Optimal allocation and processing time decisions on non-identical parallel CNC machines: epsilon-constraint approach

Date

2007-12-01

Author

Gürel, Sinan

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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 E-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.

Subject Keywords

Management Science and Operations Research, Modelling and Simulation, Information Systems and Management

URI

https://hdl.handle.net/11511/36210

Journal

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH

DOI

https://doi.org/10.1016/j.ejor.2006.10.024

Collections

Department of Industrial Engineering, Article

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Considering manufacturing cost and scheduling performance on a CNC turning machine Gürel, Sinan (Elsevier BV, 2007-02-16) A well known industry application that allows controllable processing times is the manufacturing operations on CNC machines. For each turning operation as an example, there is a nonlinear relationship between the manufacturing cost and its required processing time on a CNC turning machine. If we consider total manufacturing cost (F-1) and total weighted completion time (F-2) objectives simultaneously on a single CNC machine, making appropriate processing time decisions is as critical as making job sequencin...
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Citation Formats

S. Gürel, “Optimal allocation and processing time decisions on non-identical parallel CNC machines: epsilon-constraint approach,” EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, pp. 591–607, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36210.