An Extension to the Economic Production Quantity Problem with Deteriorating Products Considering Random Machine Breakdown and Stochastic Repair Time

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.