Blind Nonparametric Revenue Management: Asymptotic Optimality of a Joint Learning and Pricing Method
نویسندگان
چکیده
We consider a general class of network revenue management problems in which multiple products are linked by various resource constraints. Demand is modeled as a multivariate Poisson process whose instantaneous rate at each point in time is determined by a vector of prices set by the decision maker. The objective is to price the products so as to maximize expected revenues over a finite sales horizon. The decision maker observes realized demand over time, but is otherwise “blind” to the underlying demand function which maps prices into the instantaneous demand rate. Few structural assumptions are made with regard to the demand function, in particular, it need not admit any parametric representation. We introduce a general method for solving such blind revenue management problems: first a learning phase experiments with a “small” number of prices over an initial “short” time interval; then a simple optimization problem is solved using an estimate of the demand function obtained from the previous stage, and a near-optimal price is fixed for the remainder of the time horizon. To evaluate the performance of the proposed method we compare the revenues it generates to those corresponding to the optimal dynamic pricing policy that knows the demand function a priori. In a regime where the sales volume grows large, we prove that the gap in performance is suitably small; in that sense, the proposed method is asymptotically optimal.
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