Fixed allocation of capacity for multiple retailers under demand competition

Abstract

We consider a supply chain consisting of one supplier and multiple retailers, in which the supplier has limited capacity and sells one product to retailers engaged in demand competition. When the retailers’ total order quantity exceeds the supplier’s capacity, the supplier implements a preannounced allocation mechanism to fulfill part of the retailers’ orders. We examine a general fixed allocation mechanism with a guaranteed proportion of capacity allocated to each retailer and recognize the retailers’ equilibrium order quantities and the supplier’s optimal pricing strategy under this fixed allocation. We also analyze the impacts of fixed proportions on different supply chain members’ optimal decisions and profits. We find that when at least two fixed proportions differ, or all fixed proportions are identical with only part of capacity guaranteed, fixed allocation induces order inflation, which benefits the supplier. We also demonstrate that fixed allocation is equivalent to proportional allocation under multiple vectors of fixed proportions, by comparing fixed and proportional allocations in terms of the supplier’s optimal price and the supply chain members’ profits. Moreover, we find that fixed allocation can approximately coordinate the supply chain when the number of retailers is sufficiently large. Last, with capacity hoarding in consideration, retailers would hold inventory without using it under fixed allocation, which benefits the supplier.