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

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

2007-08-08

arxiv.org/abs/0708.1146v1

Economy

Quantitative Finance

Pricing of Securities

Scientific paper

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.

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