Influence of Lateral Transshipment Policy on Supply Chain Performance: A Stochastic Demand Case ()

Jingxian Chen, Jianxin Lu

**DOI: **10.4236/ib.2010.21009
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Considering the supply chain consists of one supplier and two retailers, we construct the system’s dynamic models which face stochastic demand in the case of non-lateral transshipment (NLT), unidirectional lateral transshipment (ULT) and bidirectional lateral transshipment (BLT). Numerical example simulation experiments of these models were run on Venple. We adopt customer demand satisfaction rate and total inventory as performance indicators of supply chain. Through the comparative of the simulation results with the NLT policy, we analyze the influence of ULT policy and BLT policy on system performance. It shows that, if retailers face the same random distribution demand, lateral transshipment policy can effectively improve the performance of supply chain system; if the retailers face different random distribution demand, lateral transshipment policy cannot effectively improve the performance of supply chain systems, even reduce system’s customer demand satisfaction rate, and increase system inventory variation.

Keywords

Supply Chain, Inventory System, Lateral Transshipment, Performance

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Chen, J. and Lu, J. (2010) Influence of Lateral Transshipment Policy on Supply Chain Performance: A Stochastic Demand Case. *iBusiness*, **2**, 77-86. doi: 10.4236/ib.2010.21009.

1. Introduction

Lateral transshipment, an important inventory replenishment policy, has gained a common concern of the academics and business managers in recent years. There are numerous researches about this issue. Lateral transshipment is defined as the redistribution of stock from retailers with stock on hand to retailers that cannot meet customer demands or to retailers that expect significant losses due to high risk [1]. The early pioneering work of Krishnan and Rao [2] examine a periodic review policy in a single-echelon, single-periodic setting [2]. Robinson [3] extends the research to a multi-period case, and establishes the system’s lateral transshipment model [3]. The emergency lateral transshipment model of repairable product was analyzed by Lee [4] for the two-echelon inventory system case [4]. Axsäter [5] studies the emergency lateral transshipment problem of the multi-level repairable product inventory system, and gets some interesting conclusions different from Lee’s [5]. Archibald et al. [6] develop a lateral transshipment model among the multi-retailer based on Markov decision-making methods [6]. Grahovac and Chakravarty [7] limit the research object to low demanded expensive product and analyze the lateral transshipments model in a multiechelon supply chain system [7]. Kukreja et al. [8] consider a single-echelon continuous review inventory system which contains n depots, and takes the expensive consumable product as object, study the one-to-one lateral transshipment model [8]. Rudi et al. [9] work on optimal order policy of the vendors in the existence of lateral transshipment circumstances [9]. Minner and Silver [10] provide a new decision rule of system’s lateral transshipment, and prove it can figure out the size of transshipment as well as some important problems [10]. Xu et al. [11] analyze emergency lateral transshipment policy between the two-echelon continuous review inventory system that use policy [11]. Banerjee et al. [12] study lateral transshipment of two-echelon supply chain systems which include multiple retailers and single supplier based on DOE [12]. Xu and Luo [13] use Expect Cost Method to analyze lateral transshipment policy in cross-docking system [13]. Xu and Xiong [14] analyze the best time for one-off transshipments in a cross-docking system with stochastic demand [14]. Wang et al. [15] conduct a quantitative analysis to the value of lateral transshipment policy of regional inventory distribution systems, which consist of a distribution center and multiple retail points [15]. Huo and Li [16] develop batch ordering policy in a single-echelon, multi-location transshipment inventory system [16]. Li et al. [17] study inventory management model of the cluster supply chain system with the existence of emergency lateral transshipment [17].

Most of the papers above dealing with transshipment assume that lateral transshipment already exists in system. However, lateral transshipment will make the problem complicate and tend to be very difficult to analyze analytically, especially BLT [18]. Hence, will lateral transshipment really need? This paper handles this problem from the performance measurement point. We consider one supply chain system consists of one supplier and two retailers, allowing a retailer transship from the other one for inventory replenishment besides order from supplier. System’s models were developed by system dynamics assume that all the members use the order-up-to policy, and numerical experiment was run on Venple platform.

