Lateral Transhipment with Customer Switching

We consider the inventory transshipment problem between two retailers that sell the same product to two independent markets. One assumption that distinguishes our work is that unsatisfied customers may also switch to the retailer with surplus inventory. We examine the impact of such customer switching behavior on firms' inventory decisions and profits. We identify situations when the firm with surplus inventory is willing to fully tranship, partially tranship, or not tranship. We show that there is a unique Nash Equilibrium in inventory decisions under certain conditions, and compare the case with central coordination with decentralized decision making. INTRODUCTION AND LITERATURE REVIEW When a customer walks into a retail store and finds the product she intended to purchase unavailable, both the retailer and the customer may take action. The retailer may request transhipment from a partner store where the product is available. If the retailer is not able to arrange the transhipment, the customer may turn to the partner store and buy the product by herself. The interaction of these two strategies and its impact on retailers' inventory decisions are interesting to study. Inventory transhipment between retailers has been a common strategy when stockout occurs at one location and inventory surplus exists at the other location. Such strategy can be viewed as a way of virtually centralizing stock and taking advantage of inventory pooling. Therefore, when transhipment decisions are made under a central coordination scheme, it increases profit. However, if such a central coordination scheme does not exist, transhipment decisions are made locally for the interest of each individual retailer. As pointed out by Rudi et al. [4], such interfirm transhipment, rather than intrafirm transhipment, changes firms' inventory decisions since the risks imposed upon retailers are altered. On the other hand, customer switching has been a well-observed phenomenon. If two retailers carry the same products, customers first go to their preferred retailer due to factors such as price, service, location, promotion, convenience, etc. Since the two retailers differentiate themselves in these aspects, they each have their own customer demand and do not compete directly. However, if customers cannot find the product in their preferred retailer, they may look for the product at another retailer. Not all customers do so since some of them may decide not to buy the product at all or buy a substitutable product. Such customer switching behavior is called “market search" in Anupindi and Bassok [2], where they assume that a fixed fraction of the customers will search for the goods at another retailer. However, since firms may not obtain the exact information on the proportion of customers who switch to another retailer, we consider in this paper that a random fraction of those will switch. While making inventory purchasing decisions, it is important that firms take into consideration both transhipment agreement and customer switching behavior, since they interact with each other. In this paper, we examine two situations. In the centralized case, the two retailers are coordinated to maximize total profits. In the decentralized case, each retailer maximizes its own profit. In each case, we examine the optimal inventory purchasing decisions and transhipment decisions and aim at answering following questions: • What is the optimal transhipment strategy for the firm with surplus stock? How much inventory to reserve and how much to tranship? What factors influence such decisions? • In centralized case, what is the optimal inventory purchasing strategy? In decentralized case, is there a unique Nash Equilibrium for inventory purchasing quantities? • How do the decisions in decentralized case compare to centralized case? Shall the firms order more or less inventory? Shall the firm with surplus reserve more or less inventory? • Is there a coordination transhipment price such that centralized profit can be achieved under decentralized setting? • What is the impact of customer switching behavior on inventory decisions, transhipment decisions, and profits? Should such switching behavior be encouraged? Our project is closely related to the literature focusing on lateral transshipment in a decentralized system. The typical literature study the equilibrium behavior, and check whether it is possible to design a mechanism to coordinate those independent partners to achieve the highest possible supply chain benefit. Rudi et al. [4] and Hu et al. [3] show the uniqueness of Nash equilibrium in the order quantities for two retailers, and discuss the existence of the coordinating transshipment prices. Anupindi et al. [1] study the coorperative game in transshipment stage but non-cooperative game in order stage. A common assumption shared by these papers is that one partner's demand never switches to the other partner even if the local market stocks out but the other market still has inventory. Hence, if there is no transshipment between them, each partner's market is completely separated from the other's, and there is no competition on attracting demand. While in our paper, we assume that consumers in one market do “market search'' by themselves and go to buy from the “remote'' market when they find their local market is out of stock.