A Production and Maintenance Planning Model with Restoration Cost Dependent on Detection Delay

In this paper, the joint problem of production planning and maintenance schedule is studied under the realistic assumption that the cost of process restoration is a function of the detection delay and the existence of shortages in the system. The detection delay is defined as the elapsed time since the production process has deteriorated until it is identified by some inspection procedure and repaired. Since production planning and maintenance problems have usually been studied as separate problems, this paper is an attempt to develop a formal framework for the joint problem. We have developed sufficient conditions for the optimality of the commonly used equal-interval maintenance schedule. The conditions are found to be a function of parameters such as the cost of defective items, the mean time for system deterioration, and the form of the restoration cost function. For specific restoration cost functions such as linear and exponential, an efficient solution procedure is presented for the simultaneous determination of the number of maintenance inspections in a production run, the length of the production run and consequently the economic manufacturing quantity, and the maximum level of backorders. A numerical example illustrates the use of this procedure and the differences between the optimal cost obtained by this procedure and the cost obtained by using the classical economic manufacturing quantity model.