Abstract
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 sequencing decisions. We first give an effective model for the problem of minimizing F 1 subject to a given F 2 level. We deduce some optimality properties for this problem. Based on these properties, we propose a heuristic algorithm to generate an approximate set of efficient solutions. Our computational results indicate that the proposed algorithm performs better than the GAMS/MINOS commercial solver both in terms of solution quality and computational requirements such that the average CPU time is only 8% of the time required by the GAMS/MINOS.
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