A multi-agent system model for supply chains with lateral preventive transshipments: Application in a multi-national automotive supply chain

Computers in Industry 82 (2016) 28–39

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A multi-agent system model for supply chains with lateral preventive transshipments: Application in a multi-national automotive supply chain Mualla Gonca Avci* , Hasan Selim Department of Industrial Engineering, Dokuz Eylul University, 35397 Izmir, Turkey

A R T I C L E I N F O

Article history: Received 8 July 2015 Received in revised form 2 March 2016 Accepted 17 May 2016 Available online xxx Keywords: Supply chain uncertainty Multi-agent system modeling Lateral transshipments Multi-location inventory systems

A B S T R A C T

In this study, a multi-agent system model is developed to observe the effects of ordering parameters on a supply chain with lateral preventive transshipments. The proposed model involves ordering and premium freight bidding processes of the agents. The model is implemented to a multi-national supply chain considering both supply and demand side uncertainties. Effects of safety stock and supplier flexibility levels on performance are examined by simulation from both agent and system-wide perspective. The results reveal the viability of the proposed model. ã 2016 Elsevier B.V. All rights reserved.

1. Introduction In today’s global competition, due to shorter product life cycles, cost and time pressure, companies adopt lean production concepts, global outsourcing and collaboration strategies. However, it is observed that these strategies increase supply chain complexity and vulnerability. In this sense, supply chains should be modeled as open and dynamic systems by considering complex relationships between agents. In parallel with this idea, system analysis and modeling approaches have gained importance in supply chain modeling. In particular, supply chain systems consist of autonomous, utility maximizing subsystems collaborating with each other. Hence, multi-agent system modeling is a suitable approach for conveniently modeling the decision making processes of those subsystems by considering complex relationships. In related literature, there exist vast amount of studies aimed at modeling supply chains under multi-agent setting. However, most of the studies focus on conventional supply chain structures such as serial and tree-based structures and do not provide quantitative results obtained from a real-world application. Additionally, identification of system parameters and modeling of uncertainties are rough in the previous works. In this study, a real decentralized supply chain system consisting of several plants and suppliers is

* Corresponding author. E-mail addresses: [email protected] (M.G. Avci), [email protected] (H. Selim). http://dx.doi.org/10.1016/j.compind.2016.05.005 0166-3615/ã 2016 Elsevier B.V. All rights reserved.

dealt with. Lateral preventive transshipments between agents are considered in addition to the main flows from upstream to downstream. Moreover, a bidding procedure is utilized in case of a lateral preventive transshipment requirement. In this study, a multi-agent system model is developed to examine physical flow in a decentralized supply chain system. The supply chain is a just-in-time supply chain system in which shortages are not allowed. Moreover, the plants in supply chain use single sourcing strategy under leanness concern and are exposed to a shortage risk in presence of supply problems. Therefore, lateral preventive transshipments between agents are made to mitigate the shortage risk. The proposed model implemented to a multinational automotive supply chain system located in Europe. The effects of ordering parameters on system performance are examined by simulating the proposed system model. The results and their implications encourage the focal supply chain managers to integrate the proposed multi-agent system model to their supply chain management system as a decision support tool. The organization of rest of the paper is as in the following. In Section 2, a brief introduction of multi-agent modeling of supply chain systems and recent related studies are provided. In Section 3, lateral preventive transshipments are explained and related literature is presented. In Section 4, the proposed multi-agent system model is presented. In Section 5, implementation of multiagent system model to focal supply chain is described. In Section 6, simulation experiments and results for the focal supply chain are demonstrated. Discussion and managerial implications are

M.G. Avci, H. Selim / Computers in Industry 82 (2016) 28–39

presented in Section 7. Finally, in Section 8, concluding remarks and possible future research directions are presented. 2. Multi-agent system modeling of supply chain systems Coordination in supply chains can be in two forms: centralized and decentralized. In centralized supply chains, managers tend to improve relationships between supply chain agents to improve the supply chain performance. Although high level of coordination and information sharing among various agents may be seen beneficial, it is also observed that the firms leading the supply chain have the tendency to transfer the risks to smaller agents as a result of their power. On the other hand, in decentralized supply chains, coordination is found only at the inter-firm level, which causes conflicting risk perceptions and practices to manage them [1]. As a result of global competition, most of the present supply chains are decentralized systems. Decentralized systems can be effectively modeled by using decentralized systems modeling approaches. In this study, the focal supply chain is modeled by using multi-agent systems modeling approach. Multi-agent systems consist of multiple agents, interacting to solve a common problem, compete for the use of shared resources, or simply coordinate themselves to avoid conflicts [2]. The term agent denotes a hardware or software based computer system having following characteristics: autonomy, social ability, reactivity and proactivity. Multi-agent system models are easier to understand and implement, when the problem itself is distributed. This allows the multi-agent system model to give more flexibility in dealing with the modularity of the real system [3]. As complex systems are generally distributed and decentralized, it is difficult to identify every possible interaction in the system at design stage. Multi-agent systems modeling approach handles the system complexity by decomposing the system into autonomous agents. Thanks to multi-agent systems modeling approach, there is no need to rigidly prescribe all possible interactions and control relations at design stage. Agents will act and update their state autonomously according to environment’s and other agents’ states. Thus, the control complexity of the system is reduced [4]. Supply chain systems are complex and distributed systems in their nature. Supply chain is a network of subsystems working together in complex and dynamic environment. Thus, supply chain system can be modeled as a network of agents. In parallel with multi-agent system notion, each agent prefers to maximize its profit rather than the overall profit of the supply chain. Each agent acts autonomously, interact other agents, reacts to changes in environment and make proactive decisions [3]. In this sense, there exist various studies dealing with supply chain system modeling by using multi-agent system modeling approach. In this section, recent studies related with supply chain planning via multi-agent modeling are investigated. Kwon et al. [5] model a supply chain with supply and demand uncertainties by combining multi-agent modeling and case-based reasoning approaches. Lu and Wang [6] propose a network economy based multi-agent supply chain framework and present a simple case to illustrate the operation of the proposed framework. Forget et al. [7] propose a multi-behavior planning agent model using different planning strategies and implement the proposed model to lumber industry. In a subsequent work, Forget et al. [8] analyze performance of a supply chain with multi-behavior planning agents proposed by Forget et al. [7]. Jiang and Sheng [9] propose a case-based reinforcement learning algorithm for dynamic inventory control in a multi-agent supply-chain system and implemented the proposed algorithm to a simplified two-echelon supply chain. Pan et al. [10] model a

