Competition under Capacitated Dynamic Lot Sizing with Capacity Acquisition

Hongyan Li, Joern Meissner

Abstract Lot-sizing and capacity planning are important supply chain decisions, and com- petition and cooperation affect the performance of these decisions. In this paper, we look into the dynamic lot sizing and resource competition problem of an in- dustry consisting of multiple firms. A capacity competition model combining the complexity of time-varying demand with cost functions and economies os scale arising from dynamic lot-sizing costs is developed. Each firm can replenish inven- tory at the beginning of each period in a finite planning horizon. Fixed as well as variable production costs incur for each production setup, along with inventory carrying costs. The individual production lots of each firm are limited by a con- stant capacity restriction, which is purchased up front for the planning horizon. The capacity can be purchased from a spot market, and the capacity acquisition cost fluctuates with the total capacity demand of all the competing firms. We solve the competition model and establish the existence of a capacity equilibrium over the firms and the associated optimal dynamic lot-sizing plan for each firm under mild conditions.
Keywords

Game theory, Capacity optimization, Competition, Lot sizing, Equilibrium

Status Working Paper
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