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Scientific Programming
Volume 2016 (2016), Article ID 5127253, 13 pages
Research Article

Robust Parallel Machine Scheduling Problem with Uncertainties and Sequence-Dependent Setup Time

1Logistics Engineering College, Shanghai Maritime University, Shanghai, China
2Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong

Received 6 September 2016; Accepted 11 October 2016

Academic Editor: Si Zhang

Copyright © 2016 Hongtao Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A parallel machine scheduling problem in plastic production is studied in this paper. In this problem, the processing time and arrival time are uncertain but lie in their respective intervals. In addition, each job must be processed together with a mold while jobs which belong to one family can share the same mold. Therefore, time changing mold is required for two consecutive jobs that belong to different families, which is known as sequence-dependent setup time. This paper aims to identify a robust schedule by min–max regret criterion. It is proved that the scenario incurring maximal regret for each feasible solution lies in finite extreme scenarios. A mixed integer linear programming formulation and an exact algorithm are proposed to solve the problem. Moreover, a modified artificial bee colony algorithm is developed to solve large-scale problems. The performance of the presented algorithm is evaluated through extensive computational experiments and the results show that the proposed algorithm surpasses the exact method in terms of objective value and computational time.