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textile supply chain with variable demand as a multi-agent system and determine optimal re-ordering point by using a genetic algorithm. Brintrup [11] compares the performance of a multiagent, multi-objective, multi-role supply chain with the performance of a single-objective, single-role supply chain. Datta and Christopher [12] use multi-agent system modeling approach to test different levels of information sharing and coordination for a supply chain subjected to uncertain demand. Sinha et al. [13] model a petroleum supply chain as a multi-agent system and optimize the flow in supply chain by using co-evolutionary particle swarm optimization approach. Recently, Nikolopoulou and Ierapetritou [14] propose a hybrid approach combining mathematical programming and multi-agent based simulation to model a supply chain network. However, their model does not accommodate stochastic characteristics of the real system. Miranbeigi et al. [15] deal with lot sizing operation in a decentralized multi-echelon supply chain system with variable demand by using a multi-agent system model. Chu et al. [16] propose a simulation-based optimization framework in which performance values are obtained by a multi-agent system model and inventory parameters are optimized by a cutting-plane algorithm. Costas et al. [17] model well known Beer Game supply chain model by using multi-agent system modeling approach and apply Goldratt’s Theory of Constraints to reduce bullwhip effect. Mortazavi et al. [18] integrate an agent-based simulation technique with a reinforcement learning algorithm to model a four-echelon supply chain that faces non-stationary customer demands. In this study, a multi-agent based system model is developed for a real-world multi-national supply chain. In related literature, multi-agent modeling of supply chain systems is quite common. However, majority of the existing studies roughly handle supply and demand uncertainties, and do not capture the real characteristics of supply chain uncertainties. In this study, supply chain uncertainties are modeled for each agent by using real historical data obtained from past order records. On the other hand, the existing studies mainly focus on the flow between upstream and downstream agents in serial or tree-based supply chain systems rather than complex relationships between the agents in real world supply chains. In this work, lateral preventive transshipments between the agents are considered and a bidding procedure for lateral preventive transshipments is addressed. To the best of our knowledge, there exists no study considering lateral transshipments in multi-agent systems models. 3. Lateral preventive transshipments Tagaras [19] considers inventory pooling through lateral transshipments in distribution systems. In his paper, the retailers collaborate in the presence of high demand, which may result in shortages in one or more outlets. Collaboration takes the form of lateral inventory transshipment from an outlet with a surplus of on-hand inventory to an outlet that faces a stockout. Since the cost of transshipment is generally lower than both the shortage cost and the cost of an emergency delivery from the central warehouse and the transshipment time is shorter than the regular replenishment lead time, lateral transshipment simultaneously reduces the total system cost and increases the fill rates at the retailers [20]. In recent works, Tiacci and Saetta [21] develop preventive transshipment heuristic for balancing inventories among different locations at the same echelon in order to prevent stockouts. In another work, Tiacci and Saetta [22] examine the relative effects of two lateral transshipment approaches with respect to a classical policy of no lateral transshipments on the performance of multiechelon spare parts inventory system by using a simulation model.

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Hochmuth and Köchel [23] propose a simulation-based optimization approach for a multi-location inventory system with lateral transshipments. Summerfield and Dror [24] develop stochastic programming models for a family of inventory problems by considering lateral transshipments. Li et al. [25] analyze the effects of preventive lateral transshipments on ordering quantities. Tai and Ching [26] develop a Markovian model for a two-echelon inventory system by considering re-manufacturing of returns to products and lateral transshipments. The reader may refer to Paterson et al. [27] for a comprehensive review of studies related to lateral transshipments. Tagaras [19] classifies lateral transshipments in two forms: Preventive lateral transshipments and emergency lateral transshipments. If lateral transshipment is done before the demand is realized, it is called preventive lateral transshipment. If lateral transshipment is done after the demand is observed, it is called emergency lateral transshipment. In this study, preventive lateral transshipments are considered. When a stockout risk arises, plants can request a premium freight from its supplier or other plants. In this context, premium freight may be seen as a type of preventive lateral transshipment. However, in previous studies, lateral transshipments are considered in retail systems under inventory pooling scheme. Unlike the previous studies, in this study, inventory systems of plants are isolated from each other and a plant can reject a premium freight request that may negatively affect its performance. The decision processes of agents in case of a premium freight requirement are explained in detail subsequently. 4. The proposed multi-agent system model The focal supply chain consists of multiple autonomous plants aiming to minimize their costs through a collaborative inventory management. Due to the distributed nature of the supply chain, multi-agent modeling approach is used. In this sense, daily operations of a plant during simulation are illustrated in Fig. 1. At the beginning of each day, plants check their inventory positions. Then, they place orders to corresponding agents if needed. Finally, at the end of each day, they record their daily performance values. This process continues until the simulation clock reaches to predefined simulation length. In particular, ordering policy and performance measures used by plants are explained in detail, subsequently. 4.1. The ordering policy The plants use a periodic order-up-to policy. The ERP system of plants allows an order frequency at most one order per week. Therefore, a plant checks its inventory position at the beginning of each day, however, it can place an order only once in a week. If plant’s inventory position falls into risky level and it is not the allowed time for a regular order, it has to call a premium freight from either its supplier or other plants. The reason of that is the supply chain is a just-in-time system and no shortage is allowed. The ordering policy of plants is explained in detail below by using the notations explained in Table 1. At the beginning of each day, plant checks its inventory position IPip ðtÞ. IPip ðtÞ ¼ IPip ðt  1Þ þ Dip ðtÞ  C ip ðtÞ

ð1Þ

If time t corresponds to a regular order day, the plant places an order if it is needed. Otherwise, the plant places a premium order if the inventory position falls into a risky level. The procedures of regular order and premium order are explained in detail subsequently.

