Single-Item Dynamic Lot-Sizing Models With Bounded Inventory and Outsourcing

This paper addresses a real-life lot-sizing problem which can be considered a single-item dynamic lot-sizing problem with bounded inventory. The particularity is that the demand of a period can be entirely or partially outsourced with an outsourcing cost. The goal is to minimize the total cost of production, setup, inventory holding, and outsourcing. The cost functions are linear but time-varying. We assume that the unit production cost is constant or nonincreasing over time. The problem is shown to be solvable in a strongly polynomial time with a dynamic-programming approach. The proposed algorithm can solve problems of sizes of up to 400 periods in less than 2 ms on a 1.4-GHz Pentium IV processor.