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value of the smoothing replenishment rules in the seasonal supply chain, confirming the preliminary results of Costantino et al. (2015a). It can be observed that all performances measures become less sensitive to either forecasting paramter when the smoothing level is high ( Tn 4 ). Therefore, the smoothing replenishment rule helps to alleviate the contribution of the improper selection of the
(a) Season=5, SeasonCycle=7
80.0 70.0 60.0
BWE
50.0 40.0 30.0 20.0 10.0
Retailer Wholesaler Distributor Factory
γ=0.05
γ=0.1 α=0.05
γ=0.2
1.39 2.04 3.01 4.35
1.37 1.87 2.57 3.54
1.38 1.90 2.62 3.66
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 1.89 1.88 1.89 3.71 3.55 3.60 7.14 6.72 6.84 13.03 12.40 12.70
γ=0.05
γ=0.1 α=0.2
3.19 10.29 28.31 62.40
3.21 10.28 28.38 62.35
70.0 60.0
BWE
50.0 40.0
20.0 10.0 γ=0.1 α=0.05
γ=0.2
1.27 1.75 2.46 3.42
1.32 1.75 2.31 3.07
1.33 1.78 2.39 3.21
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 1.75 1.82 1.85 3.24 3.34 3.41 5.86 5.99 6.15 9.90 10.13 10.42
γ=0.05
ED
γ=0.05
γ=0.1 α=0.05
γ=0.2
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 0.29 0.30 0.30 0.19 0.18 0.18 0.23 0.21 0.21 0.34 0.31 0.31
0.20 0.11 0.12 0.14
0.19 0.10 0.09 0.11
0.20 0.10 0.10 0.12
γ=0.05
γ=0.1 α=0.2
γ=0.2
0.55 0.47 0.63 1.13
0.57 0.49 0.63 1.10
0.57 0.49 0.64 1.12
3.01 8.80 20.00 35.62
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
3.14 9.22 20.59 35.99
3.17 9.34 20.77 36.22
0.17 0.06 0.06 0.07
0.17 0.05 0.04 0.04
0.17 0.05 0.04 0.04
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 0.26 0.27 0.27 0.11 0.11 0.11 0.11 0.09 0.09 0.15 0.12 0.12
γ=0.05
γ=0.1 α=0.2
γ=0.2
0.53 0.33 0.31 0.47
0.56 0.37 0.33 0.46
0.56 0.38 0.34 0.47
γ=0.05
γ=0.1 α=0.2
γ=0.2
1.09 1.50 2.13 3.17
1.10 1.57 2.36 3.71
1.12 1.64 2.56 4.12
(c) Season=5, SeasonCycle=14
PT
80.0 70.0 60.0 50.0 40.0
CE
BWE
3.23 10.36 28.59 62.72
M
30.0
Retailer Wholesaler Distributor Factory
γ=0.05
(b) Season=10, SeasonCycle=7
80.0
0.0
γ=0.2
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0.0
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forecasting parameters to the ordering and inventory instability in supply chains.