4.1.1. Regular order On each regular order day, the plant calculates its requirement RQ ip ðtÞ.  
  ð2Þ RQ ip ðtÞ ¼ max 0; AC ip SSip þ T p þ LT ip  IPip ðtÞ However, orders are delivered as packages. Hence, order of plant can only be an integer multiple of package size (PQ i ). To calculate order quantity, firstly, the suitable number of boxes (n) for the order quantity is determined that ensures the following inequality. ðn  1ÞPQ i < RQ ip ðtÞ  nPQ i

ð3Þ

Consequently, the order quantity will be: OQ ip ðtÞ ¼ nPQ i

ð4Þ

In the model, regular order quantities are bounded with quantity flexibility contracts between plants and their supplier. Supplier flexibility is determined as a percentage in contracts. X % flexibility means that plant cannot increase its order quantity by X % and cannot decrease order quantity by X% from the contracted quantity. Therefore, the plant checks that the order quantity ensures the flexibility limits specified in quantity flexibility contract (Eq. (5)). If the order quantity is below the lower flexibility limit, the plant increases the order quantity to lower flexibility limit. If the order quantity is above the upper flexibility limit, the plant adjusts the order quantity to the upper flexibility limit. In the simulation model, the order quantities are automatically adjusted in the same manner. AC ip T p ð1  F sp Þ  OQ ip ðtÞ  AC ip T p ð1 þ F sp Þ(5) 4.1.2. Premium order If time t does not correspond to a regular order day and inventory position of the item falls below safety stock level, the plant have to place a premium order. Premium orders are expedited orders delivered by airfreight. Due to its transportation mode, premium orders incur very high costs and plant should avoid from placing large premium orders. Therefore, premium order quantity is determined as an amount that will fulfill only the consumption until next scheduled delivery. Additionally, premium order is placed in case of no scheduled premium freight associated with item. If inventory position falls below safety stock level, plant calculates its requirement for premium order.   ð6Þ RQ ip ðtÞ ¼ AC ip T p  ðtc  to Þ þ LT ip where tc and to are current time and time of the last regular order placed by the plants, respectively. Premium orders also have packaging constraints. The resulting order quantity, OQ ip ðtÞ, is calculated as in Eqs. (3)–(4). The premium order is placed to either supplier or another plant. The plant decides where the requirement is sourced from according to expected costs of alternative sources. The expected costs of alternative sources are obtained as a result of a bidding process across plants and supplier. The bidding process is summarized in Fig. 2. In particular, after calculating the premium order quantity, Plant1 sends premium order request messages to supplier of the item (Supplier) and other plants holding inventory of the item (Plant 2). Suppliers always fill premium orders, however, plants accept premium requests only if their excess inventory on hand (EI) is sufficient to fulfill the order quantity. Excess inventory is surplus stock aroused from packaging constraints and minimum order levels specified in supplier contracts (Eq. (7)).
 EIip ðtÞ ¼ IPip ðtÞ  AC ip SSip þ T p  ðtc  to Þ þ LT ip (7) The agents accepted the plant’s premium request send their unit price for the item. Unit price offered by Supplier is the same

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Fig. 1. The simulation flow chart.

unit price contracted between Plant 1 and Supplier. Unit price offered by Plant 2 is the contracted unit price between Plant 2 and its supplier. Plant 1 collects price offers and calculates expected total cost of premium freight for each alternative. Total cost of premium freight consists of purchasing cost and transportation cost of the premium freight. Plant 1 chooses the minimum total cost alternative and places the premium order to the associated agent.

4.2. Performance measures To measure cost performance of the plants, holding, purchasing and premium freight costs and premium freight contribution of each item are recorded on daily basis. Then, daily total costs of each plant are calculated and annualized. Total cost of a plant is the summation of holding, purchasing and premium freight costs, minus premium freight contribution. The calculation of that cost items is explained subsequently.

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Fig. 2. Activity diagram for the premium freight bidding.

Holding cost is determined as a multiplication of average daily stock and carrying cost of one unit item for one day. Purchasing cost occurs when an order placed and calculated by multiplying order quantity by unit price. Premium freight cost consists of purchasing cost and airfreight transportation of item. Particularly, airfreight transportation cost is specified as transportation of 1 kg item from origin country to destination country. If premium freight is requested from a plant, the shipper plant receives a premium freight contribution as purchasing value of the item. In particular, the purchasing value of the item is calculated by unit price

contracted between shipper plant and its supplier, not by unit price contracted between requester plant and its supplier. Moreover, average annual regular order values and premium order values are recorded on daily basis to measure the performance of the plants. Regular order value and premium order value are the multiplication of order quantity and unit price of item. Those values are recorded on daily basis and like annual cost calculations, they are averaged and annualized. In this study, ratio of premium order value to regular order value, hereafter called PF ratio, is used as a performance measure. The plants seek

M.G. Avci, H. Selim / Computers in Industry 82 (2016) 28–39 Table 1 The notations for ordering policy. Notation

Explanation

Parameters Tp SSip AC ip LT ip PQ i F sp Variables IPip ðtÞ Dip ðtÞ C ip ðtÞ RQ ip ðtÞ OQ ip ðtÞ EIip ðtÞ

