Lagrangian bounds for just-in-time job-shop scheduling

Lagrangian bounds for just-in-time job-shop scheduling

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Article ID: iaor2009974
Country: United Kingdom
Volume: 35
Issue: 3
Start Page Number: 906
End Page Number: 915
Publication Date: Mar 2008
Journal: Computers and Operations Research
Authors: , ,
Keywords: production: JIT, heuristics, heuristics: local search, lagrange multipliers
Abstract:

We study the job-shop scheduling problem with earliness and tardiness penalties. We describe two Lagrangian relaxations of the problem. The first one is based on the relaxation of precedence constraints while the second one is based on the relaxation of machine constraints. We introduce dedicated algorithms to solve the corresponding dual problems. The second one is solved by a simple dynamic programming algorithm while the first one requires the resolution of an NP-hard problem by branch and bound. In both cases, the relaxations allow us to derive lower bounds as well as heuristic solutions. We finally introduce a simple local search algorithm to improve the best solution found. Computational results are reported.

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