Competition under Dynamic Lot Sizing Costs with Capacity Acquisition

Hongyan Li, Joern Meissner

Abstract We develop a competitive supply chain model which combines the complexity of timevarying demand and cost functions and that of scale economies arising from dynamic lotsizing costs. Each firm can replenish inventory in each of the T periods into which the planning horizon is partitioned. Fixed as well as variable procurement costs are incurred for each procurement order, along with inventory carrying costs. The individual orders are limited by a capacity restriction. The underlying capacity must be purchased up front. Each firm determines, at the beginning of the planning horizon, the capacity to be purchased and the optimal replenishing plan throughout the horizon. Based on the capacity demand for the competing firms, a market price is determined for the capacity acquisition. This procedure is repeated every selling season. We establish the existence of an equilibrium and associated optimal dynamic lot-sizing plans, under mild conditions. We also design efficient procedures to compute the equilibrium capacities and dynamic lot-sizing plans.
Keywords

Game theory, Capacity optimization, Supply chain management, Lot sizing, Heuristics

Status Working Paper
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