Exact formulation of stochastic EMQ model for an unreliable production system

The purpose of this paper is to present an exact formulation of stochastic EMQ model for an unreliable production system under a general framework in which the time to machine failure, corrective (emergency) and preventive (regular) repair times are assumed to be random variables. For exact financial implications of the lot-sizing decisions, the EMQ model is formulated based on the net present value (NPV) approach. Then, by taking limitation on the discount rate, the traditional long-run average cost model is obtained. The criteria for the existence and uniqueness of the optimal production time in both the models are derived under general failure and specific repair time distributions. Numerical examples are devoted to find the optimal production policies of the developed models and examine the sensitivity of the parameters involved. Computational results show that the optimal decision based on the NPV approach is superior to that based on the long-run average cost approach, though the performance level strongly depends on the pertinent failure and repair time distributions.