Probabilistic Choice Models for Product Pricing Using Reservation Prices

Abstract

The problem of pricing a product line to maximize profits is an important challenge faced by many companies. To address this problem, we discuss four different probabilistic choice models that are based on reservation prices: the Uniform Distribution Model, the Weighted Uniform Model, the Share-of-Surplus Model, and the Price Sensitive Model. They are formulated as convex mixed-integer mathematical programs. We explore the properties and additional valid inequalities of these formulations. We also compare their optimal solutions on a set of inputs. In general, the Uniform Distribution, Weighted Uniform, and Price Sensitive Models have the same optimal solution while the Share-of-Surplus Model gives a different solution in many cases.

We develop a few heuristics for finding good feasible solutions. These simple and efficient heuristics perform well and help to improve the solution time. Computational results of solving problem instances of various sizes are shown.