Dynamic supplier selection model under two-echelon supply network

Accepted Manuscript

Dynamic supplier selection model under two-echelon supply network Md Tanweer Ahmad , Sandeep Mondal PII: DOI: Reference:

S0957-4174(16)30443-2 10.1016/j.eswa.2016.08.043 ESWA 10836

To appear in:

Expert Systems With Applications

Received date: Revised date:

15 February 2016 10 August 2016

Please cite this article as: Md Tanweer Ahmad , Sandeep Mondal , Dynamic supplier selection model under two-echelon supply network, Expert Systems With Applications (2016), doi: 10.1016/j.eswa.2016.08.043

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Highlights  Dynamic supplier selection problem (DSSP) has been adopted. Two-echelon supply network (TESN) with assembly of the part-product is considered.

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A mathematical model based on mixed-integer non-linear programming (MINLP) is proposed.

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Sensitivity analysis has been conducted by Taguchi method to find out the optimum level of parameters.

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Dynamic supplier selection model under two-echelon supply network Md Tanweer Ahmada and Sandeep Mondalb a

Indian School of Mines, Dhanbad, Jharkhand, India Email - [email protected] Indian School of Mines, Dhanbad, Jharkhand, India Email - [email protected]

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Abstract With the rise in competition levels and rapid changes in customer preferences, companies feel the pressure to create an efficient and effective base of suppliers in order to achieve the competitive advantage for them. The selection parameters of suppliers do not remain constant with respect to time and moreover; with highly fluctuating market demand, the suppliers are also expected to respond to it dynamically. This paper addresses a specific dynamic supplier selection problem (DSSP) under a two-echelon supply network (TESN) for the decision maker to allocate optimum order quantities to different levels of suppliers. The problem here considers a TESN with an integrated approach where the original equipment manufacturer (OEM) selects the firsttier suppliers and in turn with their opinion decides for the second-tier suppliers. Second-tier suppliers supply raw materials/parts/components to the first-tier suppliers, and then the first-tier suppliers supply the fabricated semi-finished product to OEM. In order to solve such a kind of problem, a mixed-integer non-linear programming (MINLP) is proposed to minimize the Total Cost (TC) of procurement for satisfying the OEM‘s demand. The problem incorporates parameters relevant to supplier‘s capacity, lead time, quality level of products, and transportation costs as a function of lead time. The model is validated through two cases with randomly generated data, and sensitivity analysis is conducted through Taguchi method using LINGO 15. This method not only helps to check the robustness of the parameters involved but also to set their optimum level. The analysis shows a significant reduction in the TC of procurement and the effect of each parameter on the TC are finally identified. The methodology adopted here can be extended to other organizations.

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Keywords: Dynamic supplier selection; two-echelon supply network; assembly of multiproduct; mixed integer non-linear program; Taguchi method.

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1. Introduction

Suppliers are considered to be the important part of any supply-chain network as they play a significant role in achieving OEM‘s profitability, market competitiveness, and customer satisfaction. Thus, evaluation and selection of potential suppliers become a key decision-making area. In supplier relationship management, OEM plays a vital role in the selection of potential suppliers and in building a long-term relationship (Wang and Yang 2009). Supplier Selection (SS) problems are mostly found to be multi-objective and highly situation specific based on industry type, size, and complexities of the supply-chain network (De Boer et at. 2001). SS problems are generally classified in terms of multi-echelon, multi-product, multi-source, and

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nature of the timeframe. Multi-echelon represents a supply network where more than one-tier or levels of suppliers are involved in supplying materials/parts (Lin and Lei 2009). A multi-product problem involves suppliers who supply two or more different types of materials/parts (Benton, 1991; Kilic, 2013), in some cases; it is also termed as a single-product problem (Ghodsypour and O‘Brien, 1998; Razmi and Rafiei, 2010). A single supplier may not be able to fulfill OEM‘s demand in every situation due to limitation in supplier‘s capacity, lead time, and quality of the materials. In such cases, OEM requires multiple suppliers which are treated a case of a multisource supplier‘s problem (Ghodsypour and O‘Brien, 1998; Xia and Wu, 2007). Moreover, the timeframe of supply of materials is classified based on the length of the partnership between suppliers and manufacturers into short-term, long-term, and long-term with no ends (Lambert et al. 1996). The SS‘s parameters and OEM‘s demand fluctuate with respect to timeframe, whether it is short-term or long-term. This change to the parameter or demand values with respect to time is referred to as dynamic behavior in SS problems. So, the dynamicity in the parameters is defined with respect to time and not with short-term or long-term agreements. TESN is the special case of multi-echelon supply network, which is considered throughout this paper. Such kind of supply networks exists in many practical cases. For example, a construction company receives iron rods from a steel manufacturer, which in turn receive raw iron from iron-ore mining companies. Another example is an automotive company which has a supplier of ball bearings, which in turn has another tier of suppliers of inner races, outer races, balls, etc. Ware et al. (2014) described in his paper the difference between Traditional Supplier Selection Problem (TSSP) and DSSP, where they stated that DSSP is a more realistic approach than TSSP in the sense of dynamicity of the parameters with respect to periodic timeframe, and set of suppliers replacing the single-best supplier for order fulfillment. The implementation of DSSP for the case of a multi-period for the same traditional set of suppliers on which numerous works have been contributed might not be sufficient to deal with the problem practically. In practical situations, it is difficult for any OEM to sustain the market competition because of restrictions in capacity, raw-material availability, required machinery, capital shortage, longer distances, and their availability of skilled Manpower. The industry thus requires partners at an upstream or downstream level to overcome these difficulties. In this research, we extend the work of Ware et al. (2014) in the context of TESN that includes two-tier of suppliers with respect to OEM for order fulfillment over a periodic timeframe. To find out the optimum order quantities allocated to the first-tier suppliers from the set of suppliers of OEM, a mathematical model based on MINLP is proposed to solve the DSSP under TESN. The parameters of SS problem change over timeframe due to changes in business operations or market conditions. In order to address this, Taguchi method (Taguchi, 1990) is adopted to check the robustness of the parameters as well as the most influenced parameters involved during a particular timeframe. Two cases are discussed based on the proposed model at distinct parameter settings for consecutive timeframes. To summarize the research paper, we attempt to develop a methodology to address the following research question, (i) which suppliers to be given order at each echelon for which type of product, (ii) how much quantities to be ordered, and (iii) to check the criticality and robustness of the parameters. The paper is organized as follows: In section 2, summarization of previous work related to SS is done. In section 3, problem identification is discussed. Section 4 presents the model development and its mathematical formulation. In Section 5, two cases are discussed to demonstrate the proposed methodology. Section 6 presents the sensitivity analysis of proposed example. Section

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7 presents the result and discussion. Finally, summary work and future research direction are presented in section 8. 2. Literature Review

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A number of researchers have proposed numerous mathematical models and solutions related to SS problem, but research papers related to DSSP under multi-echelon, multi-product, and multisource were not adequately covered over the past. The extensive review on the SS problem was done by many authors; some of them are Weber et al. (1991), De Boer et al. (2001), Ho et al. (2010), and Chai et al. (2013). The existing literature shows that majority of the studies on SS problem aim to find the best supplier, and they generally described the differences in selection criteria, employed methodology, solution approach, decision environment, and sensitivity analysis. Numerous approaches on SS methodology have been discussed in the literature, are broadly they may be classified into two approaches viz. (1) Individual approach and (2) integrated approach. The adopted individual approaches for SS are MCDM, mathematical programming (MP), and artificial intelligence (AI). Whereas integrated approach comprises the analytic hierarchy process (AHP), analytic network process (ANP), data envelopment analysis (DEA), among others. In order to classify this, Table 1 is constructed for showing the background of the study based on the employed methodology related to SS problem. [Insert: Table 1 Classification of the studies related to the SS problem]

