هماهنگی قیمت گذاری و تصمیمات موجودی در زنجیره تامین چند سطحی : رویکرد تئوری بازی

This paper concerns coordination of enterprise decisions such as suppliers and components selection, pricing and inventory in a multi-level supply chain composed of multiple suppliers, a single manufacturer and multiple retailers. The problem is modeled as a three-level dynamic non-cooperative game. Analytical and computational methods are developed to determine the Nash equilibrium of the game. Finally, a numerical study in computer industry is conducted to understand the influence of the market scale parameter and the components selection strategy on the optimal decisions and profits of the supply chain as well as its constituent members. Several research findings have been obtained.

A supply chain consists of geographically distributed and administratively decentralized business partners. In such a decentralized supply chain, decisions of individual partners are often not coordinated with each other. Their local objectives are often inconsistent with those of the entire system objectives. As a result, the supply chain becomes less competitive (Porter, 1985). Many firms and researchers focus on coordinating pricing and inventory decisions to optimize the entire system and improve the efficiency of both the supply chain and individual firms (Weng, 1995 and Chan et al., 2004). Typically, a supply chain involves a variety of multiple products that are related to each other through common features. The levels of product variety offered by supply chains have demonstrated increasing trends (Macduffie et al., 1996). The product family design and platform products development have been widely used to increase variety, shorten lead times, and reduce costs (Simpson, 2005). The research in this paper has been motivated to integrate the product family design and platform products development into the pricing and inventory decisions to coordinate a decentralized supply chain. This paper focuses on joint decision-making about the selection of suppliers and components of a product family (Meyer and Utterback, 1993). The emphasis is placed upon the coordination of suppliers and components selection, pricing and inventory decisions (CSCSPI) in a multi-level supply chain consisting of multiple suppliers, one manufacturer and multiple retailers. The manufacturer purchases optional components of certain functionality from his alternative suppliers to produce a set of platform products to meet the requirements from the retailers in different markets. Each supplier faces the problem to make decisions on the prices for the components he sells to maximize his net profit. The manufacturer has to determine the setup time interval for production, the wholesale prices, and the suppliers and components selection decisions to maximize his net profit. The retailers’ problem will focus on the replenishment cycles and retail prices for the products. We describe CSCSPI problem as a three-level dynamic non-cooperative game with respect to the overall supply chain. The suppliers formulate the bottom-level non-cooperative simultaneous sub-game and at the same time as a whole play the middle-level non-cooperative simultaneous sub-game with the manufacturer. The suppliers and the manufacturer also being a group formulate the top-level non-cooperative simultaneous whole game with the retailers. Once the whole game settles an equilibrium solution, none of the any chain members is able to improve its payoff (i.e. profits) by acting unilaterally without degrading the performance of other players. We propose both analytical and computational methods to obtain the Nash equilibrium of this game. The game model and the proposed solution algorithm constitute a powerful decision support for solving the CSCSPI problem. Its use is demonstrated and tested through a numerical example. The impacts of the market scale parameter and components selection on the decisions and profits of all the chain members are also investigated. This paper is structured as follows. The next section presents a brief review of the literature related to pricing and inventory coordination, product family design, Game Theory for supply chain coordination. In Section 3, we give the problem description and some notations. We formulate the mathematical model of the CSCSPI problem in Section 4. Section 5 proposes the analytical and computational methods used to solve the CSCSPI problem in Section 4. In Section 6, a numerical study and the influence of market scale parameter and the components selection strategy have been presented. Finally, this paper concludes in Section 7 with some limitations and suggestions for further work.

In this paper, we have considered the coordination of suppliers and components selection, pricing, and replenishment decisions in a multi-level supply chain composed of multiple suppliers, one single manufacturer and multiple retailers. This coordination problem is modeled as a three-level dynamic non-cooperative game model. We use both analytical and computational methods for the derivative of the optimal decisions of all the chain members. A numerical study is conducted to examine the game model and solution algorithm. The numerical results show that the increase of one retailer’s market scale will decrease the other retailer’s profit and shorten his own replenishment cycle. Moreover, when one retailer’s market scale is large and a components selection strategy is simultaneously employed, the manufacturer tends to use high-end components to substitute the low-end ones for the product sold to this retailer and the manufacturer would generally benefit from this strategy. However, the supply chain system may become leaner with a fewer number of components and suppliers and their total profit would be lower. Individually, some suppliers may also benefit from this components selection strategy while others may suffer from a loss in profits. The contributions of the paper to the literature are as follows. Most literature to date have focused on pricing and inventory coordination in the two-echelon channel. This paper is an important addition to the literature on coordinating pricing and inventory decisions in a multi-level supply chain. Furthermore, this paper incorporates product family design with pricing and inventory coordination problem. In such a situation, products can be built more flexibly with the market. Lastly, significantly different from most extant literature in supply chain coordination which regard suppliers and components are selected already, we consider supplier selection and component selection as decision variables and determine them through a whole supply chain dynamic game. This paper has several limitations which can be extended in the further research. The competition among multiple products and among multiple retailers is not covered in this paper. Under this competition, the demand of one product/retailer is not only the function of his own price, but also the other products’/retailers’ prices. Secondly, we assume that the components can be ranked in the order of decreasing functionality, and either all or none the demand of a component is replaced by the lower order component in the same SCS. Future research should relax these constraints and include the case that the components can be partially replaced by higher functionality components. Also, we assume that the production rate is greater than or equal to the demand rate to avoid shortage cost. Without this assumption, the extra cost should be incorporated into the future work.