Stochastic demand of production-inventory system with shortage

We consider the stochastic demand of an inventory system with defective items and the weekly demand, according to the Poisson process. Our objective is to formulate a Markov decision model to minimize the total expected cost, which includes production, holding, defective, and shortage. Markov decision model is formulated to describe the stochastic demand. Also, we show two strategies for disposal of defective items; the first one at the end of the week, and the second one continues during the week. The production rate represents a function of inventory, which has limited capacity. The results show a decrease in the shortage cost and increase in the production rate, in the case of disposal of defective items continues during the week.