A permutation flow-shop scheduling problem wth convex models of operation processing times

A permutation flow-shop scheduling problem wth convex models of operation processing times

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Article ID: iaor20011760
Country: Netherlands
Volume: 96
Issue: 1
Start Page Number: 39
End Page Number: 60
Publication Date: Nov 2000
Journal: Annals of Operations Research
Authors: ,
Keywords: flowshop
Abstract:

The paper is an extension of the classical permutation flow-shop scheduling problem to the case where some of the job operation processing times are convex decreasing functions of the amounts of resources (e.g., financial outlay, energy, raw material) allocated to the operations (or machines on which they are performed). Some precedence constraints among the jobs are given. For this extended permutation flow-shop problem, the objective is to find a processing order of the jobs (which will be the same on each machine) and an allocation of a constrained resource so as to minimize the duration required to complete all jobs (i.e., the makespan). A computational complexity analysis of the problem shows that the problem is NP-hard. An analysis of the structure of the optimal solutions provides some elimination properties, which are exploited in a branch-and-bound solution scheme. Three approximate algorithms, together with the results of some computational experiments conducted to test the effectiveness of the algorithms, are also presented.

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