Allocating Capacity with Demand Competition: Fixed Factor Allocation *

We consider a supply chain consisting of a supplier and two retailers. The supplier sells a single product to the retailers, who, in turn, retail the product to customers. The supplier has limited production capacity, and the retailers compete for the supplier's capacity and are duopolists engaged in Cournot competition for their customers. When the sum of the retailers' orders exceeds the supplier's capacity, the supplier allocates his capacity according to a preannounced allocation rule. We propose a new capacity allocation rule, fixed factor allocation, which incorporates the ideas of proportional and lexicographic allocations: it prioritizes retailers as in lexicographic allocation, but guarantees only a fixed proportion of the total available capacity to the prioritized retailer. We show that (1) the fixed factor allocation rule incorporates lexicographic and proportional allocations from the perspectives of the supplier and the supply chain; (2) under fixed factor allocation, the supply chain profit is not affected by the allocation factor when it is greater than a threshold; (3) the retailers share the supply chain profit with the supplier depending on the value of the allocation factor; and (4) the fixed factor allocation coordinates the supply chain when the market size is sufficiently large. We also compare fixed factor with proportional and lexicographic allocations, respectively. Furthermore, we demonstrate how the supplier can optimize his capacity level and wholesale price under fixed factor allocation.