Revenue management of a make-to-stock queue

Motivated by recent electronic marketplaces, we consider a single-product make-to-stock manufacturing system that uses two alternative selling channels: long-term contracts and a spot market of electronic orders. At time 0, the risk-averse manufacturer selects the long-term contract price, at which point buyers choose one of the two channels. The resulting long-term contract demand is a deterministic fluid, while the spot-market demand is modeled as a stochastic renewal process. An exponential reflected random walk model is used to model the spot-market price, which is correlated with the spot-market demand process. The manufacturer accepts or rejects each electronic order, and long-term contracts and accepted electronic orders are backordered if necessary. The manufacturer's control problem is to select the optimal long-term contract price as well as the optimal production (i.e., busy/idle) and electronic-order admission policies to maximize revenue minus inventory holding and backorder costs. Under heavy-traffic conditions, the problem is approximated by a diffusion-control problem, and analytical approximations are used to derive a policy that is simple, and reasonably accurate and robust.