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Competition under Time-Varying Demands and Dynamic Lot-Sizing Costs

Awi Federgruen and Joern Meissner
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Awi Federgruen: Graduate School of Business, Columbia University

No MRG/0003, Working Papers from Department of Management Science, Lancaster University

Abstract: We develop a competitive pricing model which combines the complexity of time-varying demand and cost functions and that of scale economies arising from dynamic lot sizing costs. Each firm can replenish inventory in each of the T periods into which the planing horizon is partitioned. Fixed as well as variable procurement costs are incurred for each procurement order, along with inventory carrying costs. Each firm adopts, at the beginning of the planning horizon, a (single) price to be employed throughout the horizon. Based on each period's system of demand equations, these prices determine a time series of demands for each firm, which needs to service them with an optimal corresponding dynamic lot sizing plan. We establish the existence of a price equilibrium and associated optimal dynamic lotsizing plans, under mild conditions and employing a close approximation for the optimal lotsizing costs. We also design efficient procedures to compute the equilibrium prices and dynamic lotsizing plans.

Keywords: equilibrium; price; competition; game theory; inventory models; lot sizing; pricing; supply chain management (search for similar items in EconPapers)
JEL-codes: C61 (search for similar items in EconPapers)
Pages: 37 pages
Date: 2004-06, Revised 2008-05
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Published in Naval Research Logistics Vol 56, No 1 (February 2009), pp 57Ð73.

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