A Periodic Review Inventory Model with Demand Influenced by Promotion Decisions
用马尔可夫决策过程建模库存与促销的联合决策问题，通过动态规划求解有限时域下的最优策略，发现当库存超过某阈值时促销更优，且最优补货策略为依赖于促销决策的基础库存策略。
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.