A permutation flow-shop scheduling problem with convex models of operation processing times |
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Authors: | TCE Cheng A Janiak |
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Institution: | (1) Office of the Vice-President (Research & Postgraduate Studies), The Hong Kong Polytechnic University, Kowloon, Hong Kong;(2) Institute of Engineering Cybernetics, Wroclaw University of Technology, Janiszewskiego 11/17, 50 372 Wrocław, Poland |
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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.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | |
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