Single-resource capacity control with random-fuzzy demand

This paper studies the capacity control problem in revenue management with single resource, where the decision maker can only estimate the type of probability distribution of uncertain demand, but they do not have the necessary historic data to estimate the parameters of these distributions. We model these uncertainty parameters with fuzzy variables. Based on the theory of fuzzy satisfaction degree for objectives, the fuzzy nonlinear programming model in this paper is transformed into a convex programming problem. By using the lagrangian multiplier and the Kuhn-Tucker conditions we obtain the optimal solution of the model. Owing to the information for demand in random-fuzzy environment is less than only in the random environment, the paper reveals that the protection level for the highest class with random-fuzzy demand are more than only in random environment and it depends on the membership of the fuzzy environment, what's more, if and only if the membership equals 1, the protection level in these two situations are the same to each other. The model in this paper can be viewed as a generalization of single-resource capacity control with random demand.