30.0 20.0 10.0
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0.0
Retailer Wholesaler Distributor Factory
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γ=0.05
γ=0.1 α=0.05
γ=0.2
1.82 3.81 6.74 10.50
1.46 2.19 3.27 4.80
1.42 2.02 2.87 4.09
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 2.30 1.95 1.92 5.80 3.91 3.71 12.03 7.65 7.15 21.90 14.32 13.46
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
3.46 12.20 33.18 74.49
3.13 9.91 27.56 63.30
3.11 9.68 26.97 62.31
0.44 0.32 0.31 0.35
0.40 0.22 0.17 0.17
0.40 0.23 0.17 0.15
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 0.63 0.60 0.61 0.54 0.49 0.51 0.54 0.45 0.49 0.65 0.51 0.54
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(d) Season=10, SeasonCycle=14
80.0 70.0 60.0 50.0
BWE
40.0 30.0 20.0 10.0
Retailer Wholesaler Distributor Factory
γ=0.05
γ=0.1 α=0.05
γ=0.2
1.49 2.61 4.30 6.58
1.39 1.99 2.84 4.04
1.40 1.95 2.72 3.80
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 1.92 1.87 1.89 4.14 3.57 3.57 8.13 6.65 6.61 14.35 11.62 11.53
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
2.93 8.86 21.22 40.42
2.95 8.49 19.77 36.91
2.99 8.58 19.84 36.87
0.48 0.29 0.26 0.30
0.46 0.23 0.13 0.10
0.47 0.25 0.14 0.09
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 0.71 0.72 0.73 0.54 0.54 0.59 0.45 0.43 0.50 0.48 0.38 0.45
γ=0.05
γ=0.1 α=0.2
γ=0.2
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0.0
1.27 1.72 2.32 3.20
1.34 1.93 2.84 4.22
1.38 2.07 3.16 4.86
Figure 7. The main and interaction effects of the forecasting parameters and smoothing level on the bullwhip effect (a) Season=5, SeasonCycle=7
300.0
InvR
200.0 150.0 100.0 50.0
Retailer Wholesaler Distributor Factory
γ=0.05
γ=0.1 α=0.05
γ=0.2
4.49 6.04 8.37 12.22
4.68 6.24 8.32 11.32
4.71 6.33 8.51 11.67
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 5.27 5.47 5.51 9.38 9.75 9.86 16.62 16.98 17.22 34.36 34.72 35.56
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
6.74 18.07 48.70 164.97
6.95 18.59 49.96 170.09
6.98 18.71 50.48 171.71
3.20 1.78 1.87 2.34
3.23 1.79 1.82 2.24
3.24 1.80 1.84 2.26
M
0.0
AN US
250.0
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 3.45 3.49 3.50 2.43 2.47 2.49 3.01 3.01 3.04 4.62 4.56 4.59
γ=0.05
γ=0.1 α=0.2
γ=0.2
4.07 4.02 6.11 11.00
4.13 4.14 6.22 11.01
4.14 4.17 6.27 11.11
γ=0.05
γ=0.1 α=0.2
γ=0.2
3.94 2.68 2.81 4.37
4.04 2.89 3.00 4.42
4.05 2.94 3.07 4.49
γ=0.05
γ=0.1 α=0.2
γ=0.2
9.39 13.76 21.78 32.02
10.57 15.80 25.96 39.05
10.99 16.72 28.22 43.11
(b) Season=10, SeasonCycle=7
300.0
ED
250.0
InvR
200.0 150.0
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100.0 50.0 0.0
γ=0.1 α=0.05
γ=0.2
4.88 6.13 7.97 12.33
5.14 6.53 8.21 11.86
5.18 6.63 8.41 12.37
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Retailer Wholesaler Distributor Factory
γ=0.05
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 5.46 5.68 5.71 8.62 9.05 9.15 13.97 14.55 14.80 34.25 36.09 37.19
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
6.10 15.42 42.58 109.29
6.21 16.29 44.86 111.92
6.23 16.52 45.46 112.51
2.76 0.88 0.77 0.96
2.81 0.90 0.71 0.83
2.81 0.92 0.72 0.84
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 3.11 3.17 3.18 1.31 1.38 1.40 1.25 1.22 1.24 1.83 1.70 1.72
(c) Season=5, SeasonCycle=14
300.0
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250.0
InvR
200.0 150.0 100.0 50.0
0.0
Retailer Wholesaler Distributor Factory
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γ=0.05
γ=0.1 α=0.05
γ=0.2
5.29 8.91 16.39 27.29
6.04 8.57 12.49 17.75
6.36 8.92 12.64 17.39
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 6.26 7.06 7.41 14.12 14.13 14.67 33.53 29.97 30.81 62.63 50.09 50.30
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
