《2016 An alternative framework to Lagrangian relaxation approach for job shop scheduling》.pdfVIP

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