The recent advances in manufacturing systems motivate several studies to focus on Economic Production Quantity (EPQ) problem. Althuogh there are several extentions to the EPQ, this paper provides a new extension by considering some of the real world parameters like: (a) shortages in the form of partial backordering, (b) inventory can deteriorate stochastically, (c) machine can break down stochastically, and (d) machine repair time may change stochastically based on the failure status of machine. As far as we know, there is no study treated all these suppositions in an EPQ framework. In addition to this development, two forms of uniformly- and exponentially-distributed repair times are formulated and necessary convexity conditions are discussed. Then, the corresponding optimality conditions are written that lead to finding the roots of two equations. Due to difficulty of achieving a closed-form solution, the solution is obtained numerically by means of Newton-Raphson method. Finally, some sensitivity analyses are provided to explain the models’ applicability. The practicality and efficiency of the proposed method in this context lends weight to development of proposed EPQ with more complex elements and its application more broadly.

In this paper, we develop an economic production quantity (EPQ) model under machine breakdown and two types of repair (corrective and preventive). also, study the simultaneous effect of holding safety stock and purchasing policy. In order to avoid shortages occurring as a result of the Random repair time, in addition to keep safety stock, we suppose that the manufacturer could purchase some quantities from an external supplier. This paper addresses the following question: how the manufacturer determine the optimal values of safety stock, production and purchasing lot sizes, simultaneously, to minimize the expected total cost? The introduced model is then compared with the situations in which the manufacturer only keeps safety stock or just uses an external supplier, respectively. The results through the analysis show that using the simultaneous policy when the system is prone to shortages due to long repair times, have more improvement in the performance of the system rather than using the safety stock or purchasing policies, separately.