9.01 34.13 109.95 244.82
9.82 36.27 111.69 233.36
10.11 37.68 114.93 235.81
6.72 3.99 3.31 3.74
7.60 4.39 3.11 2.97
7.95 4.71 3.37 3.10
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 7.71 8.72 9.09 6.46 7.40 7.92 6.29 6.94 7.61 7.45 7.58 8.29
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(d) Season=10, SeasonCycle=14
300.0 250.0
InvR
200.0 150.0 100.0 50.0
Retailer Wholesaler Distributor Factory
γ=0.05
γ=0.1 α=0.05
γ=0.2
6.23 10.62 19.85 27.68
7.44 10.72 16.49 20.56
7.98 11.33 17.14 20.82
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 7.37 8.25 8.63 18.25 19.59 20.46 43.34 43.13 45.10 64.86 59.83 61.51
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
13.21 35.79 107.03 186.77
14.75 38.29 112.22 189.72
15.31 39.66 115.52 192.79
7.83 3.95 2.66 2.71
9.22 4.68 2.52 1.76
9.72 5.17 2.95 1.97
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 9.20 10.71 11.24 7.03 8.53 9.31 5.72 6.86 7.93 5.38 5.98 7.12
γ=0.05
γ=0.1 α=0.2
γ=0.2
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0.0
11.12 15.35 24.93 33.92
12.31 17.10 31.08 45.26
12.63 17.71 34.24 51.42
Figure 8. The main and interaction effects of the forecasting parameters and smoothing level on the inventory variance ratio
100.0 90.0 80.0
AFR%
70.0 60.0 50.0 40.0 30.0 20.0 10.0 γ=0.05
γ=0.1 α=0.05
γ=0.2
Retailer 100.00 Wholesaler 99.99 Distributor 99.91 Factory 99.60
100.00 99.99 99.95 99.77
100.00 99.99 99.94 99.76
90.0 80.0 60.0
20.0 10.0
γ=0.05
γ=0.1 α=0.05
γ=0.2
99.90 99.55 98.53 96.66
99.87 99.46 98.51 96.84
99.86 99.42 98.37 96.53
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0.0
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AFR%
70.0
30.0
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Retailer Wholesaler Distributor Factory
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γ=0.05
γ=0.1 α=0.2
γ=0.2
99.98 98.01 88.56 80.31
99.98 97.84 87.78 79.29
99.98 97.78 87.65 79.25
γ=0.05
γ=0.1 α=0.05
γ=0.2
100.00 100.00 100.00 100.00
100.00 100.00 100.00 100.00
100.00 100.00 100.00 100.00
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 99.99 99.99 99.99
γ=0.05
γ=0.1 α=0.2
γ=0.2
100.00 100.00 99.91 99.59
100.00 100.00 99.90 99.58
100.00 100.00 99.90 99.57
γ=0.05
γ=0.05
γ=0.1 α=0.2
γ=0.2
99.95 99.97 99.87 99.50
99.95 99.96 99.85 99.48
99.94 99.96 99.84 99.46
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100.0
40.0
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 100.00 100.00 100.00 99.89 99.89 99.88 98.88 98.84 98.80 95.84 95.63 95.45
(b) Season=10, SeasonCycle=7
110.0
50.0
γ=0.05
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0.0
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(a) Season=5, SeasonCycle=7
110.0
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 99.73 99.67 99.66 97.67 97.24 97.12 92.05 91.05 90.67 83.71 82.35 81.79
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
98.97 88.74 75.94 71.04
98.80 87.66 75.11 70.43
98.76 87.50 74.96 70.43
99.99 100.00 100.00 100.00
99.99 100.00 100.00 100.00
99.99 100.00 100.00 100.00
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 99.98 99.98 99.98 100.00 100.00 100.00 100.00 100.00 100.00 99.98 99.99 99.99
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(c) Season=5, SeasonCycle=14
110.0 100.0 90.0 80.0
AFR%
70.0 60.0 50.0 40.0 30.0 20.0 10.0 γ=0.05
γ=0.1 α=0.05
γ=0.2
Retailer 100.00 Wholesaler 99.88 Distributor 98.90 Factory 97.83
100.00 99.98 99.79 99.26
100.00 99.98 99.80 99.31
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 99.99 100.00 99.99 99.29 99.50 99.48 95.11 95.80 95.49 92.33 93.11 92.87
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
99.45 90.40 77.31 77.71
99.35 88.50 75.11 76.44
99.32 87.48 74.09 75.88
