Dynamic pricing with capacity constraints and inventory replenishment

Abstract

This paper describes a fast algorithm for solving a capacitated dynamic pricing problem where the producer has the ability to store inventory. The pricing problem described is a quadratic programming problem with a structure that can be solved e ectively by a dual algorithm. The proposed algorithm gives a solution satisfying the Karush-Kuhn-Tucker conditions. This, combined with the fact that the problem has a convex feasible region with a concave objective function which we want to maximize, implies that the proposed algorithm gives a globally optimal solution. The algorithm is illustrated by numerical examples for both the single-item and the multi-item cases.