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

Andrew Miller, George Nemhauser and Martin Savelsbergh

No 2000052, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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]).

Keywords: Mixed integer programming; production planning; polyhedral combinatorics; capacitated lot-sizing; fixed charge network flow. (search for similar items in EconPapers)
Date: 2000-11
References: Add references at CitEc
Citations:

Downloads: (external link)
https://sites.uclouvain.be/core/publications/coredp/coredp2000.html (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cor:louvco:2000052

Access Statistics for this paper

More papers in LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) Voie du Roman Pays 34, 1348 Louvain-la-Neuve (Belgium). Contact information at EDIRC.
Bibliographic data for series maintained by Alain GILLIS ().