An exact extended formulation for the unrelated parallel machine total weighted completion time problem

The plethora of research on NP -hard parallel machine scheduling problems is focused on heuristics due to the theoretically and practically challenging nature of these problems. Only a handful of exact approaches are available in the literature, and most of these suffer from scalability issues. More...

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Bibliographic Details
Published inJournal of scheduling Vol. 20; no. 4; pp. 373 - 389
Main Authors Bülbül, Kerem, Sen, Halil
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2017
Springer Nature B.V
Subjects
Artificial Intelligence
Benders decomposition
Business and Management
Calculus of Variations and Optimal Control; Optimization
Completion time
Integer programming
Iterative algorithms
Iterative methods
Job shops
Linear programming
Mixed integer
Operations Research/Decision Theory
Optimization
Preempting
Production scheduling
Scheduling
Supply Chain Management
Transportation problem
Benders decomposition
Cut strengthening
Unrelated parallel machines
Exact method
Weighted completion time
Preemptive relaxation
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Summary:The plethora of research on NP -hard parallel machine scheduling problems is focused on heuristics due to the theoretically and practically challenging nature of these problems. Only a handful of exact approaches are available in the literature, and most of these suffer from scalability issues. Moreover, the majority of the papers on the subject are restricted to the identical parallel machine scheduling environment. In this context, the main contribution of this work is to recognize and prove that a particular preemptive relaxation for the problem of minimizing the total weighted completion time (TWCT) on a set of unrelated parallel machines naturally admits a non-preemptive optimal solution and gives rise to an exact mixed integer linear programming formulation of the problem. Furthermore, we exploit the structural properties of TWCT and attain a very fast and scalable exact Benders decomposition-based algorithm for solving this formulation. Computationally, our approach holds great promise and may even be embedded into iterative algorithms for more complex shop scheduling problems as instances with up to 1000 jobs and 8 machines are solved to optimality within a few seconds.
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ISSN:1094-6136
1099-1425
DOI:10.1007/s10951-016-0485-x