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《2016 Lagrangian bounds for just-in-time job-shop scheduling 》.pdf
Computers Operations Research 35 (2008) 906–915
/locate/cor
Lagrangian bounds for just-in-time job-shop scheduling
Philippe Baptistea ,∗, Marta Flaminib , Francis Sourdc
a CNRS LIX laboratory, Ecole Polytechnique, Palaiseau, France
bDipartimento di Informatica e Automazione, University Roma 3, Italy
c CNRS LIP6 laboratory, Paris, France
Available online 11 July 2006
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.
2006 Elsevier Ltd. All rights reserved.
Keywords: Job-shop scheduling; Earliness-tardiness; Lagrangian relaxation
1. Introduction
The importance of “just-in-time” inventory management in industry has motivated the study of theoretical scheduling
models that capture the main features of this philosophy.Among these models, a lot of research effort has been devoted to
earliness–tardiness problems—where both early completion (which results in the ne
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