Optimal allocation and processing time decisions on non-identical parallel CNC machines: ε{lunate}-constraint approach
Date
2007-12-01Source Title
European Journal of Operational Research
Print ISSN
0377-2217
Electronic ISSN
1872-6860
Publisher
Elsevier Elsevier
Volume
183
Issue
2
Pages
591 - 607
Language
English
Type
ArticleItem Usage Stats
112
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Abstract
When the processing times of jobs are controllable, selected processing times affect both the manufacturing cost and the
scheduling performance. A well known example for such a case that this paper specifically deals with is the turning operation
on a CNC machine. Manufacturing cost of a turning operation is a nonlinear convex function of its processing time.
In this paper, we deal with making optimal machine-job assignments and processing time decisions so as to minimize total
manufacturing cost while the makespan being upper bounded by a known value, denoted as -constraint approach for a
bicriteria problem. We then give optimality properties for the resulting single criterion problem. We provide alternative
methods to compute cost lower bounds for partial schedules, which are used in developing an exact (branch and bound)
algorithm. For the cases where the exact algorithm is not efficient in terms of computation time, we present a recovering
beam search algorithm equipped with an improvement search procedure. In order to find improving search directions, the
improvement search algorithm uses the proposed cost bounding properties. Computational results show that our lower
bounding methods in branch and bound algorithm achieve a significant reduction in the search tree size that we need
to traverse. Also, our recovering beam search and improvement search heuristics achieve solutions within 1% of the optimum
on the average while they spent much less computational effort than the exact algorithm.
Keywords
SchedulingControllable Processing Times
Manufacturing Cost
Makespan
Non-identical Parallel Machines