Multiproduct Pricing with Discrete Price Sets

We study a multiproduct pricing problem in which the prices of the products are restricted to discrete and finite sets. The demand for a product is a function of the prices of all the products. The prices of the products can be changed through time, subject to the aggregate consumption of each resource not exceeding its availability over the planning horizon. The focus of our work is the deterministic variant of this problem (wherein customer-arrival rates are deterministic), which is a key subproblem whose solution can be used to build effective policies for the stochastic variant (as in Gallego and Van Ryzin 1997). When the demand rate of each product is a concave function of the prices, we obtain an efficient and effective solution to the deterministic problem; the worst-case optimality gap of our solution depends on the curvature of the objective function. We obtain a similar performance guarantee for our solution under the linear attraction demand model and a special case of the MNL demand model. For a general demand function, the worst-case optimality gap of our solution depends on the curvature of both the objective function and the demand function. For the special case where the demand rate of a product depends only on its own price and not on the prices of the other products, we show that the deterministic problem can be efficiently solved via a linear program