This paper demonstrates an approach to determine the EOQ of an item under a periodic review inventory system with stochastic demand. Using N-Period dynamic programming planning horizon, we analyse the ordering policy during each period considering when demand is favorable or unfavorable to determine the EOQ and the associated profit at the end of each planning horizon. The objective is to determine in each period of the planning horizon, an optimal EOQ so that at the long run profits are maximized for a given state of demand. We also generate a formula to determine the number of matrix transitions for each planning horizon until final stage and then prove the formula by the principle of mathematical induction.
