Formulations and heuristics for the multi-item uncapacitated lot-sizing problem with inventory bounds

Rafael A. Melo and Celso C. Ribeiro

International Journal of Production Research, 2017, vol. 55, issue 2, 576-592

Abstract: We consider the multi-item uncapacitated lot-sizing problem with inventory bounds, in which a production plan for multiple items has to be determined considering that they share a storage capacity. We present (a) a shortest path formulation and (b) a formulation based on the a priori addition of valid inequalities, which are compared with a facility location formulation available in the literature. Two easy-to-implement mixed integer programming heuristic frameworks are also presented, (a) a rounding scheme and (b) a relax-and-fix approach performed in a time partitioning fashion. Computational experiments are performed to evaluate the different approaches. The numerical results show that the proposed relax-and-fix heuristic outperforms all other approaches. Its solutions are within 4.0% of optimality in less than 10 minutes of running time for all tested instances, with mean gaps in the order of 2.1 and 1.8% for instances with more relaxed and tighter capacities, respectively. The obtained solutions were always better than those obtained by a commercial MIP solver running for one hour using any of the available formulations.

Date: 2017
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Citations: View citations in EconPapers (4)

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DOI: 10.1080/00207543.2016.1215567

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