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This paper analyzes the implementation of transshipments among competing firms and the impact of transshipments on their inventory replenishment decisions. Previous studies have shown that transshipments, when implemented between stocking locations operating in the same echelon, improve firm financial performance and customer service through risk sharing and inventory reallocation. However, these studies have not investigated transshipments in a competitive environment; that is an environment where two firms both cooperate through transshipments and compete for customers. In this paper, the rivalry intensity between firms is assessed through a variable, customer's switching rate, measuring the percentage of consumers switching sellers in the event of a stockout. The impact of various switching rates on the performance benefits from transshipments is investigated, leading to several important managerial implications. In particular, numerical analyses suggest that transshipment price plays a unique, crucial role in creating benefits for participating firms with asymmetric market demands and various degrees of customer loyalty.

Saturn has achieved impressive success with after-sales service through the practice of sharing automotive parts among its dealers (Cohen et al., 2000). When one dealer is out of a particular stock keeping unit (SKU), this dealer will first contact a nearby Saturn dealer to see if the SKU is available there. If the part is available, transshipments are implemented from the location with excess stock to the location with insufficient supply. Through transshipments, a dealer can quickly receive the part needed and thus satisfy customer requests for maintenance or repair faster than if the out-of-stock part were backordered from the central distribution center or the original supplier. As a risk-pooling strategy, transshipments provide an efficient and effective approach for firms to reduce inventory carrying costs without negative effects on customer service. Most previous studies follow the line that transshipments, as a mechanism to reallocate resources between two locations at the same level of a supply chain, benefit both the sending outlet and the receiving outlet (e.g., Tagaras, 1989, Krishnan and Rao, 1965 and Rudi et al., 2001). The extant literature has analyzed transshipments between firms that are either centrally controlled (e.g., Krishnan and Rao, 1965) or independently owned (e.g., Rudi et al., 2001 and Dong and Rudi, 2004). However, the previous studies did not consider the situation where transshipments are implemented among competing but connected firms. Examples include networks of independent dealers or franchise operators. In these cases, profit maximization is not conducted centrally, but each dealer/operator is engaged in its own profit maximization. Ace Hardware, for instance, is a $13 billion retail cooperative consisting of 4600 independent stores in all 50 US states and 70 other countries (Wikipedia, 2009). For these types of networks, it is not clear whether transshipments lead to increased profits, even for locations with excess inventory. It may be in the best interest of a particular Ace Hardware dealer to not transship inventory to another location with a shortage. The dealer may be able to increase its profits by waiting for consumers, themselves, to switch locations to buy directly from the dealer with surplus inventory. In this paper, we determine the conditions under which a transshipment policy is likely to increase performance in this type of competitive (but potentially cooperative) environment. Conditions examined include the competitive intensity between firms, the relative size of firms, the level of customer service offered, and the variance in demands facing the firms. In particular, we examine how variations in these conditions affect revenues, profits, and inventory levels of firms. Competitive intensity or rivalry among firms is measured by the variable customer's switching rate; the percentage of customers choosing an alternative source of supply when his or her primary supplier is out of stock. Specifically, a higher switching rate implies that firms experience a higher degree of rivalry. One of our major findings is that when rivalry is high, it is generally in the best interests of firms not to engage in transshipments but to let consumers, themselves, switch between locations. On average, firms will save transshipment costs and therefore increase their profits. Following this introduction, Section 2 provides a review of relevant literature on transshipments. Section 3 outlines the modeling framework. The inventory decisions that firms make with and without transshipments are presented in Section 4. A series of numerical examples are developed in Section 5 to illustrate the analytical results. Finally, Section 6 offers conclusions and discusses managerial implications, limitations of the current study, and future research.

