Joint determination of purchasing and production lot sizes in an unreliable production system

This paper discusses a production-inventory system under random machine breakdown. Holding safety stock is the common way to mitigate the effect of random machine breakdown on shortages that may occur during machine repair time. Since holding safety stock can be costly, especially for expensive products, this paper investigates an alternative strategy in which it is assumed that the production manager can purchase the same products from a supplier in order to meet the demands that may be lost due to the depletion of the inventory after the machine breakdown. The supplier has known lead-time and reliability with the quality assured products. Despite holding safety stock, purchasing occurs only when the machine breakdown happens. The question is about the optimal amount of production and purchasing lot sizes to minimize the total expected costs. The optimality of the model is investigated when failure and repair time follow an exponential distribution, and a computational algorithm for finding the optimal lot sizes is presented. A comparison between the purchasing strategy and holding safety stock is performed through a sensitivity analysis regarding some effective parameters. This study shows using the purchasing strategy when holding or production cost rises is more beneficial than holding safety stock.