An evaluation of semidefinite programming based approaches for discrete lot-sizing problems

•We study a lot-sizing problem with sequence-dependent changeover costs and times.•This problem is formulated as a quadratically constrained quadratic binary program.•We compute lower bounds using a semidefinite rather than a linear relaxation.•Comparison with the best known linear relaxations shows...

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Bibliographic Details
Published in:European journal of operational research Vol. 237; no. 2; pp. 498 - 507
Main Authors: Gicquel, C., Lisser, A., Minoux, M.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.09.2014
Elsevier Sequoia S.A
Elsevier
Subjects:
Comparative analysis
Competitive advantage
Computation
Computer programs
Computer Science
Cutting planes
Discrete lot-sizing and scheduling problem
Integer programming
Lower bounds
Manufacturing
Mathematical models
Mathematical problems
Mathematical programming
Operational research
Operations Research
Optimization
Quadratic programming
Quadratically constrained quadratic binary programming
Semidefinite programming
Semidefinite relaxation
Sequence-dependent changeover costs and times
Solution strengthening
Studies
Quadratically constrained quadratic binary programming
Discrete lot-sizing and scheduling problem
Semidefinite relaxation
Manufacturing
Cutting planes
Sequence-dependent changeover costs and times
semidefinite relaxation
manufacturing
quadratically constrained quadratic binary programming
cutting planes
discrete lot-sizing and scheduling problem
sequence-dependent changeover costs and times
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:•We study a lot-sizing problem with sequence-dependent changeover costs and times.•This problem is formulated as a quadratically constrained quadratic binary program.•We compute lower bounds using a semidefinite rather than a linear relaxation.•Comparison with the best known linear relaxations shows a significant improvement.•The SDP relaxation provides the optimal integer value for 83% of the small-size instances. The present work is intended as a first step towards applying semidefinite programming models and tools to discrete lot-sizing problems including sequence-dependent changeover costs and times. Such problems can be formulated as quadratically constrained quadratic binary programs. We investigate several semidefinite relaxations by combining known reformulation techniques recently proposed for generic quadratic binary problems with problem-specific strengthening procedures developed for lot-sizing problems. Our computational results show that the semidefinite relaxations consistently provide lower bounds of significantly improved quality as compared with those provided by the best previously published linear relaxations. In particular, the gap between the semidefinite relaxation and the optimal integer solution value can be closed for a significant proportion of the small-size instances, thus avoiding to resort to a tree search procedure. The reported computation times are significant. However improvements in SDP technology can still be expected in the future, making SDP based approaches to discrete lot-sizing more competitive.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2014.02.027