This article is motivated by the case of a company manufacturing industrial equipment that faces two types of demand: on the one hand there are the so-called regular orders for installations or refurbishing of existing facilities, these orders have a relatively long lead time; on the other hand there are urgent orders mostly related to spare parts when a facility has a breakdown, the delay in such case is much shorter but higher margins can be obtained. We study the order acceptance problem for a firm that serves two classes of demand over an infinite horizon. The firm has to decide whether to accept a regular order (or equivalently how much capacity to set aside for urgent orders) in order to maximize its profit. We formulate this problem as a multi-dimensional Markovian Decision Process (MDP). We propose a family of approximate formulations to reduce the dimension of the state space via aggregation. We show how our approach can be used to compute bounds on the profit associated with the optimal order acceptance policy. Finally, we show that the value of revenue management is commensurate with the operational flexibility of the firm. 
Revenue management for operations with urgent orders