Summary: OPERATIONS RESEARCH
Vol. 53, No. 4, JulyAugust 2005, pp. 711730
issn 0030-364X eissn 1526-5463 05 5304 0711
© 2005 INFORMS
Lot Sizing with Inventory Bounds and Fixed Costs:
Polyhedral Study and Computation
Alper Atamtürk, Simge Küçükyavuz
Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 947201777
We investigate the polyhedral structure of the lot-sizing problem with inventory bounds. We consider two models, one
with linear cost 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 bounds explicitly and give exact separation algorithms. We also
describe a linear programming formulation of the problem when the order and inventory 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.
Subject classifications: lot sizing; facets; separation algorithms; computation.
Area of review: Optimization.
History: Received July 2003; revision received February 2004; accepted July 2004.