Ordering period of plant p Safety stock in days for item i in plant p Average daily consumption of item i in plant p Transportation lead time of item i for plant p Package quantity of item i Flexibility limit contracted between supplier s and plant p

Inventory position of item i in plant p at time t Delivery amount of item i to plant p at time t Amount of item i consumed in plant p at time t Requirement of plant p from item i at time t Order quantity for item i of plant p at time t Excess inventory on hand of item i in plant p at time t

33

from plan for every part spreadsheets available in the ERP system. Quantity flexibility limits are the same and 50% for each material. Suppliers transmit orders at the same day with order placed. Production and storage processes of suppliers are not considered in this study. Supply risks associated with the suppliers are delivery variability and transportation time variability. To model supply risks, delivery quantity gap data and delivery lateness data of each supplier are obtained from past order records of plants and are fitted to a number of distributions. Delivery quantity gap is considered as a ratio of lost delivery quantity to order quantity. Delivery lateness is the lateness of delivery arrival in days. Probabilities of both undesirable delivery situations are obtained by past order data and are provided in Table 2. For each supplier, delivery quantity gap is best fitted to normal distribution with parameters given in Table 2. On the other hand, delivery lateness is best fitted to Weibull distribution with parameters provided in Table 2. 6. Simulation experiments

for low PF ratio values to ensure the stability of their inventory management system and associated cost levels. Furthermore, system bullwhip is specified as a performance measure. Bullwhip is defined as the amplification of the demand variability through the upstream levels. Bullwhip is generally quantified as ratio of demand variability to order variability. In this study, as demand and order values of the agents may be in different extents, variation coefficient used to measure the demand and order variability. Consequently, bullwhip is quantified as the ratio of demand variation coefficient to the order variation coefficient in this study. 5. Implementation of multi-agent system model to focal supply chain The focal supply chain is a decentralized just-in-time automotive supply chain system consisting of nine plants and five suppliers. Plants and suppliers operate five days in a week, 48 weeks in a year. Plants use a periodic order-up-to policy described previously. Plants place their orders at the beginning of each week. Shipments and deliveries are made only in working days. Plants determine their order quantities by considering average daily consumption of material, package sizes and quantity flexibility limits. As the system is a just-in-time supply chain system, shortage is not allowed. If inventory position of an item decreases to a risky level, a premium freight is requested either from supplier or another plant as explained previously in Section 4.1. Premium freights are delivered certainly in right time and right quantity. 17 items are considered in this study. As the plants use single sourcing strategy, each item is supplied by a single supplier. On the other hand, an item can be consumed multiple plants, but inventory management system of the plants is decentralized. Therefore, 58 records related with 17 items in the plants should be considered independently. Required data associated with items (i.e. unit price, transportation time, safety stock level) are obtained

The system model is developed under MATLAB environment to examine the effects of supplier flexibility and ordering parameters on the supply chain performance. First of all, the simulation parameters such as replication length, replication number and warm-up period length are determined. Then, the simulation model is verified and validated by taking the advantage of opinion of the logistic manager of the firm. Afterwards, an experimental design is developed to investigate the effects of supplier flexibility and ordering parameters on the supply chain performance. The experiments are conducted in two parts. In the first part of experiments, general effects of the factors on system performance are investigated and discussed. In the second part, alternative supplier flexibility and safety stock levels are evaluated for a plant in terms of plant performance. All experiments are conducted by using the same simulation parameters and assumptions. 6.1. The simulation model parameter setting Due to the high complexity and uncertainty level of the system, determination of the simulation parameters is crucial. As initial condition of the system, inventory levels of plants are initialized by first ordering period requirement. However, the system reaches to steady-state at third week. Therefore, warm-up period length of the simulation is determined as 15 working days. As the system has high level of uncertainty and complexity, a long replication length, 2400 days (ten years), is specified to obtain reliable results. To estimate means of performance values at a predefined precision, a number of replications should be made for each experiment. Replication number for each experiment is determined by the procedure described by Law [28]. Let X be the estimate of mean m with a specified relative error g ¼ jX  mj=jXj. Suppose that a confidence interval for m has been constructed based on a fixed number of replications n, and estimates of population mean and variance will not change as the number of

Table 2 The supplier risk structure. Delivery quantity gap

Delivery lateness

Suppliers

Probability

Distribution

Mean

Std. dev.

Probability

Distribution

Shape

Scale

S1 S2 S3 S4 S5

0.04 0.05 0.01 0.01 0.05

Normal Normal Normal Normal Normal

0.49 0.52 0.51 0.49 0.45

0.25 0.23 0.27 0.30 0.17

0.09 0.05 0.05 0.06 0.09

Weibull Weibull Weibull Weibull Weibull

1.43 2.79 1.44 1.46 1.66

2.63 5.16 2.60 2.59 1.61

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M.G. Avci, H. Selim / Computers in Industry 82 (2016) 28–39

replications increases. An approximate number of replications required nr ðg Þ to obtain specified relative error g is given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8 9 2 < = S t ð n Þ=i i1;1 a =2 ð8Þ nr ðg Þ ¼ min i  n :  g0 : ; jX ðnÞj where ti1;1a=2 be the upper 1  a=2 percentage point of the t distribution with degree of freedom i  1, and S2 ðnÞ is the sample variance. g 0 ¼ g =1 þ g is the adjusted relative error needed to obtain an actual relative error of g . nr ðg Þ is approximated as the  2 smallest integer i satisfying i  S2 ðnÞ z1a=2 =ðg 0 X ðnÞÞ , where z1a=2 is the upper 1  a=2 percentage point of standard normal distribution. If nr ðg Þ > n, nr ðg Þ  n additional replications is

