Dual-supply inventory problem with capacity limits on order sizes and unrestricted ordering costs

Abstract

This paper considers a single-product dual-supply problem under a periodically reviewed, finite planning horizon. The downstream party, the manufacturer, is supplied by two upstream parties, local and global suppliers, with consecutive leadtimes. Both suppliers place per period minimum and maximum capacity limits on the manufacturer's orders. It is shown that a two-level modified base stock policy is optimal without any restrictions on the ordering costs. Using various analytical results, it is illustrated how the optimal policy parameters change as a function of the problem parameters. To prove the analytical results, a new functional property—bounded increasing [decreasing] differences—which is a subset of the increasing [decreasing] differences property commonly used in the literature is introduced. Numerical analyses are used to explain the trade-offs between complementary services in terms of prices, leadtimes and order capacity limits. For example, it is shown that the manufacturer follows different strategies for different product types: for inventory-cost-driven products, she relies on the local supplier to keep her supply chain responsive. Furthermore, the manufacturer procures from the local supplier as part of a balanced supply portfolio, i.e., orders from the local supplier are not limited to emergency situations. This role of the local supplier diminishes, however, as the leadtime increases. It is also found that increases in minimum capacity limits are generally more favorable to the local supplier. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resources: Appendix with additional proofs and further details of numerical analysis.]