Optimal machining conditions with dual criteria and applications to scheduling

Abstract

A bicriterion machining economics problem is presented, considering the minimization of the unit production cost and the maximization of the production rate. The bicriterion machining time is first defined as a weighted average of the maximum production rate machining time and of the minimum unit cost machining time using a weighted-sums technique and an arbitrary weighting factor. Then using a vector-maximum approach, a bicriterion machining lime is defined through the introduction of an optimal weighting factor. This weighting factor reflects the relative importance of the two criteria and it is a function of the delay time cost, that is, the cost associated with the difference in actual processing times between the two criteria. It is shown that the vector-maximum approach outperforms the weighting-sums technique. Furthermore, the bicriterion machining lime leans towards the maximum production rate machining time as the delay time cost increases. It is also shown that the actual processing time is proportional to a machining constant regardless of the objective function utilized when tools with similar characteristics are used. Based upon this finding the mean flowtime can be minimized by processing the parts in ascending order of the machining constant values.