The optimality of myopic stocking policies for systems with decreasing purchasing prices

This paper studies the stocking/replenishment decisions for inventory systems where the purchasing price of an item decreases over time. In a periodic review setting with stochastic demands, we model the purchasing prices of successive periods as a stochastic and decreasing sequence. To minimize the expected total discounted costs (purchasing, inventory holding and shortage penalty) for systems with backlogging and lost sales, we derive conditions, regarding the cost parameters, under which myopic stocking policies are optimal.