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On the polyhedral structure of a multi-item production planning model with setup times

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  • MILLER, Andrew
  • NEMHAUSER, George
  • SAVELSBERGH, Martin
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    Abstract

    We present and study a mixed integer programming model that arises as a substructure in many industrial applications. This model provides a relaxation of various capacitated production planning problems, more general fixed charge network flow problems, and other structured mixed integer programs. After distinguishing the general case, which is N P-hard, from a polynomially solvable case, we analyze the polyhedral structure of the convex hull of this model, as well as of a strengthened LP relaxation. Among other results, we present valid inequalities that induce facets of the convex hull in the general case. These inequalities suffice to solve this model by linear programming in the polynomially solvable case mentioned above, and they have proven computationally effective in solving capacitated lot-sizing problems (see also Miller et al. [2000a, 2000b]).

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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 2000052.

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    Date of creation: 00 Nov 2000
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    Handle: RePEc:cor:louvco:2000052

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    Keywords: Mixed integer programming; production planning; polyhedral combinatorics; capacitated lot-sizing; fixed charge network flow.;

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