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Lot Sizing with Inventory Bounds and Fixed Costs: Polyhedral Study and Computation

Alper Atamturk (atamturk***at***ieor.berkeley.edu)
Simge Kucukyavuz (simge***at***ieor.berkeley.edu)

Abstract: We investigate the polyhedral structure of the lot-sizing problem with inventory bounds. We consider two models, one with linear costs on inventory, the other with linear and fixed costs on inventory. For both models, we identify facet-defining inequalities that make use of the inventory capacities explicitly and give exact separation algorithms. We also give a linear programming formulation of the problem when the order and inventory variable costs satisfy the Wagner-Whitin nonspeculative property. We present computational experiments that show the effectiveness of the results in tightening the linear programming relaxations of the lot-sizing problem with inventory bounds and fixed costs.

Keywords: Lot sizing, facets, separation algorithms, computation.

Category 1: Applications -- OR and Management Sciences (Production and Logistics )

Category 2: Integer Programming (Cutting Plane Approaches )

Citation: Operations Research 53, 711-730, 2005


Entry Submitted: 07/15/2003
Entry Accepted: 07/15/2003
Entry Last Modified: 04/15/2008

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