Mathematical models for preemptive shop scheduling problems

被引:7
|
作者
Ebadi, Abbas [1 ]
Moslehi, Ghasem [1 ]
机构
[1] Isfahan Univ Technol, Dept Ind & Syst Engn, Esfahan 8415683111, Iran
关键词
Job shop scheduling problem; Flow shop scheduling problem; Preemption; Integer Linear Programming; FLOWSHOP SEQUENCING PROBLEM; JOBS; FORMULATIONS; NUMBER;
D O I
10.1016/j.cor.2011.09.013
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
More than half a century has passed since Bowman and Dantzig (1959) [13,14] introduced their models for preemptive shop scheduling problems. A more efficient model seems to be needed to address all the aspects involved in the problem. We introduce a new Integer Linear Programming (ILP) formulation as a new method for solving the preemptive Job Shop Scheduling Problem (pJSSP). The dimension of the new model, unlike those of the existing ones, depends solely on the number of jobs and machines irrespective of processing times. The proposed model is used as an optimal, two-phase approach. In phase one, the model is solved to obtain the start and completion times of each operation on each machine. In phase two, a simple algorithm in O(mn log n) steps is used to turn these times into a complete and optimal schedule. Different preemptive flow shop problems are studied as special cases of the pJSSP while some related properties are also discussed. Finally, the higher efficiency of the proposed model is verified both theoretically and computationally through its comparison with conventional methods commonly in use. (C) 2011 Elsevier Ltd. All rights reserved.
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页码:1605 / 1614
页数:10
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