Optimal lot sizing for an unreliable production system based on net present value approach

The paper considers the net present value (NPV) approach to determine the economic manufacturing quantities for an unreliable production system over an infinite planning horizon. The NPV of the expected total cost is obtained under general failure time and general repair time distributions and its asymptotic characteristics are examined by perturbation of the instantaneous discount rate. The criteria for the existence and uniqueness of the optimal production time (lot size) are derived under exponential failure and constant/zero repair time. The performance of the NPV model is compared with the traditional long-run average cost model in terms of the NPV of the expected total cost based on the optimal decisions of the two models. From numerical experiments, it is observed that the decision based on the average cost can be 10% worse than the decision based on the NPV depending upon the machine failure rate.