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Masella and Rangone (2000) highlighted the four different vendor selection systems in the timeframe (short-term versus long-term) for different types of supplier/customer relationships based on the logistic integration versus strategic integration. Ustun and Demirtas (2008) proposed the multi-objective decision making for SS in multi-period lot sizing by consideration of tangible and intangible factors. In the consideration of non-linear programming (NLP) in the SS problem, Ghodsypour and O'Brien (2001) proposed the MINLP for solving the SS problem for multisource and multiple criteria under limited supplier‘s capacity. Zhang and Ma (2009) presented an MINLP formulation for supply network from one manufacturer to multiple suppliers for multiproduct and price-discount. Razmi and Rafiei (2010) addressed the SS with the order allocation problems in two steps, firstly, apply the ANP for filtered the suppliers among available one regarding their qualitative attributes, and secondly; MINLP was applied to allocate the order quantities for the planning period. Similar proposal in the past was proposed with AHP by Mendoza and Ventura (2008). Rezaeia and Davoodi (2012) integrated the problem as a multiobjective nonlinear programming (MONLP) model and genetic algorithm (GA) for three strategies such as pricing, lot-sizing and SS with a number of Pareto-optimal solutions. Ware et al. (2014a) considered the flexibility as most influenced factors for SS problem under the case of multi-product, multi-source, and multi-period for which MINLP and AHP was proposed. Ware et al. (2014) evaluated the SS problem as DSSP in which parameter's values to the problem changes from period to period and finding the optimum order quantities for selected suppliers for which MINLP was proposed. Most of the proposed models discussed above have been designed for single-echelon systems. Guo and Li (2014) applied the MINLP for the SS under multiechelon inventory problem. Pazhani et al. (2016) proposed the MINLP model to determine the trade-off between sequential versus an integrated approach through optimal allocation of orders among the suppliers for the stages in the supply chain.

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The related studies of Taguchi Method The Taguchi method founded by Genechi Taguchi is capable of developing optimal parameter settings even when interactions exist among the control variables, (Taguchi, 1990, Bendell et al. 1989). Taguchi parameter design reduces the sensitivity to the system performance to sources of variation and can increase the robustness of systems through the settings of design parameters (Bendell et al. 1989; Hong, 2012). His approach implements whether the objective is minimization, maximization or approaching to certain target (Tansel et al. 2011). Numerous applications using Taguchi method have been used in different area by many authors, to name a few of them is Refaie and Tahat (2011), Chen et al. (2010), Hou et al. (2007), and Chien and Tsai (2003). However, while considering SS problems, authors have not yet used this approach of implementing MINLP in the context of TESN for the sensitivity analysis. In order to highlight the contribution, and indicate its novelty and significance to our study within the literature, Table 2 is constructed. It summarizes the literature on the SS problem in the methodology of MINLP with regards to suppliers (single source/multiple sources), number of items (single/multi), nature of parameters (static/dynamic), and their adopted methodology for the sensitivity analysis. [Insert: Table.2 Contribution of the proposed study based on different approaches]

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From Table 2, we may infer that the existing papers adopted the MINLP for SS problem in distinct conditions/situations, and by a different way of sensitivity analysis conducted such as comparative analysis (Ustun and Demirtas, 2008), pareto-optimal evaluation (Rezaeia and Davoodi, 2012), and deviational matrix (Ware et al., 2014a). In comparative analysis, an additive utility function with varied weights was used to compare the quality of final solution obtained by distinct methods. In pareto-optimal evaluation, a trade-off between different conflicting objectives has been evaluated. In the deviational matrix, the flexibility was varied by decision maker from lowest to the highest deviation for knowing the fluctuation in the objective value. Often it is also desirable to know the optimum value of the parameters level through sensitivity analysis. Taguchi method can thus be useful in improvement of the objective function value (output) through optimum parameter settings (input). Moreover, this method is widely used in manufacturing for minimization of experimental cost and suggesting the optimal solution for the process (Tansel et al. 2011). It also reduces the sensitivity of the process to various sources of variation. As per methodology, if this variation could be well controlled or eliminated, then process variation would be reduced, and therefore, cost or quality could be improved. So, in the similar problem, this method of sensitivity analysis is valuable so that suppliers could improve the process to reach near the optimal parameter‘s level in order to gain the competitive advantage and simultaneously, OEM finds the improvement in the TC. This study also differs from the existing studies; mainly by the situations considered, and way of sensitivity analysis conducted. We finally adopt the MINLP for SS, but with a different approach of sensitivity analysis such as Taguchi method. The literature shows that there is not an integrated approach, including MINLP and Taguchi method for solving SS problem dealing with dynamic parameters under multiple-suppliers in the context of TESN. 3. Problem Identification

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The current research problem relates a TESN with a set of suppliers supplying rawmaterials/parts/components to the next level of suppliers who in turn supplies the assembled product to OEM. Hence, we consider a single product to be ordered by the OEM. The order is placed to the first-tier of suppliers, who in turns, requires raw-material/components for manufacturing the product. They, thus, place an order to the second-tier of suppliers for obtaining raw-material/component/parts. Here, it is to be noted that the second-tier of suppliers are capable of supplying all the components/parts/raw-materials required for manufacturing the product. The first-tier of the suppliers basically engaged in the assembly as well as machining operations. Under the above circumstances, the OEM simultaneously selects the best strategy for each-echelon through a set of suppliers (first-tier) who can satisfy the demand. The selection is based on multi-criteria like unit cost, quality level, variable transportation cost, lead time, and the capacity of the suppliers in order to optimize the TC of procurement for the consideration of parts-product from multiple suppliers. It is obvious that each supplier claims the validity of data supplied to the next level of suppliers from the experience, and it is levied the penalty by the OEM if the suppliers fail to provide expected lead time and quality level of the product in terms of the cost irrespective of the supplier‘s internal issues. It is assumed that a number of rawmaterial/component required to assemble the product depends upon the product type needed to OEM. The fluctuation in the parameters of the suppliers is inherent properties of any business organization with respect to the timeframe so that we could tackle the different demand in the distinct timeframe. In this integrated approach of SS problem, the single centralized decision maker considered is the OEM (Guo and Li, 2014; Pazhani et al. 2016). The OEM controls the chain as per its requirement and further to overcome issues such as price negotiation, quality control of rawmaterial, supply risk, lack of coordination, and variability in product demand. Such kind of integrated approach can be commonly used in firms engaged in manufacturing high-value product in terms of accuracy, durability, and quality such as automotive companies, gear motor companies, pump manufacturers, and conveyor manufacturers, etc. 4. Proposed Methodology

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In this paper, a mathematical model based on MINLP is proposed to solve the multi-objective DSSP which includes minimization of unit cost, transportation cost, penalty cost for late delivery, and penalty cost for quality rejection. The decision of the proposed model is to find; how much to order and whom to order at each echelon so that the TC of the procurement for the entire timeframe must be minimized. The methodology includes the following steps: STEP- I Pre-study of the supplier list:A set of suppliers at each-echelons of the system are included in the proposed model based on the past performance in terms of the intangible factors (reciprocal trust, history, brand value, etc.), and OEM‘s qualitative criteria (technical features, economical aspect, social aspect, etc., as defined by Yousefi et al. 2010). It is also assumed that these factors influence the relationship between supplier and OEM having an equal weight. STEP-II Computing an amount of material required through Bill of Material (BOM): Evaluate the parts/components required to assemble a semi-finished or finished product at the first-tier suppliers by using the concept of the BOM. The number of components needed to assemble one unit of the final product is also estimated.

