This paper studies a revenue management problem in which a finite number of substitutable commodities are sold to two different market segments at respective prices. It is required that a certain number of commodities are reserved for the high-price segment to ensure a minimum service level. The two segments are served concurrently at the beginning of the season. To improve revenues, management may choose to close the low-price segment at a time when the chance of selling all items at the high price is promising. The difficulty is determining when such a decision should be made. We derive the exact solution in closed form using the theory of optimal stopping time. We show that the optimal decision is made in reference to a sequence of thresholds in time. These time thresholds take both remaining sales season and inventory into account and exhibit a useful monotone property.
