عنوان مقاله [English]
Capacity allocation plays an important role in supply chain management. In this study, a multi-period scenario is considered for a distribution system with one supplier and two retailers. The supplier may have infinite or finite capacity and allocates one product to the retailers at the beginning of a selling season. The retailers have a general cost structure and make ordering decisions to maximize their own profits. The order strategy of one retailer affects the order strategies of all other retailers, which results in a strategic interaction among the decision making of all retailers. The quantity requested by a retailer is called an order, or a claim. When the total quantity of orders from retailers exceeds the supplier's capacity, some rules are followed to allocate the capacity to the two retailers. The quantity of product that a retailer actually receives is called an allocation. In general a retailer's allocation is different from its order. The customer demand at each retailer is random in every period of time, and when a demand cannot be met by one retailer due to a stockout, the customers may go to the other retailer. This phenomenon is often referred to as market search. Since the two retailers compete for both supply and demand, the ordering decision at one retailer affects the demand of the competing retailer, thereby creating a strategic interaction among the retailers' inventory decisions. We analyze the inventory control decisions for the retailers using a game theoretical approach. In this paper game theory is used to study this problem. We are able to derive some necessary and sufficient conditions for the existence of a unique Nash equilibrium. It is shown that if the supplier's capacity is unlimited, there will always be a unique equilibrium; if capacity is limited, there is an equilibrium only under certain conditions.