required to estimate X with specified relative error g. In this study, g is specified as 0.15 and 15 preliminary replications are made for each experiment. According to the simulation output analysis results, 15 replications are sufficient to estimate system performance values with specified relative error for each experiment. 6.2. Verification and validation of the simulation model First of all, accuracy of the simulation results is verified. In this context, the MATLAB program related to the simulation model is debugged and internal logic of the program is investigated carefully. After verification of the simulation model, a set of preliminary simulation experiments are conducted to investigate the behavior of the model. Purposely, simulation experiments are conducted under various setting of input parameter levels and the model behavior under different settings is compared to the real system behavior. The simulation model is validated both qualitatively and quantitatively. In qualitative validation, we broadly benefit from the comments of logistic manager of the firm. Specifically, the manager has examined the results obtained for different parameter settings and criticized them as they are valid or not. For example, according to the results of the preliminary simulation experiments, an increase in the safety stock levels causes an increase in total cost. The manager has stated that this relationship is realistic. Second, he has commented the strength of the relationship intuitionally whether the relationship is weaker or stronger than the reality. Furthermore, the model is validated quantitatively by benefiting the historical system performance values under different input parameter settings. As a result of the validation experiments, the simulation model is confirmed to be valid as it reflects the characteristics of the real system.

safety stock level means that safety stock level is 50% of the predefined safety stock levels (3.5 days) for each material. As stated previously, supplier flexibility is described in supplier contracts. The supplier requests a unit price increase in case of a plant desires to form a contract with higher flexibility. The unit price levels associated with the prespecified flexibility levels are reported in Table 4. As the current supplier flexibility level in the system is 50%, current unit prices are valid for that flexibility level. If the flexibility level is less than 50%, the unit prices are decreased, and it is greater than 50%, the unit prices are increased. The simulation experiments are conducted under three material consumption variability scenarios, namely, low variability, moderate variability and high variability scenarios. Material consumption variability is expressed as a percentage (i.e.a%) and assumed to follow a uniform distribution with parameters ða%; a%Þ. In this study, three consumption variability levels, namely, low (50%), moderate (100%) and high (150%) variability levels are considered. To sum up, 25 simulation experiments are conducted for each consumption variability scenario. Performance measures for the plants are determined as average total cost, average PF ratio and average bullwhip. General and agent-level effects of flexibility and safety stock levels are investigated in the subsequent section. 6.4. General effects of supplier flexibility and safety stock levels on system performance

In this study, a full factorial experimental design approach is utilized to examine the effects of supplier flexibility and ordering parameters on the supply chain performance. Particularly, five factor levels including the existing factor levels of the real-system are considered (see Table 3). Currently, the flexibility limit is 50% and safety stock level is 3.5 days for each material. In Table 3, 50%

First of all, effects of supplier flexibility and safety stock levels on general system performance are examined by using variance analysis. As the general effects on performance are examined, supplier flexibility and safety stock levels (Table 3) are the same for each supplier and each material, respectively. Moreover, performance measures of plants are averaged to obtain unique performance measure for the supply chain system. Firstly, factor effects are investigated under low consumption variability (50%) scenario. To ensure that performance values holds homogeneity of variances assumption of ANOVA, Levene test is conducted for average total cost, average PF ratio and average bullwhip. Test statistics are 0.92, 0.64 and 0.93 for total cost, PF ratio and bullwhip, respectively. As a result, the homogeneity of variances assumption is hold by all performance measures at significance level 0.05. Results of ANOVA for total cost, PF ratio and bullwhip are given in Tables 5–7 . According to the results, supplier flexibility and safety stock has a significant effect on total cost. However, those factors have no significant effect on PF ratio and bullwhip. The main effects of factors on performance values are illustrated in Figs. 3–5. As illustrated in Fig. 3, there is an almost linear relationship between the total cost and the factors. However, one cannot reach to a conclusion about the relationship between PF ratio and the factors as well as between bullwhip and the factors from the main effects plots, since the factors do not significantly affect the PF ratio and bullwhip. Moreover, ANOVA is conducted for moderate consumption variability (100%) scenario. Similarly, variances of performance values are equal according to Levene test results (Test statistics are

Table 3 Factor levels.

Table 4 Candidate supplier flexibility contracts.

6.3. Experimental design

Level

Supplier Flexibility (%)

Safety Stock (%)

Level

Supplier Flexibility (%)

Unit Price

1 2 3 4 5

25 50 75 100 125

50 75 100 125 150

1 2 3 4 5

25 50 75 100 125

0.94* Current Unit Price Current Unit Price 1.07* Current Unit Price 1.13* Current Unit Price 1.19* Current Unit Price

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Table 5 Results of ANOVA for total cost under low consumption variability scenario. Source

DF

Adj SS

4 6.63080E + 11 Flexibility Safety Stock 4 2.06E + 16 Flexibility  Safety Stock 16 60241415 Error 350 2.19E + 09 Total 374 4.36E + 17

Adj MS

F-Value

P-Value

1.66E + 16 26442.75 0.000 5.14E + 10 8206.78 0.000 3765088 0.60 0.883 6269020

Table 6 Results of ANOVA for PF ratio under low consumption variability scenario. Source

DF

Adj SS

Adj MS

F-Value

P-Value

Flexibility Safety Stock Flexibility  Safety Stock Error Total

4 4 16 350 374

0.000006 0.000016 0.000035 0.000460 0.000503

0.000002 0.000004 0.000002 0.000001

1.22 3.00 1.66

0.303 0.019 0.053

Table 7 Results of ANOVA for bullwhip under low consumption variability scenario. Source

DF

Adj SS

Adj MS

F-Value

P-Value

Flexibility Safety Stock Flexibility  Safety Stock Error Total

4 4 16 350 374

0.000486 0.000767 0.002514 0.030920 0.034013

0.000122 0.000192 0.000157 0.000088

1.38 2.17 1.78

0.242 0.072 0.033

Fig. 5. Main effects for bullwhip under low consumption variability scenario.

