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A strong preemptive relaxation for weighted tardiness and earliness/tardiness problems on unrelated parallel machines

Şen, Halil and Bülbül, Kerem (2015) A strong preemptive relaxation for weighted tardiness and earliness/tardiness problems on unrelated parallel machines. Informs Journal on Computing, 27 (1). pp. 135-150. ISSN 1091-9856 (Print) 1526-5528 (Online)

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Official URL: http://dx.doi.org/10.1287/ijoc.2014.0615

Abstract

Research on due date-oriented objectives in the parallel machine environment is at best scarce compared to objectives such as minimizing the makespan or the completion time-related performance measures. Moreover, almost all existing work in this area is focused on the identical parallel machine environment. In this study, we leverage on our previous work on the single machine total weighted tardiness (TWT) and total weighted earliness/tardiness (TWET) problems and develop a new preemptive relaxation for both problems on a bank of unrelated parallel machines. The key contribution of this paper is devising a computationally effective Benders decomposition algorithm to solve the preemptive relaxation formulated as a mixed-integer linear program. The optimal solution of the preemptive relaxation provides a tight lower bound. Moreover, it offers a near-optimal partition of the jobs to the machines. We then exploit recent advances in solving the nonpreemptive single-machine TWT and TWET problems for constructing nonpreemptive solutions of high quality to the original problem. We demonstrate the effectiveness of our approach with instances of up to five machines and 200 jobs.

Item Type:Article
Uncontrolled Keywords:unrelated parallel machines; weighted tardiness; weighted earliness and tardiness; preemptive relaxation; Benders decomposition; transportation problem; lower bound; heuristic
Subjects:T Technology > T Technology (General) > T055.4-60.8 Industrial engineering. Management engineering
T Technology > T Technology (General) > T055.4-60.8 Industrial engineering. Management engineering > T57.6-57.97 Operations research. Systems analysis
ID Code:26908
Deposited By:Kerem Bülbül
Deposited On:16 May 2015 21:07
Last Modified:16 May 2015 21:07

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