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STEP- III Deciding the criteria for SS:Ware et al. (2014) have discussed in his paper that unit cost, the quality level of the product; average transportation cost; and delay cost are the major criteria to the problem. We also consider these criteria in our discussed problem on the assumption that average transportation cost is replaced by transportation cost as a function of lead time to make the situation more realistic. In order to clarify this, we only consider the case of the full load truck (TL) in which the shipment cost is independent from the size (quantity) of the shipment for a given truck (Pazhani et al. 2016). In the TL case, transportation cost depends on the many factors but the foremost factor is the distance between loading and unloading point. So, we can say that the time elapsed for the same distance travel may be varied due to many reasons in which some of the main reasons are unavailability of the vehicle at loading point, material unavailability, a bottleneck at loading points, process delay, and a sudden breakdown in the vehicle during transport. In order to overcome these difficulties, the transportation cost may be considered as a function of time elapsed or lead time instead of the distance. So, higher lead time leads to the higher transportation cost. Furthermore, as per the assumptions; the transportation cost depends upon the lead time, but lead time remains independent of the transportation cost. This assumption motivates the suppliers to place the delivery in as minimum lead time as possible, failing which they are incurred with higher transportation cost. STEP-IV Mathematical formulation to the problem:The basic structure of the model is depicted in Fig.1 in which set of suppliers at second-tier (Ti) can supply required type of raw-material to the set of suppliers at first-tier (Si) which is engaged in machining as well as the assembly of the product.

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[Insert: Fig.1 Basic structure of the model for the periodic timeframe (k)]

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The notations, parameters and decision variables used for the mathematical formulation are defined as below:k: periodic timeframe; 1, 2, 3......., t. supplier at second-tier of echelon supplier at first-tier of echelon set of suppliers at second-tier of echelon, where i = 1,2,3...,m set of suppliers at first-tier of echelon, where r = 1,2,3...,n type of raw-material/component/parts ‗j‘ needed to supply to first tier supplier ‗r‘ by secondtier supplier ‗i‘, where j = 1, 2, 3, .......,q product finished by first-tier supplier and directly supplied to OEM Parameters:unit cost of raw-material/components 'j' of second-tier supplier ‗i‘ for timeframe ‗k‘ unit manufacturing cost of semi-finished product 'p' of first-tier supplier ‗r‘ for time frame ‗k‘ transportation cost of raw-material/components 'j' per unit lead time of second-tier supplier ‗i‘ for timeframe ‗k‘ transportation cost of semi-finished product 'p' per unit lead time of first-tier supplier ‗r‘ for timeframe ‗k‘ lead time of raw-material/components 'j' shipped from second-tier supplier ‗i‘ to firsttier supplier for timeframe ‗k‘

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lead time of semi-finished product 'p' supplied by first-tier supplier ‗r‘ to OEM for timeframe ‗k‘ unit capacity of second-tier supplier ‗i‘ of raw-material 'j' for timeframe ‗k‘ unit penalty cost for defectiveness on raw-material ‗j‘ of supplier 'i' for timeframe ‗k‘ unit penalty cost for defectiveness on semi- finished product 'p' of supplier ‗r‘ for for timeframe ‗k‘ unit delay cost for delivery lateness on raw-material ‗j‘ of supplier 'i' for timeframe ‗k‘ unit delay cost for delivery lateness on semi-finished product ‗p‘ of supplier ‗r‘ for timeframe ‗k‘ delay lead time of supplier 'i' for raw-material 'j' for timeframe ‗k‘ delay lead time of supplier 'r' for product 'p' for timeframe ‗k‘ quality level (percentage acceptance) of supplier 'i' of raw-material 'j' for timeframe ‗k‘ quality level (percentage acceptance) of supplier 'r' of assembled semi-finished product 'p' for timeframe ‗k‘ quality level(percentage acceptance) fixed by OEM for timeframe ‗k‘ demand supplied by first-tier supplier ‗r‘ to OEM for timeframe ‗k‘ total demand of the OEM for timeframe ‗k‘ : percentage wastage during manufacturing at first-tier for timeframe ‗k‘, Let = 10%. total number of parts/components needed to produce one unit of semi-finished product for timeframe ‗k‘

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Decision variables:number of unit of raw-material/components 'j' supplied by second-tier supplier 'i' to first-tier supplier ‗r‘ for time frame ‗k‘ number of unit of semi-finished product 'p' supplied by first-tier supplier ‗r‘ to OEM for time frame ‗k‘ assignment between second-tier supplier 'i' and first-tier-supplier 'r' for time frame ‗k‘ assignment between first-tier supplier 'r' and OEM for time frame ‗k‘

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Objective functions of the model: - The four objectives defined in this paper are represented by the nomenclature of O1, O2, O3, and O4. All the objective functions are of minimization type and equal in weight, so for the sake of simplicity, it is converted into single objective function by simply addition and it is represented by eq. (1).

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Basic cost of product (O1) =Min ∑ [∑ [∑

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Penalty Cost for defectiveness (O2) = Min

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Penalty cost for lateness (O4) = Min

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Total transportation cost (O3) = Min

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TC of procurement for timeframe k = Min (O1 + O2 + O3 + O4)

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Constraints of the model, Assembly Constraint: number of raw-material needed to make single semi-finished product with the assumption of wastages.

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Capacity Constraint:-capacity of each supplier at second-tier supplier

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Quality Level Constraint:- quality level of assembled product at first-tier suppliers ∑

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Demand Constraints:- demand of OEM for timeframe ‗k‘ ∑

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Assignment Constraint: - interaction between suppliers and OEM {

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Assumptions:-

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Each supplier has limited number of capacity level as represented by eq. (3). The eq. (4) represents the quality level of assembled product at first-tier supplier and is computed from the product of the probability of acceptance quality level of individual parts/components make to the assembly. For example, if Q1 and Q2 represent the percentage acceptance for component-1 and component-2 respectively, then the final quality level (percentage acceptance) will be Q 1×Q2. Binary variables are defined for the supplier‘s interaction as represented by (7) and (8). The assumption has been made that one unit of semi-finished product is assembled at first-tier from one unit of each raw-materials needed, and it must be equal in between as it is represented by eq. (9) and eq. (10) respectively. The parameters, demand, parts/component needed, and quality level (fixed by OEM) of the model changes over the periodic timeframe. It is assumed that the timeframe start with k=1, thereafter k=2, k=3 and so on. It is assumed that equal number of the parts needed for assembly of the product as described in eq. (10), but in many cases, parts quantity(needed) are not equal in between. Furthermore, only TESN is considered that limit the usage of the model. The complete formulation to the problem is modeled as mentioned above from eq. (1) to eq. (10). Multiple suppliers in the model are considered at each-echelon. Sometimes, an OEM may only select single supplier for supplying the raw materials/parts simultaneously at each-echelon. If so, two new constraints may be introduced for single sourcing model as:For a single supplier at second-tier,

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∑ For single supplier at first-tier, ∑

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STEP V Sensitivity analysis through Taguchi method:-

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In SS problems, OEM may be interested in knowing the influence on the parameters in the particular timeframe for decision-making regard to (1) which parameters are most important or significant, (2) what is the percentage contribution of each parameter, (3) what are the best set within the parameters, and (4) how much improvement in the TC can be done through the optimum set within the parameters. Furthermore, optimum parameter's level suggests the secondtier suppliers for the forthcoming improvement in their performances so as to win orders in the prospective assignment (timeframe). In this context, we adopt the Taguchi method for the area of SS. To obtain the best set of parameter setting to the problem, a systematic approach based on Taguchi method is used. Taguchi‘s views on engineering optimization of the process or product in three-manifolds that are parameter design, system design, and tolerance design. In this study, the concept of parameter design is implemented. In general, the parameter design is the main thrust of the Taguchi method which is used to optimize the quality level of the product or process without taking the causes of variation. According to Taguchi, the parameter is separated into two groups such as control parameter and noise parameter. Basically, the methodology is a procedural tool for the optimal design of the parameters on the performance, quality, and cost. A control parameter referred to a parameter which is controlled by the experimenter, and the noise parameter is the one has no direct control of the experimenter but changes in the environment of the problem such as decision variables. The basic approach for implementing the Taguchi method for proposed model is shown in Fig.4. [Insert: Fig.2 the basic process for Taguchi method in the proposed model]

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Another advantage of using Taguchi‘s experimental design by Orthogonal Arrays (OA); is that the experimenter may not have to conduct a large number of trials or experiments when handling with a large number of parameters at different levels. In a full-factorial experiment, there is, at least, 3n possible experiment, if each factor has three levels. To overcome this, Taguchi used the concept of OA. It provides well-balanced and optimum settings of the control parameters. The number of experiment is conducted as per the OA. The selection of the OA depends upon the degree of freedom (DOF) involved in the study. The DOF of any parameter can be defined as the number of levels involved minus one (Ross, 1988). An OA is selected based on that DOF of the OA which must be greater than or at least equal to the DOF of the parameters involved. The analysis of an experimental results are then transformed into the signal-to-noise (S/N) ratio. The S/N ratio is classified as per objective of the problem into three categories such as lower-thebetter, nominal-the-better, and higher-the-better. In this paper, we consider the lower-the-better due to minimization type of the objective value. The characteristics' equation for lower-the-better is shown in eq. (13).

