A stochastic lot sizing model with partial backordering and imperfect production processes

This research presents an inventory system with partial backordering and imperfect process with a stochastic numbers of products that are defective per order. This problem is known and there are some customers that do not wait for their orders to be fulfilled so a particular proportion of backordered items become lost sales. This paper considers both mentioned situations simultaneously while the number of defective items follows a uniform distribution and the proportion of backordering is constant. This condition is modelled. The cost function of this inventory model includes order cost, holding cost and two types of shortage costs, one of them is related to backordered items and the other one is related to lost sales. This paper also provides a solution method to obtain optimum values for the decision variables, order quantity and total shortage, then we derive the value of the total cost function according to the optimum values obtained for the decision variables. Finally, some numerical results and diagrams are provided to show how some parameters affect the values of the decision variables and the cost function.