Replenishment and pricing decisions for inventory systems with random supply in a fluctuated environment

This article considers the problem of joint replenishment and pricing decisions for a single product with fixed ordering costs and random supply in a fluctuated environment. We assume that the environment comprises a Markov chain with finite states and all the parameters are dependent on the environment states, such as supply, demand, and cost structure. Our objective is to maximize the total expected profit during the whole sales horizon by choosing an appropriate replenishment and pricing policy. We show that the form of the optimal ordering and pricing policy has an environment-dependent (s, S, p)-type. Moreover, we analyze the operational effects of random supply on the optimal policy and obtain that the optimal profit increases with the probability of receiving orders. The optimal profit function for the finite horizon problem converges to that for the infinite horizon problem under some mild conditions.