Dynamic Pricing and Inventory Control in a Make-to-Stock Queue With Information on the Production Status

This paper addresses the dynamic pricing problem of a single-item, make-to-stock production system. Demand arrives according to Poisson processes with changeable arrival rate dependent on the selling price. Item processing times follow an Erlang distribution, which allows to use the information on the production status in a tractable way. The objective is to identify a dynamic control policy that decides production and adjusts the price to maximize the long-run total discounted profit. An optimal policy is based on the so-called work-storage level that captures the information of the inventory level and the status of ongoing production process. Specifically, we show that: 1) the finished goods inventory is optimally managed by a critical stage level policy: when the inventory is below a certain work-storage level, production is started if the system is currently idle and 2) the price is optimally set by threshold levels: a certain price is posted when the work-storage level is at or below a threshold corresponding to that level of price. Moreover, we develop an efficient algorithm to compute the optimal policy.