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Where ‗g‘ is the number of replication and ‗Ye‘ is the TC of eth trial. However, the S/N ratios at each level of parameters are calculated in order to obtain their optimum level. The higher value of S/N ratio is preferred regardless of the objective of the experiment (maximum or minimum).The variability involved is inversely proportional to the S/N ratio; it means that a larger S/N ratio corresponds to a more robust system. Finally, the relative impact of the parameters on the objective value of the problem needs to know that, which parameter is significant and what the degree of their contribution is. For this purpose, analysis of variance (ANOVA) is used. It was first introduced by Fisher (1930) in his agricultural experiment. ANOVA is based on statistics which follows the procedure such as:- (i) the correction factor (CF) is calculated by using eq. (14), (ii) to calculate the total sum of square by using eq.(15), and it is the summation of the sum of square of the parameter ( ) and the sum of the square of error , (iii) to calculate the ( )by using eq. (16), (iv) to find the DOF of the parameters which is the difference between number of levels of the parameters minus one, (v) the ‗F‘ value of each parameter is found out by dividing the ( ) to DOF, and (vi) The percentage contribution (C) for each parameter is calculated by dividing the ( )to . In eq. (16), the R1, R2 and R3 are the sums of S/N response for level-1, level-2, and level-3 respectively, while nL1; nL2; and nL3 are the number of trials for level-1, level-2, and level-3 respectively.

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F-test is performed on the basis of the ANOVA table. Statistically, Fisher (1925) used the tool known as the F-test for evaluating the parameter‘s effect on the objective value of the problem. To perform the F-test, usually limiting value ‗F0‘ is found from the F-table (standard) based on the assumption of the significance level. In this study, we assume to 5% significance level, based on that if F > F0 then the parameter is said to be significant. To summarize, the parameter design of the Taguchi method for the SS problem includes the following steps:(1) identification of the control factors, noise factors, and their responses; (2) selection of the appropriate OA and assignment of parameters values to that OA; (3) to evaluate the number of levels of the parameter as per OA; (4) to run the experiments for each trial based on the OA‘s settings; (5) plot the S/N response graph, and to prepare the ANOVA table; (6) selection of the optimal levels of parameters for each second-tier suppliers;

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(7) obtaining the effect and their percentage contribution of each parameter from ANOVA table; (8) to get the improved allocated unit quantities at each echelon (or decision variables) as well as TC of the procurement. The validity of the model is tested by using some real-world cases in the following sections. 5. Application of the model

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In order to support in the real-world applications of the proposed model and algorithm, a hypothetical case study of TESN connecting suppliers, manufacturers, and OEM as shown in Fig. 1 is considered. It is practically a representation of a manufacturing company (representing the OEM) needs for requisite product. The OEM has options for the requisite product, either make or outsource. In order to make, the industry needs to invest high set up cost, high-skilled manpower, raw-materials, and costly engineering design. For this, high-skilled manpower, engineering design or most frequently raw-material are very hard to achieve. Besides, it is very difficult to win the manufacturer who has been the expertise or reputation on the market for a decade. To tackle these situations, a proposed model can be implemented. The OEM has already collaborated with manufacturers who are in the business since a decade to develop an efficient and responsive supply chain and moreover, it would be beneficial for all the stakeholders with respect to (i) suppliers or manufacturers find the permanent customer, (ii) OEM finds the product from the reputed or branded sources, and (iii) it provides an integrated decision-making process for OEM.

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Case:-1

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This case is practically a representation of an automotive company (the OEM) requires gearboxes. The gear-box manufacturers represent the first-tier of suppliers (the manufacturer).The gear box manufacturers require bearings, splined shafts, and gears as its raw-material. The suppliers at second-tier are capable of supplying all the required parts to gear-box manufacturers. When gear-boxes are ordered by the OEM, it is placed to the first-tier manufacturers, who in turns, requires bearing (q1), splined shaft (q2), and gear (q3) for manufacturing the gear box. Thus, they place the order to the second-tier suppliers for obtaining rawmaterial/components/parts. Here, it is to be noted that the second-tier suppliers are capable of supplying all the components such as bearing, splined shaft, and gear required for manufacturing the gear box for three timeframes (k=1; k=2; k=3). The manufacturers are basically engaged in the assembly as well as machining operations for the required product. Under the above circumstances, OEM has to select a set of gear-boxes and components from first-tier and secondtier suppliers respectively. The selection is based upon different criteria like unit cost, quality level, transportation cost, lead time, and capacity of the supplier in order to satisfy the demand of OEM. In this case, four distinct component/parts suppliers (T1, T2, T3, T4) are considered at second-tier, and three gear box manufacturers (S1, S2, S3) at first-tier. The OEM decides the gear-box ‗p‘ for which first-tier suppliers require three distinct types of parts (q1, q2, q3), which is to be supplied by second-tier suppliers. To test the behavior to the model with data sets, the parameter values from the model are randomly generated based on some previous knowledge of the supply chain at both the levels of

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echelon. The demand of OEM also changes with respect to the timeframe due to variations of the market (situations). The input data of suppliers at second-tier for three consecutive timeframes such as capacity ( ), unit cost ( ), quality level ( ), unit penalty cost due to poor quality of the supplying material ( ), unit delay cost due to lateness in delivery ( ), transportation cost ( ), and lead time ( ), and it is shown in Table 3. The gear-box (p) is manufactured by first-tier suppliers to supply the OEM with unit manufacturing cost ( ), unit penalty cost on defectiveness ( ), unit delay cost due to lateness ( ), transportation cost per unit lead time incurred ( ). The demand of OEM for timeframe ―k‖ is represented by ‗ ‘. The proposed model is solved by LINGO 15.0 in such a way that the demand of the OEM must be fulfilled in each timeframe in order to minimize the TC of procurement. [Insert: Table.3 Input data of case-1 for timeframe k=1, k=2, and k=3]

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After solving the problem, the order allocation for each supplier at each-echelon is depicted by Fig.2 for k=1, k=2, and k=3. From Fig.2, the second-tier suppliers T1, T2, T3, T4 supplying the units of q1, q2, q3 to first-tier suppliers S1, S2, S3 as per demand. The first-tier suppliers S1, S2, S3 produces 107 units of ‗p‘, 1530 units of ‗p‘, 1863 units of ‗p‘ in k=1, 3087 units of ‗p‘, 108 units of ‗p‘, 2005 units of ‗p‘ in k=2, and 1944 units of ‗p‘, 736 units of ‗p‘, 1620 units of ‗p‘ in k=3 respectively. It is supplied the same unit of produced product to OEM to fulfill the demand of 3500 units in k=1, 5200 units in k=2, and 4300 units in k=3.

