A periodic review inventory model with demand influenced by promotion decisions

In this paper, we use a Markov decision process (MDP) to model the joint inventory–promotion decision problem. The state variable of the MDP represents the demand state brought about by changing environmental factors as well as promotion decisions. The demand state in a period determines the distribution of the random demand in that period. Optimal inventory and promotion decision policies in the finite horizon problem are obtained via dynamic programming. Under certain conditions, we show that there is a threshold inventory level P for each demand state such that if the threshold is exceeded, then it is desirable to promote the product. For the proportional ordering cost case, the optimal inventory replenishment policy is a base-stock type policy with the optimal base-stock level dependent on the promotion decision.