The analytical model developed in this paper investigates the practice of transshipments between two competing firms. It contributes to the existing literature on transshipments in several ways. First, previous studies have modeled the performance impacts under various uncertainties, such as demand and lead time variability, and their implications for inventory management. The role of competition between firms has not received much attention. This paper examines inventory replenishment decisions and the application of the transshipment strategy in various competitive environments. The results suggest that the implementation of transshipments may not be cost effective if the firms operate in an environment that allows consumers to easily switch between firms. In such an environment, firms compete more intensely with one another and consumers have less loyalty towards firms, both of which result in a high consumer switching rate. Under this circumstance, it is more cost effective to just allow consumers to switch between competing firms, rather than to implement a costly transshipment program. In other words, it is more desirable for the firms to just allow consumers to “transship themselves!” However, in an environment where there is little switching between consumers among competing firms, they can substantially increase their revenues and profits by implementing a transshipment program. Second, the analysis incorporates the role that transshipment price plays in reallocating the benefits from transshipments between firms. It is found that the use of an appropriate transshipment price is an effective tool for firms to optimize their inventory level decisions and maximize performance improvements from transshipments. In particular, there exists a unique transshipment price that is optimal for both firms when the two firms are identical in market demand and inventory-related cost parameters. However, it is found that when the two firms are not identical, the firm with relatively low penalty costs, or with relatively small demand variance, will prefer a lower transshipment price, and achieve greater benefits from transshipments. Third, implementing transshipments provides differential benefits when firms have asymmetric market demands and switching rates. This result suggests that the practice of transshipments actually enables the firm with smaller mean demand and lower demand variance to “free ride” on the greater amount of inventory that the larger firm holds. Moreover, it shows that at a given transshipment price, the gains from transshipments are greater for the smaller firm whose customers are more likely to switch to its larger rival firm than the other way around. Under the case of asymmetric switching rates between two firms with different demands, the implementation of transshipments is found to be more desirable for the smaller firm as compared to the case where the two firms have identical switching rates. Fourth, the opportunity for such a free ride also exists when two firms target distinct customer service levels by taking different penalty costs. In this case, the low penalty cost firms tends to hold fewer inventories, but can fulfill sales by transshipping goods from the high cost rival, which tends to hold more inventories. As switching rates increases from 0 to 1, both firms with high penalty costs and low penalty costs will obtain less profit improvements from implementing transshipments. More importantly, it becomes more difficult for the two firms to reach a common transshipment price that can provide an equal profit gain for both firms. Under these circumstances, the design of a proper incentive mechanism (e.g., side payments, flexible transshipment price) is needed to make transshipments pay off for both firms. Overall, several factors are found to moderate the performance benefits that firms can achieve from implementing transshipments. These factors include: the rivalry intensity between firms, the transshipment price, the relative cost parameters, and the relative demand variances of firms. We conclude that as long as firms have identical demand variances and cost parameters, they will obtain the same profit increases from implementing transshipments even if they might have different mean demands. Most importantly, it is the difference in demand variance rather than the difference in demand volume that leads to the differential benefits for firms from the implementation of transshipments. The firm with a smaller variance in its demand tends to get greater profit improvements from implementing transshipments, ceteris paribus. In this paper, the consumer's switching rate, product price, and transshipment price are all considered to be exogenous. The use of fixed, constant values for these variables makes analytical solutions tractable and explicable. For future research, the practice of transshipments may be viewed in a multi-stage sequential-game modeling framework. For example, firms make stock level decisions in the first stage; pricing decisions in the second stage; and finally, in the third stage, firms decide whether to implement transshipments, how many products to transship, and at what transshipment price. In such a three-stage game, both the price and inventory decisions could be thought of as endogenous variables, and switching rates need to be considered in determining transshipment price. As well, by incorporating the consumer's utility function into the classic newsvendor model (see Dana and Petruzzi, 2001 as an example), the product pricing decision of firms can be jointly analyzed with their inventory and transshipment decisions from the strategic perspective. Our analysis has other limitations as follows. First, we only consider a two-location newsvendor model with and without transshipments for a single replenishment period. Generalizing the findings from the current paper into a larger system consisting of more than two firms would be necessary. Moreover, it is worthwhile to consider non-stationary demand for competing firms in a multi-period, long-term horizon. In such a framework, the switching customers who are satisfied with the alternative firm are more likely to switch to that firm for their next purchase. Therefore, the competing firms will have interdependent, dynamic demand functions. Last but not least, the analysis developed in this paper relies on a major assumption for consumer switching behavior. According to this assumption, no consumers switch firms when transshipments are implemented in the event of a stockout. However, it would be useful to extend the current model into other more complex, dynamic situations. For instance, consumers might switch before or after the occurrence of transshipments. Since the performance impacts of transshipments are subject to the specification of the sequence of events, it would be important to examine transshipments in other hypothetical settings. Future research should use simulation to quantify the performance impacts from transshipments in a large number of complicated scenarios.