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[Insert: Fig.3 Allocated parts at each-echelon of case-1 for timeframe k=1, k=2 and k=3]

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Case – 2

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An HVAC company (the OEM) purchases industrial pumps for a set of suppliers. Industrial pump manufacturers represent the first-tier of suppliers (the manufacturer). The pump manufacturers require valve components (q1), impellers (q2), ball bearings (q3), and rotating shaft (q4) as its raw-material. The suppliers at second-tier are capable of supplying all the required parts to pump manufacturers. When pump manufacturer is ordered by the OEM, it is placed to the first-tier, who in turns requires the parts q1, q2, q3, q4 for manufacturing the pump. Thus, they place an order to the second-tier suppliers for obtaining raw-material/component/parts. Here, it is to be noted that the second-tier suppliers are capable of supplying all the components required for manufacturing the pump. The manufacturers are basically engaged in the assembly as well as machining operations for the required product. Under the above circumstances, OEM has to select a set of pumps and components from first-tier and second-tier suppliers respectively. The selection is based upon different criteria like unit cost, quality level, transportation cost, lead time, the capacity of the supplier in order to satisfy the demand of OEM. In this case, six different components suppliers (T1, T2, T3, T4, T5, T6) are considered at secondtier and six pump manufacturers (S1, S2, S3, S4, S5, S6) at first-tier for two timeframes (k=1 and k=2) involved with OEM. In this case, OEM needs the pumps ‗p‘ for industrial application. The input data of each supplier for raw-materials at second-tier as well as first-tier is generated randomly. The input data for both levels of the supplier are tabulated, and it is shown in Table 4. The problem is tested by Lingo 15.0, and the solution is depicted in Fig.3.

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[Insert: Table.4 Input data of case-2 for timeframe k=1 and k=2] [Insert: Fig.4 Allocated parts at each echelon of case-2 for timeframe k=1 and k=2]

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From the Fig.3, the first-tier suppliers S1, S2, S3, S4, S5, S6 produces 729 units of ‗p‘, 634 units of ‗p‘, 730 units of ‗p‘, 851 units of ‗p‘, 576 units of ‗p‘ and 980 units of ‗p‘ for k=1 respectively, and produces 729 units of ‗p‘ , 634 units of ‗p‘, 730 units of ‗p‘, 851 units of ‗p‘, 576 units of ‗p‘ and 980 units of ‗p‘ for k=2 respectively. It is supplied the same unit of produced product to OEM to fulfill the demand of 4500 units for k=1 and 5400 units for k=2. 6. Sensitivity Analysis

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In this section, the numerical experiment on case-1 is carried out on the proposed mathematical model by the variation in parameter settings for the timeframe (k=1). The main purpose of conducting this experiment is to show the improvement in the objective value or TC of the procurement through knowing the optimum parameter settings of second-tier suppliers and to find the criticality of the parameter. The considered parameters are capacity( ), unit cost( ), quality level( ), unit penalty cost( ), unit delay cost( ), delay lead time( ), transportation cost( ), and lead time( )for the second-tier. We assume the parameters that are considered for the first-tier and OEM‘s demand remains constant during experiment for knowing the effect of second-tier‘s parameters. As discussed under the methodology section, we implement the Taguchi method in the parameter design, for which OA is to be selected as per the number of parameters, their levels, and interactions of the parameters needed for the study. However, in this study, eight parameters are considered, and the interaction between the parameters is neglected. Therefore, the total DOF of the parameters are 15 [7*(3-1) + 1*(2-1) = 15]. The OA should be such that which have at least fifteen DOF and eight columns. An L18 OA has eight columns and eighteen rows with seventeen DOF (18-1=17), due to which it is selected. The selected L18 OA is shown in Table 5 in which each row and each column represent the number of trials/experiments and parameter‘s position respectively. The OA suggests that any seven parameters have three levels, and one has two levels. [Insert: Table.5 L18 Standard Orthogonal Array (OA), (Taguchi and Wu, 1979)] ) at column-1 which requires two levels, and remaining parameters such as:, at column- 2, 3, 4, 5, 6, 7, and 8, which require three levels as it is shown in Table 6.

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We assign(

[Insert: Table.6 Parameters and their level] The parameter value is assigned for each trial as per L18 OA into a proposed mathematical model. As an example for trial number-1, the parameter settings at level-1 are assigned on the proposed mathematical model in Lingo 15.0, and minimized TC of procurement (outcome) is found. In such a manner, the eighteen trials are conducted from trial number one to eighteen one

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by one, and the outcome is obtained. Thereafter, the S/N ratio is calculated by using eq. (13) on the basis of the outcome of each trial and it is listed down in Table 7. [Insert: Table.7 The outcome and their S/N ratios]

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Simply, the total S/N ratio for each parameter at level-1, level-2, and level-3 is calculated by adding the S/N values. For example, the S/N ratio value for ( ) is calculated by adding the S/N values from 1-9 trial numbers for level-1 and 10-18 trials numbers for level-2. Similarly, for( ) by adding the S/N ratio values from trials 1-3 and 10-12 for level-1, 4-6 and 13-15 for level-2, and 7-9 and 16-18 for level-3. Similarly, the total S/N values are calculated for other parameters. Furthermore, the mean S/N ratios of the parameters for level-1, level-2 and level-3 are calculated upon the basis of total S/N ratio values for level-1, level-2 and level-3 by dividing the number of the trial conducted for each level. The mean S/N ratio for ( ) is obtained by dividing nine in the total S/N ratio for level-1 and level-2 respectively, while for other parameters divided by six to get the mean S/N ratio. Because in ( ) there are nine level-1 and level-2 trials, while in other parameters, there are six level-1, level-2, and level-3 trials. Besides, the difference between the maximum and minimum value from mean S/N ratio for each parameter is calculated and based on that we rank the parameters, and it is shown in Table 8. [Insert: Table.8 Total S/N ratio, mean S/N ratio, and rank of the parameters at each level]

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Furthermore, the S/N response graph is drawn based on mean S/N ratio for each parameter at each level in order to see the optimum level of the parameter settings, and it is shown in Fig.5.

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[Insert: Fig.5 S/N response graph for the parameters at each level]

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ANOVA table is prepared for each parameter as per the step as discussed in the methodology, by using eq. (14), (15), (16), and it is tabulated in Table 9. The ANOVA (Final) is implemented through error (pooled) in which the low parameters are pooled into the error. [Insert: Table.9 ANOVA table and their interpretations]

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7. Results and Discussions

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Based on the limiting value to the parameters such as (F0) 0.05, 2, 11 = 3.98, it found out that , are significant; whereas the other parameters are insignificant or less significant. From the S/N response graph and ANOVA table, we can see the optimum level which lies at level-2 for , level-1 for , level-2 for , level-2 for , level-1 for , level-1 for , level-3 for , and level-3 for . From this analysis, OEM and second-tiers find the optimum level of the parameters. It suggests the suppliers to improve the parameter levels towards optimum level in order to win the order in subsequent timeframe. The following managerial implications are discussed in the following:Computational testing and managerial analysis

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The computational testing is conducted on a computer with Windows 7 (2 GB of RAM). The adopted MINLP model is hard to solve. Here we investigate a solution approach through LINGO 15.0 optimization software, with its integrated multiple solvers for MINLP. It has four solvers such as direct solver, linear solver, nonlinear solver, and a branch-and-bound solver. To solve the case-1 and case-2 problem, the software directly suggests to branch and bound (B&B) solver. The case-1 for three timeframes consists of the entire variables of 189, which taken the 1712 iterations per second, while in case-2 for two timeframes consist of the total variables of 420, which taken the 117.9 iterations per seconds. The runtime of case-2 is much higher than case-1, as the parameters and variables of the problem increase due to increase in the size (suppliers and raw-materials) of the problem. In order to tackle these difficulties, restrict the number of suppliers at each-echelon for effective utilization of the model. In order to optimize the number of suppliers at each-echelon of the OEM, maximum demand strategy is needed to implement. Maximum demand versus capacity of second-tier suppliers There are‗m‘ suppliers at second-tier and ‗q‘ raw-materials is needed to assemble, it is much needed to know that the maximum demand that model can tackle for each timeframe, for this purpose eq. (17) is defined as below:∑

