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Lot-sizing with stock upper bounds and fixed charges

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  • DI SUMMA, Marco
  • WOLSEY, Laurence A.
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    Abstract

    Here we study the discrete lot-sizing problem with an initial stock variable and an associated variable upper bound constraint. This problem is of interest in its own right, and is also a natural relaxation of the constant capacity lot-sizing problem with upper bounds and fixed charges on the stock variables. We show that the convex hull of solutions of the discrete lot-sizing problem is obtained as the intersection of two simpler sets, one involving just 0-1 variables and the second a mixing set with a variable upper bound constraint. For these two sets we derive both inequality descriptions and polynomial-size extended formulations of their respective convex hulls. Finally we carry out some limited computational tests on single-item constant capacity lot-sizing problems with upper bounds and fixed charges on the stock variables in which we use the extended formulations derived above to strengthen the initial mixed integer programming formulations.

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    File URL: http://www.uclouvain.be/cps/ucl/doc/core/documents/coredp2009_25.pdf
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    Bibliographic Info

    Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2009025.

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    Date of creation: 01 Apr 2009
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    Handle: RePEc:cor:louvco:2009025

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    Keywords: mixed integer programming; discrete lot-sizing; stock fixed costs; mixing sets;

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