Partial objective inequalities for the multi-item capacitated lot-sizing problem

Document Type

Article

Publication Date

3-1-2018

Abstract

In this paper, we study a mixed-integer programming model of the single-level multi-item capacitated lot-sizing problem (MCLSP), which incorporates shared capacity on the production of items for each period throughout a planning horizon. We derive valid bounds on the partial objective function of the MCLSP formulation by solving the first t periods of the problem over a subset of all items, using dynamic programming and integer programming techniques. We also develop algorithms for strengthening these valid inequalities by back-lifting techniques. These inequalities can be utilized within a cutting-plane algorithm, in which we perturb the partial objective function coefficients to identify violated inequalities to the MCLSP polytope. Our computational results show that the envelope inequalities are very effective for the MCLSP instances with different capacity and cost characteristics, when compared to the (l, S) inequalities.

Identifier

85034966328 (Scopus)

Publication Title

Computers and Operations Research

External Full Text Location

https://doi.org/10.1016/j.cor.2017.11.006

ISSN

03050548

First Page

132

Last Page

144

Volume

91

Grant

CBET-1554018

Fund Ref

National Science Foundation

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