∑

∑

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From eq. (17), the maximum demand of case-1 is 3982.5 units, 6030 units and 7128 units for timeframe k=1, k=2, and k=3 respectively. Actual demands (D1, D2, D3) are 3500, 5200, and 4300 for three timeframes respectively. For optimum utilization of the supplier‘s capacity, the OEM should try to move towards the maximum demand. There is demand slack available in case-1 for k=1, k=2, and k=3 are 482.5 units, 830 units, and 2828 units respectively. Similarly, for case-2, the demand slack is 8730 units for k=1 and 7830 units for k=2. The maximum demand is the limiting value on the model for each timeframe, if actual demand exceeds the maximum demand then either increase the capacity of the second-tier suppliers or to add the more suppliers. However, increment in the supplier‘s capacity in substantial quantities is not easy, and practically it is very difficult to achieve for the suppliers. So it can be better to add the suppliers at each echelon to cope with the demand. Even though, the OEM has the slack in demand in sizable quantities, so it can be removed the supplier who is not able to perform. Comparatively, we may analyze the percentage utilization of the supplier‘s capacity at secondtier for each timeframe for the required raw-material, and it is shown in Table 10. From the table 10, it can be seen that the average utilization of the suppliers that suggest about the uniformity allocation to the suppliers. It means that the higher average utilization leads to improvement in the allocation, while lower average utilization indicates that skewed allocation. The skewed allocation relates to the more allocation from the limited suppliers. For effective utilization, the supplier gets improved the higher average allocation. [Insert: Table.10 Percent capacity utilization of 2nd-tier suppliers for k=1, k=2, and k=3] Criticality of the parameters From Table 9, the parameter by of 43%, and

has a maximum contribution of 54% followed of 2%.The , and are significant,

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which suggests the second-tier suppliers that they should much focus on these three parameters for the improvement in order to win the order allocation in the next timeframe. We look back to the input data of the proposed case-1 to check the significant effect of the parameters as follows:In the k=1 for q1, T3 has the slightest value of the (multiplication of UD1 and DLT1) as compared to other second-tier suppliers, got the full allocation of the 1630 units followed by T1, T4, and T3. For q2, T2 has the slightest value, got the full allocation of 1075 units followed by T3, T4, and T1. For q3, T2 has the least value, got the full allocation of 1815 units followed by T3, T4 and T1. The similar kind of effect on the parameters can be observed in the timeframe k=2 and k=3. The similar procedure can be implemented for case-2 in order to find the criticality of the parameters. The criticality of the parameters can be varied from problem to problem. Improvement in the TC of the procurement Table 11 shows the comparison between initial level of parameters taken initially and the optimum level of the parameters. It found from the current study that the variability of is too small and is also insignificant which is why we test the LT1 at level-1, level-2 and level-3 one by one. It is observed that the total value is least at level-1 for despite the optimum level for lies at level-3. The improvement of the S/N ratio from initial to optimal is 3.459 dB. It means that the decreased in TC from initial level to optimum level by 33%, which indicates the applicability of method for significant reduction in the TC of the procurement. Based on the optimal level of the parameters, we calculate the optimum allocation of the partproduct. The complete optimum solution of case-1 for k=1 is depicted in fig.6. From the fig.6, it is found that OEM‘s order got affected in which the supplied quantity got increased for S 1 and decreased for S2 and S3. The S1 got the competitive edge with the improvement in the supplied quantity to OEM by 783 units. It reveals that the suppliers needed the improvement in the parameters to get the competitive edge, and OEM got the flexibility to shift the order from one supplier to other for getting the least possible TC of procurement. It can be extended to each timeframe to check the robustness and to get the optimum allocation in order to achieve the least possible TC of the procurement. In another perspective, TC of procurement of the proposed model is highly improved in order to find the optimal set of the parameters through the approach. [Insert: Table.11 Result of the experiment based on the optimum level]

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[Insert: Fig.6 Improved allocation of parts at each-echelon of real-world case-1 for k=1]

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8. Conclusion

In this paper, we investigate a dynamic supplier selection problem under TESN for conversion of multi-parts/components/raw-materials into single semi-finished products through a machining process for the defined periodic timeframe. A mathematical model is proposed to obtain the best interaction of OEM for order allocation in between first-tier supplier and second-tier supplier for the particular timeframe. The two echelon of the supply chain is discussed in order to minimize the TC of procurement with two manifolds; i) whom to order, and ii) how much to order. The proposed model is tested through LINGO15.0 optimization software through randomly generated data for the two cases. Moreover, sensitivity analysis has been conducted though Taguchi method for parameter designs to check the criticality and robustness of the parameters. It is

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identified the optimum level, significant level, ranking, and percentage contribution of the parameters from ANOVA table and response graph, which suggests the suppliers for future improvement. It can be seen that significant reduction in the TC of procurement through the approach. The proposed model has numerous realistic managerial implications such as flexibilities in OEM‘s demand with periodic timeframe; type of raw-materials/parts/components can be added or removed as per the OEM‘s requirement, the suppliers at second-tier and manufacturers at first-tier can be included or removed as per their performance, and it also provides insight for suppliers for improvement in parameters to win the competitive advantage. This paper considered only the TESN; intangible factors could not be taken into account, using randomly generated data, and neglected the interaction of parameters in Taguchi method is the limitations of the paper. To increase the level of echelon, single semi-finished can be replaced with the multi semi-finished product, incorporated the uncertainties in supplier existence with risk, implementation of the real data for the proposed model, and take into account the intangible factors into the decision model would be the promising direction for the future research.

Acknowledgment:The authors thank the two anonymous reviewers for these valuable comments and suggestions, which has improved the quality and readability of this research paper.

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Taguchi G., (1990), Introduction to Quality Engineering, Asian Productivity Organization, Tokyo. Tahriri, F., Osman, M. R., Ali, A., Yusuff, R. M., & Esfandiary, A. (2008). AHP approach for supplier evaluation and selection in a steel manufacturing company. Journal of Industrial Engineering and Management, 1(2), 54-76. Tansel, I. N., Gülmez, S., Demetgul, M., & Aykut, S. (2011). Taguchi method–GONNS integration: complete procedure covering from experimental design to complex optimization. Expert Systems with Applications, 38(5), 4780-4789.

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Talluri, S., & Narasimhan, R. (2003). Vendor evaluation with performance variability: A max–min approach. European Journal of Operational Research,146(3), 543-552. Toloo, M., and Nalchigar, S. (2011). A new DEA method for supplier selection in presence of both cardinal and ordinal data. Expert Systems with Applications, 38(12), 14726-14731.

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Ustun Ozden and Ezgi Aktar Demirtas, (2008). An integrated multi-objective decision-making process for multi-period lot-sizing with supplier selection.Omega, 36, 509 – 521. Vinodh, S., Ramiya, R. A., & Gautham, S. G. (2011). Application of fuzzy analytic network process for supplier selection in a manufacturing organisation. Expert Systems with Applications, 38(1), 272-280. Wadhwa, V., & Ravindran, A. R. (2007). Vendor selection in outsourcing.Computers & operations research, 34(12), 3725-3737.

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Wang, J. W., Cheng, C. H., & Huang, K. C. (2009). Fuzzy hierarchical TOPSIS for supplier selection. Applied Soft Computing, 9(1), 377-386. Wang, T. Y., & Yang, Y. H. (2009). A fuzzy model for supplier selection in quantity discount environments. Expert Systems with Applications, 36(10), 12179-12187.

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Ware Nilesh R, S.P. Singh & D.K. Banwet. (2014). A mixed-integer non-linear program to model dynamic supplier selection problem. Expert Systems with Applications, 41, 671–678.

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Ware, N. R., Singh, S. P., & Banwet, D. K. (2014a). Modeling flexible supplier selection framework. Global Journal of Flexible Systems Management, 15(3), 261-274.

PT

Weber Charles A, John R. Current & W.C. Benton. (1991). Vendor selection criteria and methods, European Journal of Operational Research, 50, 2-18.

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Wu Teresa & Jennifer Blackhurst. (2009). Supplier evaluation and selection: an augmented DEA approach.International Journal of Production Research, 47:16, 4593-4608.

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Xia Weijun & Zhiming Wu, (2007). Supplier selection with multiple criteria in volume discount environments. Omega, 35, 494 – 504. Yahya S. & B. Kingsman, (1999). Vendor rating for an entrepreneur development program: a case study using the analytic hierarchy process method.Journal of the Operational Research Society, 50, 916-930.

