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A study of the lot-sizing polytope

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Abstract.

The lot-sizing polytope is a fundamental structure contained in many practical production planning problems. Here we study this polytope and identify facet–defining inequalities that cut off all fractional extreme points of its linear programming relaxation, as well as liftings from those facets. We give a polynomial–time combinatorial separation algorithm for the inequalities when capacities are constant. We also report computational experiments on solving the lot–sizing problem with varying cost and capacity characteristics.

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Authors and Affiliations

  1. Department of Industrial Engineering and Operations Research, University of California, 4135 Etcheverry Hall, Berkeley CA, 94720–1777, USA

    Alper Atamtürk

  2. Department of Civil and Environmental Engineering, University of California, 416G McLaughlin Hall, Berkeley, CA, 94720–1720, USA Currently in Pontificia Universidad Católica de Chile.

    Juan Carlos Muñoz

Authors
  1. Alper Atamtürk
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  2. Juan Carlos Muñoz
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Correspondence to Alper Atamtürk.

Additional information

Supported, in part, by NSF Grants 0070127 and 0218265, and a grant from ILOG, Inc.

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Atamtürk, A., Muñoz, J. A study of the lot-sizing polytope. Math. Program., Ser. A 99, 443–465 (2004). https://doi.org/10.1007/s10107-003-0465-8

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  • DOI: https://doi.org/10.1007/s10107-003-0465-8

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