Inventory allocation with full downward substitution and monotone cost differences

Abstract

We study a single-period multi-product inventory allocation problem with full downward substitution and monotone cost differences. The cost structure with monotone differences is more general than the additive cost structure usually assumed in literature. Using the notion of Monge sequences, we identify conditions under which the problem can be solved efficiently using greedy allocation. For problems that do not meet these conditions, we develop an efficient algorithm that solves the problem to optimality. For this specific problem, our algorithm has substantially lower computational complexity than existing efficient algorithms for the more general transportation problem; we numerically confirm this superior computational efficiency and illustrate the importance of using efficient algorithms at the allocation stage of the inventory management problem.