《2016 An alternative framework to Lagrangian relaxation approach for job shop scheduling》.pdf
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《2016 An alternative framework to Lagrangian relaxation approach for job shop scheduling》.pdf
European Journal of Operational Research 149 (2003) 499–512
/locate/dsw
Discrete Optimization
An alternative framework to Lagrangian relaxation
approach for job shop scheduling
Haoxun Chen * ,Peter B. Luh
Department of Electrical and Computer Engineering, University of Connecticut, Storrs, CT 06269, USA
Received 9 May 2000; accepted 8 May 2002
Abstract
A new Lagrangian relaxation (LR) approach is developed for job shop scheduling problems. In the approach
operation precedence constraints rather than machine capacity constraints are relaxed. The relaxed problem is de-
composed into single or parallel machine scheduling subproblems. These subproblems ,which are NP-complete in
general ,are approximately solved by using fast heuristic algorithms. The dual problem is solved by using a recently
developed ‘‘surrogate subgradient method’’ that allows approximate optimization of the subproblems. Since the al-
gorithms for subproblems do not depend on the time horizon of the scheduling problems and are very fast ,our new LR
approach is efficient ,particularly for large problems with long time horizons. For these problems ,the machine de-
composition-based LR approach requires much less memory and computation time as compared to a part decom-
position-based approach as demonstrated by numerical testing.
2002 Elsevier Science B.V. All rights reserved.
Keywords: Scheduling; Job shops; Lagrangian relaxation; Manufacturing systems
1. Introduction
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