Capacity allocation with minimum order quantity: Fixed allocation and turn-and-earn allocation

Abstract

We consider a two-stage supply chain consisted of one supplier and two retailers in a two-period selling, where retailers compete for limited capacity, and the supplier adopts both a minimum order quantity contract and allocation mechanisms during dealing with retailers. In this study, we solve the equilibrium order quantities of retailers in the presence of the minimum order quantity under fixed and turn-and-earn allocations by game theory. Further, we compare two allocations on inducing the downstream order, and explore the impact of the minimum order quantity on retailers’ ordering decisions as well as the supply chain profit. We find that turn-and-earn allocation induces more order quantity in low demand state than fixed allocation. Moreover, compared to the case without the minimum order quantity, when the minimum order quantity is on a certain interval, it can help shrink the gap of equilibrium order quantities between turn-and-earn allocation and fixed allocation in the first period. Besides, under the two allocation mechanisms, the profits of the supplier and the supply chain are both non-decreasing while each retailer’s profit is non-increasing with the minimum order quantity. Last, in the extension of allocation mechanisms by involving inventory, both the first period order quantity and selling quantity under turn-and-earn allocation are still more than that under fixed allocation, when capacity is large.