A General EMQ Model with Machine Breakdowns and Two Types of Failure

In this paper, we consider a production-inventory control problem for an Economic Manufacturing Quantity (EMQ) model with machine breakdowns and planned preventive replacement (overhaul) of the production unit. Two types of failure are considered. When type I failure occurs (major failure), the unit is replaced by a new one and the interrupted lot is aborted. Starting a new lot after a replacement or after a complete production run incurs a setup cost. Type II failures (minor failures) are corrected by minimal repairs which take negligible time. After performing a minimal repair, production can be resumed immediately at a cost lower than the setup cost. It is assumed that both preventive and failure replacement times are random and the demand that cannot be satisfied during these replacement times is lost.The objective is to determine the lot sizing and preventive replacement policy minimizing the long-run expected average cost per unit time. The structure of the optimal policy is found by formulating and analyzing the problem in the framework of the semi-Markov decision processes. It is shown that if the replacement times are negligible, the optimal preventive replacement is the age replacement and the optimum lot size is a function of the age of the production unit. The EMQ model with lost sales is studied under the assumption of a constant production lot size. The formula for the expected average cost is obtained in the general case and analyzed under certain assumptions. A special case is discussed and numerical results are provided.