99.99 100.00 99.99 99.98
99.99 100.00 100.00 100.00
99.99 100.00 100.00 100.00
(d) Season=10, SeasonCycle=14
110.0 100.0 90.0 80.0 70.0
50.0 40.0 30.0 20.0 10.0 0.0
Retailer Wholesaler Distributor Factory
γ=0.05
γ=0.1 α=0.05
γ=0.2
99.47 96.35 90.66 90.84
99.38 97.24 92.58 92.27
99.24 96.85 91.94 91.86
γ=0.05
γ=0.1 γ=0.2 α=0.1 Classical OUT (Tn=1.0) 97.91 97.45 97.05 84.56 81.88 80.27 73.21 71.56 70.21 76.56 75.60 74.75
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 99.99 99.98 99.98 100.00 99.99 99.99 99.98 99.99 99.98 99.92 99.95 99.92
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AFR%
60.0
γ=0.05
γ=0.05
γ=0.1 α=0.2
γ=0.2
γ=0.05
γ=0.1 α=0.05
γ=0.2
86.36 70.34 60.51 66.76
83.26 66.98 57.60 64.39
81.87 65.70 56.56 63.67
99.10 99.93 99.82 99.71
98.57 99.91 99.99 100.00
98.33 99.87 99.99 100.00
γ=0.05
γ=0.1 α=0.2
γ=0.2
CR IP T
0.0
γ=0.05
γ=0.1 γ=0.2 α=0.1 Smoothing OUT (Tn=4) 98.47 97.69 97.35 99.25 98.73 98.42 99.27 99.18 98.88 99.22 99.27 98.97
99.97 99.63 97.88 96.08
99.96 99.48 96.99 94.61
99.95 99.37 96.44 93.78
γ=0.05
γ=0.1 α=0.2
γ=0.2
96.64 90.98 83.28 83.91
95.28 87.36 76.56 78.41
94.69 85.55 73.22 75.77
Figure 9. The main and interaction effects of the forecasting parameters and smoothing level on the
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average fill rate
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5. Discussion and Implications
Previous research has confirmed the effectiveness of the smoothing replenishment rules in supply
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chains under non-seasonal demand. They have shown that shifting from the traditional replenishment rules to the smoothing replenishment rules can mitigate and eliminate the bullwhip
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effect but it has been shown that dampening the bullwhip effect might affect the inventory stability. In particular, increasing the order smoothing level may increase the inventory instability causing a
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lower average fill rate. The present study has attempted to extend the previous researches by investigating the value of smoothing inventory decision rules in seasonal supply chains. The seasonality phenomenon of demand is a common occurrence in many supply chains where it may stem from factors such as weather, which affects many business and economic activities like clothing and food industries. The seasonality can potentially cause mismatch between supply and demand in supply chains.
This paper has attempted to evaluate the impact of smoothing replenishment rules in a seasonal Page 33 of 41
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supply chain in which the demand pattern has seasonal components modified by random variation. A simulation study has been conducted to evaluate the performance of a four-echelon supply chain facing a seasonal demand and employs a generalized order-up-to inventory policy (with smoothing capability) integrated with Holt-Winters forecasting method (Triple Exponential Smoothing). The supply chain performance has been evaluated under the different ordering policies in terms of
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bullwhip effect ratio, inventory variance ratio and average fill rate. The results have shown that shifting from the traditional OUT to the smoothing OUT improves the ordering and inventory stability in the seasonal supply chain. It has further been shown that increasing the smoothing level leads to lower bullwhip effect, lower inventory variance ratio, and higher average fill rate. This conclusion has been confirmed under the various combinations of the seasonal parameters.
