The Optimal Number of Machines to be Operated by a Single Worker : 1st Report, The Condition for the Existence of the Optimal Number

Abstract

This paper considers a man-machine system consisting of some numerically -controlled (NC) machines and a single worker. This system processed many kinds of items. The role of worker is loading the workpieces on and unloading the workpieces from machines. In such a system design, it is an important problem to determine the number of machine5 to be operated by the worker. First. we formulate the system as a stochastic model to analyze the above optimal problem. The desicion variable is the number of machines and the optimal criteria are 'the maximum production rate', 'the minimum total cost', 'the maximum profit rate' and 'the maximum return's rate of operating cost'. It is shown that the optimal numbers under these criteria depend on only the utilization of the worker. and hence the minimum total cost, and the maximum return's rate criteria are the same. It is proved that there exist the optimal numbers under these criteria if the worker's utilization is a concave function of the number of machines used. Furthermore, an ordering between the optimal numbers under the minimum total cost and the maximum profit rate criteria is suggested theoretically. The validity of the concavity and the ordering is established by many numerical experiments. The applicability of the results to practical problem is discussed via a case study.