The paper is organized as follows: in Section 2, the models with lateral transshipment were developed, as well as without lateral transshipment. The accuracy of the model is tested against simulation in Section 3; Section 4 deals with the influence of ULT and BLT. The conclusion of this paper was presented in Section 5.

2. Model Description

We consider two retailers facing independent stochastic customer demand and one supplier (Figure 1). Without lateral transshipment, retailers order from suppliers to replenish inventory in case of stock out. In order to respond to customer demand quickly, they can use lateral transshipment policy besides order from the supplier, which means they replenish inventory from the other one if there exist surplus stock on hand.

2.1 Model Assumption

Development of the model needs the following assumptions.

• Customer1 and Customer2 face independent stochastic demand;

• Both retailers adopt order-up-to policy, the ordering period is constant;

• Lateral transshipments take no time;

• Transshipments take place when there are surplus stocks. That is, if retailer 1 needs transshipment from retailer 2, retailer 2 only transships the redundant stock.

2.2 System Model

As a modeling and simulation technology, system dynamics has a wide range of applications since its birth, especially in dealing with long-term, chronic, dynamic management problems [19]. Forrester [20] applies system dynamics in industrial business management, addressing issues such as fluctuations in production and employees, instability of market shares and market growth [20]. Logistics and Supply Chain Management is an important area of System Dynamics. Sterman [21]designs the well-known beer game by System Dynamics, and carries out detailed analysis on feedback loops, nonlinear, time-delay and management behavior in the system [21]. Diseny et al. [22] analyze VMI in transport operation by system dynamics [22]. Marquez [23] establishes a model for measuring financial and operational performance in the supply chain based on System Dynamics [23], and so on.

Generally speaking, a complete system dynamics model usually consists of three parts: model variables, causal loop diagrams and mathematical description. We analyze the three part of model in turn as follows.

2.2.1 Model Variables

The structure of a system dynamics model contains stock, smoothed stock, flow rate, auxiliary variables and constants. Stock variables are used to describe the cumulative effect of the system. Smoothed stock variables are the expected values of specific variables obtained by exponential smoothing techniques. Flow rate describes the rate of the cumulative effect of the system. Auxiliary variables are the middle variables which express the decision-making process. Constants change little or relatively do not change during the study period. The fundamental notations of the model are following:

Figure 1. 2-echelon supply chain. Filled arrows represent the flow of regular replenishments while dashed arrows represent the lateral transshipment flow

2.2.2 Causal Loop Diagrams

Causal loop diagram is a tool that expresses the structure of the system, playing an extremely important role in system dynamics. There are two reasons for that. First, during model development, they serve as preliminary sketches of causal hypotheses and secondly, they can simplify the representation of a model.

The first step of our analysis is to capture the relationship among the system operations in a system dynamics manner and to construct the appropriate causal loop diagram.

Figure 2. Causal loop diagram of the supply chain without lateral transshipment

Figure 2 describes the causal loop of the supply chain without lateral transshipment.

The system structure in Figure 2 contains supplier and retailers. For the supplier, is decided by and. is determined commonly by and. Delivery rate is determined by and. Supplier adjust inventory level by setting, together with determine. and determine, in turn, has a direct impact on

and an indirect impact on. For retailers, is determined by and. is the delay of, delay time is. is decided by and. is obtained from after the time. Retailers also adjust inventory level by setting. is decided by and. and jointly determine. and commonly determine. If is greater than 0, Retailer sent orders to suppliers, order quantity is decided by

., , and determine. There are two performance variables, customer demand satisfaction rate and total inventory. is decided by inventory and customer demands, is a accumulation sum of supplier inventory and.

Figure 3. Causal loop diagram of the supply chain with unidirectional lateral transshipment

Figure 3 describes the causal loop diagram of supply chain with ULT. means the transshipment from retailer 2 to retailer 1. It is a flow rate variable and means that when retailer 1 out of stock, retailer 2 will replenish retailer 1 by transshipment on condition that it has surplus stock. is decided by and, and influence.

Conflicts of Interest

The authors declare no conflicts of interest.

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