Yousefi Ali, Abdollah and Hadi-Vencheh. (2010). An integrated group decision making model and its evaluation by DEA for automobile industry. Expert Systems with Applications, 37, 8543–8556. Yucel, A., & Guneri, A. F. (2011). A weighted additive fuzzy programming approach for multi-criteria supplier selection. Expert Systems with Applications, 38(5), 6281-6286.

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Fig.1.Basic structure of the model for periodic timeframe (k)

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Fig.2. the basic process for Taguchi method in the proposed model

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Fig.3. Allocated parts at each-echelon of case-1 for timeframe k=1, k=2 and k=3

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Fig.4. Allocated parts at each echelon of case-2 for timeframe k=1 and k=2

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Fig.5 S/N response graph for the parameters at each level (LT1)-3

(LT1)-2

(LT1)-1

(TC1)-3

(TC1)-2

(TC1)-1

-118.4

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(DLT1)-3

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(DLT1)-2

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(DLT1)-1

(UD1)-3

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(Q1)-1

(UC1)-3

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(SC)-2

(SC)-1

Mean S/N ratio (dB)

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Mean S/N ratio

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Fig.6. Improved allocation of parts at each-echelon case-1 for k=1

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Approach Techniques Methods

MOLP MP MILP

MINLP GA NN

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Fuzzy, ANP

Fuzzy, TOPSIS

Fuzzy, LP Fuzzy, ANP, NLP

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Descriptions Simple pair wise comparison based on multi-criteria, factors and sub-factors for assessing the suppliers.

Developed the interrelationships among the criteria and calculated the priorities for each supplier. Wu and Blackhurst (2009); Evaluated suppliers in an efficient manner Falagario et al. (2012) for multiple criteria. Anthony and Buffa (1977); Talluri Minimized the total purchasing cost with and Narasimhan (2003); Ng, (2008) single objective. ; Wadhwa and Ravindran (2007); Minimized the total procurement cost for Narasimhan and Talluri (2006); multiple products in a multiple sourcing network. Narasimhan and Stoynoff (1986); Allocated the order quantities for the Kasilingam and Lee (1996); suppliers based on multiple criteria for Jayaraman et al. (1999); Hong et multiple products. al. (2005); Amin and Zhang (2012); Wang and Yang (2009); Proposed study (as described in Briefly described in the literature review section. Table 2) Guneri et al. (2011) Multiple criteria analysis. Lee and Ouyang (2009) Bid price forecast and negotiation process. Chan and Kumar (2007);Rezaei et Simple pair wise comparison in the fuzzy al. (2014); Kilincci et al. environment. (2011);Chan et al. (2008); Chamodrakas and Martakos (2010); Kar (2014); Deng et al. (2014) Represented to the uncertain information by using D numbers, a D-AHP method is proposed for SS. Onut et al. (2009); Lin (2012); Proposed a framework comprising of the Vinodh et al. (2011) ; Dargi et al. most critical factors for the aim of SS. (2014); Boran et al. (2009); Kelmenis and Group decision-making problem. Askounis (2010); Wang et al. (2009) Arikan (2013); Guneri et al. Multiple sourcing for tangible and (2009); Ozkok and Tiryaki intangible factors. (2011);Yucel and Guneri (2011); Razmi et al. (2009); Global competitive market for long-term relations.

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References Saaty, (1980, 1990); Yahya et al. (1999); Akarte et al. (2001); AHP Levary (2008); Tahiri et al. (2008); Bruno et al. (2012). Gencer and Gurpinar (2007); ANP Bayazit (2006).

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Hsu et al. (2010); Rajesh and Malliga (2013)

Quality-based SS and evaluation. Considered the ―voice‖ of company‘s stake AHP, QFD holders. Ha and Krishnan (2008) An evaluated the process in order to select AHP, DEA, NN competitive suppliers in the supply chain industries. Choudhary and Shankar (2015) ; Used the preemptive GP, non-preemptive Igoulalene et al. (2015); Jadidi et GP and weighted max–min fuzzy GP to MOLP, GP al. (2015). solve the multi-objective optimization problem. Razmi and Rafiei (2010) Evaluated suppliers regarding their ANP, MINLP qualitative attributes, then allocate order quantities to the chosen suppliers. Mendoza and Ventura (2008). A list of potential suppliers was ranked by AHP, and then a mathematical model is AHP, MINLP used to properly allocate the order quantities. Demirtas and Ustun (2008); Maximized the total value of purchasing in ANP, MILP the budget and defect rate minimization with tangible and intangible factors. Toloo and Nalchigar (2011); Identified the most efficient supplier in DEA, MILP presence of both cardinal and ordinal data. ANP, TOPSIS, Lin et al. (2011). The concept of push and pull, and an ERP LP system is implemented. Table.1 Classification of the studies related to the SS problem

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Fuzzy, NLP

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Table.2 Contribution of the proposed study based on different approaches Suppliers Items Parameters Employed single- multipledynam Methodolog single multi static y source source ic

Paper







MINLP







ANP + MILP

In this paper











MINLP ANP + MINLP









 





Paretooptimal AHP + IRP + deviational MINLP matrix MINLP





MINLP





MINLP

Taguchi method

Not-considered

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MONLP

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 Considered

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Comparative analyses

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Ghodsypour and O'Brien (2001) Ustun and Demirtas (2008) Zhang and Ma (2009) Razmi and Rafiei (2010) Rezaeia and Davoodi (2012) Ware et al. (2014a) Guo and Li (2014) Ware et al. (2014)

Sensitivity Analysis

Table.3 Input data of case-1 for timeframe k=1, k=2, and k=3 Suppliers (2nd-tier)

q1

T1 T2 T3 T4 Periodic timeframe K=1 1600,35,0.930,5,6,5* 1650,37,0.940,6,7,6 1630,32,0.956,3,4,5 1620,35,0.949,7,7,5 K=2 2000,35,0.972,7,6,5 1600,42,0.988,8,3,6 1950,33,0.990,2,2,2 1900,37,0.970,6,6,7

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q3

(

)

(

)

2400,28,0.980,4,2,4 1100,40,0.959,4,7,6 1300,42, 0.940,6,2,2 1750,25,0.960,7,8,1 1800,33,0.960,6,8,6 1700,36,0.990,7,2,6 1960,33,0.985,6,9,6 690

2200,35,0.970,3,2,6 1075,34,0.955,7,4,7 1700,32, 0.960,2,4,8 1900,24,0.976,7,2,6 1815,33,0.950,7,4,6 1700,34,0.982,5,2,0 1800,31,0.985,3,6,2 635

2030,31,0.979,7,9,5 1120,35,0.940,7,6,6 2000,35,0.982,7,8,5 2090,22,0.984,9,8,2 1785,37,0.965,6,7,4 1900,31,0.973,8,8,1 2160,30,0.970,5,8,2 670

2080,34,0.975,8,7,3 1130,39,0.965,5,6,6 1700,36,0.955,8,7,6 2100,27,0.985,8,6,4 1810,38,0.965,5,8,7 2200,30,0.990,5,6,4 2000,32,0.986,8,4,4 660

K=2

720

870

690

775

K=3

900

940

805

795

K=1

20

18

K=2

22

20

K=3

25

24

*(

)

Suppliers (1st-tier)

S1

)

(

)

*(

) K=1 3500

19

21

21

19

S3

54,12,2,0 58,6,5,3 53,6,4,3 59 56 50 1 3 2

50,11,1,0 60,7,2,3 55,7,3,3 61 65 58 2 3 2

K=2 5200

K=3 4300

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Periodic timeframe OEM‘s demand

20

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55,11,1,0 56,7,4,2 57,7,5,2 60 60 57 2 2 2

S2 *

19

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Table.4. Input data of case-2 for timeframe k=1 and k=2 Suppliers

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T1 Periodic Timeframe

q3 q4 (

)

(

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2600,30,0.980,2,4,3* 2700,29,0.982,2,2,2 2500,26,0.960,3,3,3 2600,26,0.970,2,2,2 2100,31,0.950,7,2,3 2100,30,0.960,6,1,2 2800,28,0.970,5,4,1 2800,28,0.970,5,4,1 800 800 15 16

