Stochastic Knapsack Problem Revisited: Switch-Over Policies and Dynamic Pricing

TL;DR

This paper revisits the stochastic knapsack problem in the context of revenue management, proposing switch-over policies for dynamic pricing, establishing their asymptotic optimality, and developing models to optimize price reductions over time.

Contribution

It introduces and analyzes switch-over policies for stochastic knapsack problems, demonstrating their asymptotic optimality and applying them to dynamic pricing models.

Findings

Switch-over policies are asymptotically optimal.

Optimal switch-over times are determined via convex programming.

Pricing models based on these policies improve revenue management strategies.

Abstract

The stochastic knapsack has been used as a model in wide ranging applications from dynamic resource allocation to admission control in telecommunication. In recent years, a variation of the model has become a basic tool in studying problems that arise in revenue management and dynamic/flexible pricing; and it is in this context that our study is undertaken. Based on a dynamic programming formulation and associated properties of the value function, we study in this paper a class of control that we call switch-over policies -- start from accepting only orders of the highest price, and switch to including lower prices as time goes by, with the switch-over times optimally decided via convex programming. We establish the asymptotic optimality of the switch-over policy, and develop pricing models based on this policy to optimize the price reductions over the decision horizon.