0.94, 0.59 and 0.84 for total cost, PF ratio and bullwhip, respectively.). Results of ANOVA for total cost, PF ratio and bullwhip are given in Tables 8–10 . According to the results flexibility and safety stock have significant effect on total costs. Additionally, safety stock has a significant effect on PF ratio. The main effects of factors on performance values are illustrated in Figs. 6–8 . According to the results, there is an almost linear relationship between the total cost and the factors (see Fig. 6). Likewise, there is a nearly linear relationship between PF ratio and safety stock (see Fig. 7). For the remaining analyses, we cannot come up with a conclusion about the relationship between the performance values and factor levels as effects of the factor levels on the performance values are statistically insignificant.

Table 8 Results of ANOVA for total cost under moderate consumption variability scenario.

Fig. 3. Main effects for total cost under low consumption variability scenario.

Source

DF

Adj SS

Flexibility Safety Stock Flexibility  Safety Stock Error Total

4 4 16 350 374

6.63E 2.13E 1.98E 6.51E 4.38E

+ 16 + 16 + 08 + 09 + 17

Adj MS

F-Value

P-Value

1.66E + 16 5.32E + 10 12386308 18601114

8908.12 2858.77 0.67

0.000 0.000 0.827

Table 9 Results of ANOVA for PF ratio under moderate consumption variability scenario. Source

DF

Adj SS

Adj MS

F-Value

P-Value

Flexibility Safety Stock Flexibility  Safety Stock Error Total

4 4 16 350 374

0.000005 0.000021 0.000034 0.000783 0.000868

0.000001 0.000005 0.000002 0.000002

0.55 2.34 0.94

0.699 0.054 0.518

Table 10 Results of ANOVA for bullwhip under moderate consumption variability scenario.

Fig. 4. Main effects for PF ratio under low consumption variability scenario.

Source

DF

Adj SS

Adj MS

F-Value

P-Value

Flexibility Safety Stock Flexibility  Safety Stock Error Total

4 4 16 350 374

0.000051 0.000055 0.000271 0.006444 0.006914

0.000013 0.000014 0.000017 0.000018

0.69 0.74 0.92

0.599 0.564 0.544

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M.G. Avci, H. Selim / Computers in Industry 82 (2016) 28–39 Table 11 Results of ANOVA for total cost under high consumption variability scenario. Source

DF

Adj SS

Adj MS

F-Value

P-Value

Flexibility Safety Stock Flexibility  Safety Stock Error Total

4 4 16 350 374

3.35E + 12 1.10E + 12 7.75E + 08 1.22E + 10 4.47E + 12

8.39E + 11 2.75E + 11 48433967 34861227

24053.26 7880.82 1.39

0.000 0.000 0.144

Table 12 Results of ANOVA for PF ratio under high consumption variability scenario.

Fig. 6. Main effects for total cost under moderate consumption variability scenario.

Source

DF

Adj SS

Adj MS

F-Value

P-Value

Flexibility Safety Stock Flexibility  Safety Stock Error Total

4 4 16 350 374

0.000006 0.000193 0.000109 0.001562 0.00187

0.000002 0.000048 0.000007 0.000004

0.34 10.78 1.53

0.848 0.000 0.088

Table 13 Results of ANOVA for bullwhip under high consumption variability scenario. Source

DF

Adj SS

Adj MS

F-Value

P-Value

Flexibility Safety Stock Flexibility  Safety Stock Error Total

4 4 16 350 374

0.000057 0.00037 0.000108 0.003291 0.003826

0.000014 0.000093 0.000007 0.000009

1.51 9.84 0.72

0.199 0.000 0.778

Fig. 7. Main effects for PF ratio under moderate consumption variability scenario.

Fig. 9. Main effects for total cost under high consumption variability scenario.

Fig. 8. Main effects for bullwhip under moderate consumption variability scenario.

Furthermore, ANOVA is conducted for high consumption variability (150%) scenario. Levene test results reveal that performance values hold the equality of variances assumption (Test statistics are 1.22, 0.67 and 0.54 for total cost, PF ratio and bullwhip, respectively.). ANOVA results for total cost, PF ratio and bullwhip are given in Tables 11–13 . According to the results, supplier flexibility and safety stock has a significant effect on total cost. Additionally, safety stock level has significant effect on PF ratio and bullwhip. The main effects of the factors on system performance values are illustrated in Figs 9–11 .

Fig. 10. Main effects for PF ratio under high consumption variability scenario.

M.G. Avci, H. Selim / Computers in Industry 82 (2016) 28–39

Fig. 11. Main effects for bullwhip under high consumption variability scenario.

