To formulate a single-leg seat inventory control problem in an airline ticket sales system, the concept and techniques of revenue management are applied in this research. In this model, it is assumed that the cabin capacity is stochastic and hence its exact size cannot be forecasted in advance, at the time of planning. There are two groups of early-reserving and late-purchasing customers demanding this capacity. The price rate as well as the penalty for booking cancellation caused by overbooking is different for each group. The model is developed mathematically and we propose an analytical solution method. The properties of the optimal solution as well as the behavior of objective function are also analyzed. The objective function is neither concave nor convex in general. However, we prove it is a unimodal function and by taking advantage of this property, the optimal solution is determined.