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A polyhedral approach to a production planning problem

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  • Miguel Constantino

Abstract

Production planning in manufacturing industries is concerned with the determination of the production quantities (lot sizes) of some items over a time horizon, in order to satisfy the demand with minimum cost, subject to some production constraints. In general, production planning problems become harder when different types of constraints are present, such as capacity constraints, minimum lot sizes, changeover times, among others. Models incorporating some of these constraints yield, in general, NP-hard problems. We consider a single-machine, multi-item lot-sizing problem, with those difficult characteristics. There is a natural mixed integer programming formulation for this problem. However, the bounds given by linear relaxation are in general weak, so solving this problem by LP based branch and bound is inefficient. In order to improve the LP bounds, we strengthen the formulation by adding cutting planes. Several families of valid inequalities for the set of feasible solutions are derived, and the corresponding separation problems are addressed. The result is a branch and cut algorithm, which is able to solve some real life instances with 5 items and up to 36 periods. Copyright Kluwer Academic Publishers 2000

Suggested Citation

  • Miguel Constantino, 2000. "A polyhedral approach to a production planning problem," Annals of Operations Research, Springer, vol. 96(1), pages 75-95, November.
    • Handle: RePEc:spr:annopr:v:96:y:2000:i:1:p:75-95:10.1023/a:1018963805173
    DOI: 10.1023/A:1018963805173
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    Cited by:

    1. Karina Copil & Martin Wörbelauer & Herbert Meyr & Horst Tempelmeier, 2017. "Simultaneous lotsizing and scheduling problems: a classification and review of models," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 1-64, January.
    2. Bernardo Almada-Lobo & Diego Klabjan & Maria Carravilla & José Oliveira, 2010. "Multiple machine continuous setup lotsizing with sequence-dependent setups," Computational Optimization and Applications, Springer, vol. 47(3), pages 529-552, November.
    3. Gruson, Matthieu & Cordeau, Jean-François & Jans, Raf, 2018. "The impact of service level constraints in deterministic lot sizing with backlogging," Omega, Elsevier, vol. 79(C), pages 91-103.

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