Lot-sizing with stock upper bounds and fixed charges
AbstractHere 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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Bibliographic InfoPaper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2009025.
Date of creation: 01 Apr 2009
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mixed integer programming; discrete lot-sizing; stock fixed costs; mixing sets;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-03-28 (All new papers)
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