Distribution-Free Models for Machine Interference Problems

Abstract

This paper presents binomial and multinomial models for special cases of the machine interference problem (MIP), where a production system consists of one or several groups of identical machines. All the machines produce the same product in parallel and independently of each other. Each machine randomly requests several different service types. The service is provided by a group of operators such that one operator can provide only one service type. The presented models allow the calculation of the expected interference time in the queue for each service type, depending on the number of operators. The key point is the fact that the proposed models do not use any restrictive assumptions about failure rate and service distribution, as the Markovian models. The expected interference times attained by utilization of the proposed models enable practitioners to determine the optimal number of operators in order to minimize the manufacturing cost per unit of product or maximize the total profit, or to set other performance measures.