*( Suppliers (1st-tier) Periodic Timeframe

T3

T4

T5

T6

2800,32,0.970,8,3,1 2850,31,0.980,7,3,2 2700,25,0.965,6,2,3 2800,24,0.975,5,2,3 2900,27,0.960,2,1,1 3000,26,0.980,2,1,0 2600,29,0.965,6,3,2 2750,27,0.970,4,3,2 1100 1170 17 18

2900,28,0.975,7,2,0 2950,28,0.980,6,2,0 2800,24,0.975,5,3,1 2850,23,0.980,4,2,1 2800,28,0.970,8,3,3 2900,27,0.980,6,2,2 2500,30,0.960,7,5,3 2600,29,0.970,6,4,2 900 900 14 13

2000,27,0.985,6,5,3 2100,27,0.990,5,4,2 2900,28,0.990,8,4,0 2900,28,0.990,8,4,0 2900,27,0.983,4,2,2 2900,26,0.990,3,1,1 2100,32,0.990,3,3,3 2200,30,0.990,2,2,2 1000 1030 16 17

2500,29,0.983,2,3,2 2600,27,0.990,2,3,2 2200,28,0.984,2,3,3 2300,26,0.980,2,2,2 2200,25,0.975,3,1,3 2200,25,0.975,3,1,3 2000,33,0.980,2,2,2 2200,31,0.982,1,1,1 850 860 18 19

2200,31,0.976,5,2,3 2200,31,0.976,5,2,3 2400,30,0.979,9,2,1 2400,30,0.979,9,2,1 2600,27,0.975,7,2,4 2600,27,0.975,7,2,4 2700,32,0.980,1,1,1 2700,32,0.989,1,1,1 900 925 15 16

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S2

S3

S4

S5

S6

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K=1 K=2 K=1 K=2 K=1 K=2

62,7,9,2 64,9,12,4 35 40 3 4

58,6,11,3 63,8,14,4 38 41 2 3

K=1 4500

61,4,8,3 66,6,11,4 42 43 3 4

63,3,9,3 68,5,12,4 41 44 3 4

K=2 5400

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60,5,10,2* 62,7,13,4 40 44 2 3 )

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Table.5 L18 Standard Orthogonal Array (OA) (Taguchi and Wu, 1979)

64,5,10,2 65,7,12,4 43 47 2 3

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3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

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(

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(

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(

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(

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Table.6 Parameters and their levels Parameters (

)

Product Type q1

Level 1 *1600

T1 Level 2 1680

Level 3 -

T2 T3 T4 Level Level Level Level Level Level Level Level Level 1 2 3 1 2 3 1 2 3 *1650 1700 - *1630 1790 *1620 1650 -

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S/N Ratio for each level

Parameters

(

q2 q3 q1 q2 q3 q1 q2 q3 q1 q2 q3 q1 q2 q3 q1 q2 q3 q1 q2 q3

)

(

)

(

)

(

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(

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(

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1180 1890 32

*35

1075 1105 1120 1140 1815 1850 1785 1798 31 34 *37 29 31

Mean S/N Ration for each level

1130 1200 1810 1850 30 33

Mean

*35

MaxRank Min

35 31 0.95 0.96 0.97 5 7 4 2 3 4 2 3 2

37 34 0.94 0.956 0.965 6 5 5 4 5 7 4 4 4

40 33 *0.93 0.959 0.96 *5 4 6 *6 7 8 *5 6 6

33 32 34 34 36 35 36 37 39 31 36 33 33 36 37 34 37 38 0.96 0.95 *0.94 0.965 0.961 *0.956 0.955 0.958 *0.949 0.94 0.945 0.955 0.95 0.96 0.94 0.96 0.97 0.965 0.98 0.97 0.95 0.975 0.96 0.965 0.98 0.97 0.965 7 4 *6 6 5 *3 8 6 *7 6 6 7 8 4 7 4 6 5 8 6 7 7 5 6 7 6 5 3 5 *7 3 6 *4 2 5 *7 3 6 4 2 5 6 4 5 6 3 5 4 3 6 7 3 6 8 2 5 *6 3 4 *5 2 4 *5 2 4 7 2 4 6 4 5 6 3 5 6 2 3 4 2 5 7

729

640

*690

698

608 *635 745

640

*670

735

640

*660

15

18

*20

14

16

18

*19

15

17

*20

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*Initial Parameters

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Table.7 the outcome and their S/N ratios Trial No. Outcome S/N Ratio 1 690500.8 -116.783 2 865701.1 -118.747 3 981132.9 -119.835 4 899521.6 -119.08 5 1005489 -120.048 6 717358.5 -117.115 7 839716.7 -118.483 8 790783.6 -117.961 9 936134.8 -119.427 10 876492.3 -118.855 11 795498.6 -118.013 12 771646.4 -117.748 13 796753.2 -118.026 14 775699 -117.794 15 989930.2 -119.912 16 994769.6 -119.954 17 814446.2 -118.217 18 778741.1 -117.828

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Level-1 Level-2 Level-3 Level-1 Level-2 Level-3 -118.483 NA 0.126 6 ) 1067.48 1066.35 118.609 118.546 -711.87 -118.33 -118.662 0.332 3 709.981 711.975 118.645 118.546 -710.78 -118.53 -118.463 0.181 4 711.182 711.864 118.644 118.546 -710.88 0.106 7 -118.48 711.432 711.514 118.572 118.586 118.546 -118.901 1.399 2 706.015 713.404 714.408 117.669 119.068 118.546 -118.622 1.732 1 705.851 711.731 716.244 117.642 119.374 118.546 -118.555 0.169 5 711.754 711.329 710.743 118.626 118.457 118.546 -118.547 0.038 8 711.387 711.283 711.157 118.564 118.526 118.546

Table.9 ANOVA table and their interpretations

)

(

)

(

)

(

)

(

)

(

)

CE

Error (Pure) Total

0.0710 0.4196 0.1002 0.0396 7.0016 9.0528 0.0859 0.0044 0.0687 16.8438

)

(

)

(

)

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Degree Mean Percentage of Square F Contribution freedom (C ) (DOF) 1 0.0710 2.066 0.421 2 0.2098 6.108 2.491 2 0.0501 1.458 0.595 2 0.0198 0.576 0.235 2 3.5008 101.923 41.568 2 4.5264 131.782 53.746 2 0.0430 1.251 0.510 2 0.0022 0.064 0.026 2 0.0343 0.408 17 100 ANOVA (Final) 2 2 0.2098 6.241323 2 42 3.5008 104.1408 2 54 4.5264 134.6496

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Sources of variation

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Table.8 Total S/N ratio, mean S/N ratio, and rank of the parameters at each level

0.4196 7.0016 9.0528

Error 11 0.3698 (Pooled) 16.8438 17 Total From F-table, (F0) 0.05, 2,11 = 3.98

0.0336 0.2098

-

2

-

100

Table.10 Percent capacity utilization of 2nd-tier suppliers for k=1, k=2, and k=3

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q2

q3

Parameters ( ( (

T2

T3

T4

13.27 100 81.81 100 100 94.73 100 100 100

100 100 28.47 100 92.5 58.75 98.34 97.36 100

27.28 12 0 84.07 54.59 0 52.48 24 0

)

Level-1 Level-3

Level-1 Level-2

)

Level-3

(

)

Level-3

(

)

Level-3

Level-1

Level-3

Level-3

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-120.157

Improvement in the S/N ratio in dB.

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Table.11 Result of the experiment based on optimum level

Level-2

Level-3

)

)

60.78 78 52.57 87.92 86.77 63.37 62.76 80.34 60.43

Initial level of Parameters Optimal level of Parameters )

(

Avg. (%)

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Level-2 Level-1

Level-3

Level-2

Level-1

695060.9 692340.3 683760.9 -116.84

-116.806

-116.698

3.317

3.351

3.459