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In this research, we have also quantified the contribution of the seasonal demand parameters to the bullwhip effect and inventory performance measures, under the traditional and smoothing replenishment rules. The results reveal that longer seasonal cycle increases the bullwhip effect while high seasonal level leads to a lower bullwhip effect. However, it has been found that the adoption of the smoothing OUT with selecting high smoothing level can mitigate the contribution
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of the seasonal cycle to the bullwhip effect and therefore high smoothing levels is recommended for seasonal supply chains with longer seasonal cycles to counteract the bullwhip effect. The results
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have also shown that the inventory variance ratio is less sensitive to the seasonal level while it is highly sensitive to the seasonal cycle regardless of the replenishment rule. However, this sensitivity decreases considerably as the smoothing level increases. In general, smoothing replenishment rules
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can improve the ordering and inventory stability in the seasonal supply chains.
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Demand forecast updating has been recognized as a major cause of the bullwhip effect and inventory instability in supply chains. Therefore, we have quantified the impact of the smoothing
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parameters of the HW method on the bullwhip effect and inventory performances under the different ordering policies. The results have shown that the smoothing parameter of the level component ( ) has the major contribution to the bullwhip effect and inventory performances. It has been found that the value of should always be set to low level since any increase in this parameter leads to higher bullwhip effect and inventory instability. The smoothing parameter of the seasonal component ( ) has been found to be of less contribution to the performance measures. The results have also shown that the sensitivity of all performance measures to the smoothing parameters of the forecasting method is reduced under the smoothing OUT compared to the Page 34 of 41
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traditional OUT. In other words, the contribution of the forecasting parameters to the bullwhip effect and inventory instability becomes lower under the smoothing OUT.
The strength of this research emerges from its uniqueness since the literature shows limited research that has attempted to evaluate the effectiveness of the smoothing replenishment rules in seasonal
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supply chains (see, Table 1). The results of this paper confirm that employing the smoothing replenishment rules (e.g., smoothing OUT) improves the ordering and inventory stability in seasonal supply chains. Another possible strength, concluded from the sensitivity analysis, is that employing the smoothing replenishment rules reduces the impact of the demand parameters and the poor selection of the forecasting parameters on the ordering and inventory stability. In this research, the smoothing OUT replenishment rule which is a modified version of the traditional OUT policy
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was considered to evaluate the impact of smoothing in seasonal supply chains. The traditional OUT, which is commonly used in practice, can simply be converted into smoothing OUT by adding two proportional controllers to the gaps of the net inventory and supply line (see, equation (11-12)). Therefore, the current seasonal supply chains that employ traditional OUT can largely benefit from the concepts and results presented in this study, to counteract the bullwhip effect. However, a
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possible weakness of the smoothing replenishment rules is that dampening the order variability has a negative impact on customer service due to an increased inventory variance. We have noticed that
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this trade-off between the bullwhip effect and inventory stability might happen at the most downstream echelons in seasonal supply chains when the seasonal cycle is long. This might limit the applications of smoothing replenishment rules especially when the inventory cost is an issue and
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that the supply chain consists of a few number of echelons and facing a seasonal demand with high seasonal cycle. However, this issue can be managed by enabling incentive schemes between
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upstream and downstream echelons to achieve coordination in seasonal supply chains.