Again, there is a strong relationship between total cost and the factors. Moreover, safety stock has a positive effect on bullwhip generally. Besides, safety stock has a negative effect on PF ratio, surprisingly. The relationship between safety stock and those performance values cannot be observed clearly due to instability of the system arising from the high consumption variability. That is, one cannot infer about the relationship between flexibility and those performance values, because of the insignificant relationship. To sum up, the experimental results reveal that flexibility and safety stock levels have significant effect on total cost for all scenarios. Although total costs do not affected by consumption variability, PF ratio and bullwhip performances are significantly affected. PF ratio increases in higher consumption variability scenarios as expected. Conversely, bullwhip decreases as consumption variability is increased. The reason for that is the dampening effect of supplier flexibility limit on transfer of consumption variability to upstream. Rong et al. [29] observe this effect on multi-echelon systems with capacitated suppliers, and entitled as reverse bullwhip effect. As expected, high flexibility and safety stock levels involve higher total costs due to the increase in purchasing cost and inventory holding costs. On the other hand, supplier flexibility has no significant effect on PF ratio and bullwhip. However, PF ratio is significantly affected by safety stock levels in all scenarios. Lower safety stock levels causes a considerable increase in regular order quantities. Consequently, as the regular order value is the denominator of PF ratio, PF ratio decreases in the presence of low safety stock values. Finally, bullwhip is affected significantly by safety stock level in high consumption variability scenario. As expected, bullwhip decreases as safety stock is increased. If the firm prefers to reduce the PF ratio of the system, it should increase the flexibility levels and/or decrease the safety stock levels. However, both of these strategies incur higher costs. It should be stated here that this observation is not reliable enough as the factor levels are equal for each agent. Hence, interrelationships and individual performances of the agents should be considered. In this regard, effects of the factor levels on the agent-level performance should be investigated. The following section presents such an analysis. 6.5. Effects of supplier flexibility and safety stock levels on plant performance In this section, effects of supplier flexibility and safety stock levels on plant performance are examined by focusing on the relationship with a plant and its supplier. First of all, current performance values of the plants (safety stock level of 3.5 days and

37

supplier flexibility of 50%) are obtained for moderate consumption variability scenario (Table 14). As P9 has the largest share in total cost of supply chain, P9 is selected as the focal plant. In Table 15, the performance values of P9 are provided in terms of its suppliers. As S3 is not a supplier of P9, performance values associated with S3 are not given. As one can see from Table 15, the largest total cost share arises from relationships between P9 and S5. In particular, P9 supplies two materials from S5. The current flexibility level provided by S5 to P9 is 50% and safety stock level of each material is 3.5 days. In this sense, the system is 27 simulation experiments are conducted for various supplier flexibility and safety stock levels and results are given in Table 16. As the bullwhip values are generally at desired levels, the bullwhip values are not presented in Table 16. In Table 16, SS1 and SS2 presents safety stock level of materials supplied from S5. PF ratio (s) is PF ratio of P9 in terms of S5. Likewise, PF ratio (p) and total cost (p) present PF ratio and total cost of P9, respectively. The values in bold are the performance values obtained by considering base case with current factor levels. As one can infer from Table 16, higher flexibility levels incur higher costs. If the plant needs to decrease its total cost, it would prefer the supplier flexibility level of 25% along with the safety stock levels of 2.5 and 3.5 days for materials 1 and 2, respectively. However, PF ratio increases approximately by 0.1% compared to the PF ratio of the base case. If the plant needs to decrease its PF ratio, it would prefer the supplier flexibility level of 75% along with the safety stock level of 2.5 days for each material. However, this option incurs 100,000 Euro extra cost relative to the base case. Alternatively, if the current supplier contract will remain, the plant can gain cost advantage by updating the safety stock levels to 2.5 and 4.5 days for materials 1 and 2, respectively. 7. Discussion and managerial implications As expected, PF ratio increases and bullwhip decreases in the higher consumption variability scenarios. Conversely, total cost is not significantly affected by consumption variability. This results from the inability of average performance values in measuring the system stability. In particular, higher consumption variability causes fluctuations in order quantities. However, supplier flexibility contracts constrain the order quantities from exceeding the flexibility limits. Therefore, the plant is forced to order under or Table 14 Performance values of the plants under moderate consumption variability scenario. Plants

Total Cost

PF Ratio

Bullwhip

P1 P2 P3 P4 P5 P6 P7 P8 P9

1,264,434 545,174 703,406 1,059,061 832,203 1,264,088 247,715 3,369,409 4,036,868

0.0175 0.0206 0.0213 0.0551 0.0536 0.0679 0.0359 0.0208 0.0189

0.8968 0.8832 0.9609 0.7654 0.6688 0.6408 0.8878 0.8410 0.9046

Table 15 Performance values of Plant 9 in terms of its suppliers. Supplier

Total Cost

PF Ratio

Bullwhip

S1 S2 S4 S5

92,575 337,290 21,624 3,585,380

0.0278 0.0421 0.0337 0.0163

1.0214 0.5369 1.4144 0.7168

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M.G. Avci, H. Selim / Computers in Industry 82 (2016) 28–39

Table 16 Simulation results. Flexibility

PF Ratio (s)

25%

SS1

2.5 3.5 4.5

2.5 0.0189 0.0179 0.0180

SS1

2.5 3.5 4.5

2.5 0.0172 0.0179 0.0184

SS1

2.5 3.5 4.5

2.5 0.0155 0.0174 0.0172

50%

75%

SS2 3.5 0.0177 0.0157 0.0182 SS2 3.5 0.0176 0.0163 0.0172 SS2 3.5 0.0184 0.0185 0.0157

PF Ratio (p) 4.5 0.0203 0.0185 0.0187 4.5 0.0162 0.0194 0.0171 4.5 0.0156 0.0177 0.0181

