Existence of Coordinating Transshipment Prices in a Two-Location Inventory Model

Abstract

We consider a two-location production/inventory model where each location makes production decisions and is subject to uncertain capacity. Each location optimizes its own profits. Transshipment (at a cost) is allowed from one location to another. We focus on the question of whether one can globally set a pair of coordinating transshipment prices, i.e., payments that each party has to make to the other for the transshipped goods, that induce the local decision makers to make inventory and transshipment decisions that are globally optimal. A recent paper suggests, for a special case of our model, that there always exists a unique pair of coordinating transshipment prices. We demonstrate through a counterexample that this statement is not correct and derive sufficient and necessary conditions under which it would hold. We show that in some conditions, coordinating prices may exist for only a narrow range of problem parameters and explore conditions when this can happen. Finally, we study the effects of demand and capacity variability on the magnitude of coordinating transshipment prices.supply chain, uncertain capacity, coordination

Managing transshipments in a multi-retailer system with approximate policies

“…Das (1975) extends the model of Gross (1963) by allowing transshipment in the middle of each period for the redistribution of inventories. In many follow-up studies with similar one-time transshipment opportunity models, the transshipments are analysed in terms of their effect on stocking decisions either in centrally (Robinson, 1990;Tagaras and Cohen, 1992) or decentrally managed settings (Hu et al, 2007;Zhao and Atkins, 2009).…”

“…Using a cooperative game framework, Huang and Sošić (2010) compare the performances of profit allocations and constant transshipment prices to coordinate retailers' decisions. Hu et al (2007) derive conditions for the existence of coordinating transshipment prices. Rong et al (2010) conclude that with the preventive transshipments, there are no coordinating transshipment prices.…”

The transshipment fund mechanism: Coordinating the decentralized multilocation transshipment problem

“…As mentioned in the Introduction, these problems exist even for two retailers [11]. First, because each of the retailers cares about the transshipment payment arrangement with the transshipment fund and not about arrangements with the other retailers, this separation is potentially useful in solving transshipment incentive conflicts.…”

“…For each value of τ 12 , Fig. 2 plots the range of possible net transshipment prices c is − c sj paid by the transshipment fund, as implied by the necessary and sufficient conditions (11) and (12). The figure shows the maximal and minimal net transshipment prices for various sets of coordinating transshipment payments.…”

“…Hu et al [11] show with a counter example that such coordinating prices do not always exist and demonstrate this limitation for a wide range of instances. They analyze conditions under which coordinating unit transshipment prices exist in a similar system with uncertain production capacity and conclude that "further research is needed to develop implementable transshipment pricing schedules that achieve coordination in a wider range of situations".…”