Competition under capacitated dynamic lot‐sizing with capacity acquisition

Lot‐sizing and capacity planning are important supply chain decisions, and competition and cooperation affect the performance of these decisions. In this paper, we look into the dynamic lot‐sizing and resource competition problem of an industry consisting of multiple firms. A capacity competition model combining the complexity of time‐varying demand with cost functions and economies of scale arising from dynamic lot‐sizing costs is developed. Each firm can replenish inventory 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 constant 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.