SS1

2.5 3.5 4.5

2.5 0.0208 0.0200 0.0205

SS1

2.5 3.5 4.5

2.5 0.0197 0.0202 0.0204

SS1

2.5 3.5 4.5

2.5 0.0176 0.0190 0.0192

over its requirement in some cases. Consequently, holding costs and/or premium freights increase during the fluctuation periods. However, these fluctuations cannot be evaluated by average performance values properly as they occur instantaneously. Accordingly, there is a need for an additional measure to evaluate the system stability. In this context, PF ratio is proposed to be used as a proper system stability measure. In fact, PF ratio and bullwhip are employed to measure the system stability, and total cost is utilized as an average system performance measure. As expected, high flexibility and safety stock levels incur higher total costs since they incur higher purchasing and inventory holding costs. On the other hand, low safety stock values yields low PF ratios, as they involve lower regular order values which is the denominator of PF ratio. Finally, in high consumption variability scenarios, bullwhip decreases as safety stock is increased, unsurprisingly. The proposed model takes the advantage of evaluating performance at agent-level along with system-level. The logistics manager can evaluate suppliers’ or plants’ performances in addition to the overall system performance. Therefore, the proposed model can serve as a flexible decision support tool for evaluating new supplier contracts. Accordingly, the proposed system model is found to be useful by the logistics manager of the firm, and it is decided that it will be integrated to the supply chain decision support system which is currently utilized by the firm. 8. Conclusion In this study, a multi-agent system model is proposed for supply chains with lateral preventive transshipments. Unlike the majority of the previous studies, a decentralized supply chain system with complex relationships is dealt with and a real-world application is presented. In addition to the main flows between the agents, lateral preventive transshipments are considered. This study differs from the previous studies in the field in that it considers lateral preventive transshipments in which a plant can reject a premium freight request that may negatively affect its performance. This issue is presented by premium freight bidding process in the proposed system model. The validity and reliability of the proposed model are evaluated through simulation experiments by using the data obtained from a real-world automotive supply chain system. Firstly, the effects of safety stock and supplier flexibility levels on general system performance are examined in the analysis. Afterwards, the effects of these factors on agent performance are investigated and an example analysis is presented. The results reveal that the proposed system model provides flexibility in evaluating both agent-level

SS2 3.5 0.0198 0.0180 0.0206 SS2 3.5 0.0197 0.0189 0.0192 SS2 3.5 0.0204 0.0205 0.0177

Total Cost (p) 4.5 0.0198 0.0203 0.0207 4.5 0.0187 0.0214 0.0195 4.5 0.0178 0.0198 0.0199

SS1

2.5 3.5 4.5

2.5 3,799,451 3,816,971 3,823,532

SS1

2.5 3.5 4.5

2.5 3,974,479 3,993,247 4,005,463

SS1

2.5 3.5 4.5

2.5 4,158,980 4,164,210 4,172,760

SS2 3.5 3,853,886 4,036,725 3,867,654 SS2 3.5 4,021,308 4,036,868 4,065,135 SS2 3.5 4,207,917 4,036,787 4,228,080

4.5 3,913,195 3,916,474 3,928,400 4.5 4,021,308 4,090,971 4,104,115 4.5 4,260,663 4,265,815 4,280,688

and system-level performance. In this sense, the proposed model is found to be practical by the logistics manager of the firm. The next step of the study will be to integrate the proposed system model with the supply chain decision support system of the firm. In future studies, effects of external factors on agent and system performance can be investigated. Moreover, designing of a learning algorithm to find best ordering parameter values for the agents is a promising future study. Acknowledgment This work was supported in part by Dokuz Eylul University under Grant 2015.KB.FEN.016. References [1] P. Singhal, G. Agarwal, M.L. Mittal, Supply chain risk management: review, classification and future research directions, Int. J. Bus. Sci. Appl. Manag. 6 (2011) 15–42. [2] L. Cloutier, J.-M. Frayret, S. D’Amours, B. Espinasse, B. Montreuil, A commitment-oriented framework for networked manufacturing coordination, Int. J. Comp. Integr. Manuf. 14 (2001) 522–534. [3] T. Moyaux, B. Chaib-draa, S. D’Amours, Supply chain management and multiagent systems: an overview, in: B. Chaib-draa, J. Müller (Eds.), Multiagent Based Supply Chain Management, Springer, Berlin, Heidelberg, 2006, pp. 1–27. [4] N.R. Jennings, On agent-based software engineering, Artif. Intell. 117 (2000) 277–296. [5] O. Kwon, G. Im, K. Lee, MACE-SCM: a multi-agent and case-based reasoning collaboration mechanism for supply chain management under supply and demand uncertainties, Exp. Syst. Appl. 33 (2007) 690–705. [6] L. Lu, G. Wang, A study on multi-agent supply chain framework based on network economy, Comp. Ind. Eng. 54 (2008) 288–300. [7] P. Forget, S. D’Amours, J.-M. Frayret, Multi-behavior agent model for planning in supply chains: an application to the lumber industry, Robotics Comp. Integr. Manuf. 24 (2008) 664–679. [8] P. Forget, S. D’Amours, J.-M. Frayret, J. Gaudreault, Study of the performance of multi-behaviour agents for supply chain planning, Comp. Ind. 60 (2009) 698– 708. [9] C. Jiang, Z. Sheng, Case-based reinforcement learning for dynamic inventory control in a multi-agent supply-chain system, Exp. Syst. Appl. 36 (2009) 6520– 6526. [10] A. Pan, S.Y.S. Leung, K.L. Moon, K.W. Yeung, Optimal reorder decision-making in the agent-based apparel supply chain, Exp. Syst. Appl. 36 (2009) 8571–8581. [11] A. Brintrup, Behaviour adaptation in the multi-agent, multi-objective and multi-role supply chain, Comp. Ind. 61 (2010) 636–645. [12] P.P. Datta, M.G. Christopher, Information sharing and coordination mechanisms for managing uncertainty in supply chains: a simulation study, Int. J. Prod. Res. 49 (2011) 765–803. [13] A.K. Sinha, H.K. Aditya, M.K. Tiwari, F.T.S. Chan, Agent oriented petroleum supply chain coordination: Co-evolutionary particle swarm optimization based approach, Exp. Syst. App. 38 (2011) 6132–6145. [14] A. Nikolopoulou, M.G. Ierapetritou, Hybrid simulation based optimization approach for supply chain management, Comp. Chem. Eng. 47 (2012) 183–193. [15] M. Miranbeigi, B. Moshiri, A. Rahimi-Kian, J. Razmi, Demand satisfaction in supply chain management system using a full online optimal control method, Int. J. Adv. Manuf. Technol. 77 (2014) 1401–1417.

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