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6. Conclusions
Smoothing inventory decision rules have been proposed as a mitigation/avoidance solution for the bullwhip effect. However, most of the previous studies have evaluated the impact of smoothing replenishment rules under non-seasonal and stationary demand processes. This paper has attempted to fill this research gap by evaluating the impact of smoothing replenishment rules in a multiechelon supply chain facing a seasonal demand modified by a random variation. A simulation study has been conducted to study the supply chain performances under the traditional and smoothing
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OUT replenishment rules, both integrated with the Holt-Winters forecasting method. The results have shown that shifting from the traditional replenishment rule to the smoothing one leads to a higher ordering and inventory stability across the supply chain. It has further been found that increasing the smoothing level leads to lower bullwhip effect, lower inventory variance ratio and higher average fill rate across the supply chain. The impact of the forecasting parameters has also
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been investigated showing that smaller value of the smoothing parameter of the level component are best suited to improve the ordering and inventory stability in the seasonal supply chain, especially under the traditional OUT policy. Most importantly, it has been found that employing the smoothing replenishment rules limiting the impact of the demand parameters and the improper selection of the forecasting parameters on the ordering and inventory stability. Therefore, it can be
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concluded that the smoothing replenishment rules have a great value in seasonal supply chains.
This research contributes towards advancing the knowledge in the areas of forecasting and inventory control in seasonal supply chains as it provides useful insights to improve the ordering and inventory stability in such supply chains. This research has extended the previous contribution of Costantino et al. (2015a) in ESWA in which they provided an evidence of the value of order
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smoothing in seasonal supply chains. Costantino et al. (2015a) have proposed a real-time SPC inventory replenishment system that relies on control chart system to forecast demand and adjust
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inventory position whilst providing smoothing capability to counteract the bullwhip effect. In this research, alternatively, we have proposed the application of the smoothing OUT replenishment rule in seasonal supply chains, and compared to traditional OUT. The results have shown the
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effectiveness of applying smoothing replenishment rules (e.g., smoothing OUT) in seasonal supply chain, confirming the preliminary results of Costantino et al. (2015a). The results have further
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confirmed that the proper selection of the forecasting parameters is essential to improve the ordering and inventory stability in seasonal supply chains. The research relied on the smoothing
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OUT which is a modified version of the traditional OUT (commonly used in practice) and relied on the HW forecasting method which is commonly used to forecast seasonal demand, to be consistent with real applications. The results thus provide useful managerial insights that can be utilized by supply chain managers of seasonal supply chains to re-engineer their decision support systems, and they can further utilize these insights to develop expert systems.
The previous research on the bullwhip effect can be classified into two broad categories, i.e. theoretical and empirical research (Costantino et al., 2015b), where both categories have been Page 36 of 41
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utilized to prove the bullwhip existence, to understand and identify its causes, and to evaluate proposed mitigation/avoidance approaches. The above conclusions and implications have been obtained based on a simulation study which follows the first category of the bullwhip effect research. This modeling approach has already been shared by many other researchers to investigate the bullwhip effect under various settings (Chatfield, 2013; Costantino et al., 2015a, b). However, in
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order to further validate the effectiveness of smoothing replenishment rules in seasonal supply chains, the study should be extended to real applications or the same study can be repeated with real data from industry but this is not always convenient. Nevertheless, the simulation model used for the analysis that resulted in the above promising conclusions has been validated with previous leading research in the literature and thus the obtained conclusions are valid and can be useful for both academics and practitioners. Another limitation is that the current simulation study has
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neglected the impact of the lead-time and its interaction with seasonal cycle where some earlier researches have highlighted the significance of this relationship through analytical modeling studies (Cho and Lee, 2012, 2013).
The present study can be extended further to investigate the impact of both information sharing and
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smoothing replenishment rules on the performances of seasonal supply chains. The future work can also consider the main and interaction effects of the important operational parameters such as lead-
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time, forecasting parameters, smoothing level, and information sharing. This goal can be achieved through a similar simulation study supported by experimental design approach. The future research should also study the value of smoothing replenishment rules under a wider range of the seasonal
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