Approximating the Value Functions of Stochastic Knapsack Problems: A Homogeneous Monge-Ampére Equation and Its Stochastic Counterparts

Details Approximating the Value Functions of Stochastic Knapsack Problems: A Homogeneous Monge-Ampére Equation and Its Stochastic Counterparts Approximating the Value Functions of Stochastic Knapsack Problems: A Homogeneous Monge-Ampére Equation and Its Stochastic Counterparts

2008-05-12

arxiv.org/abs/0805.1710v1

Mathematics

Optimization and Control

Scientific paper

Stochastic knapsack problem originally was a versatile model for controls in telecommunication networks. Recently, it draws attentions of revenue management community by serving as a basic model for allocating resources over time. We develop approximation schemes for knapsack problems in this paper, a system of nonlinear but solvable partial differential equations and stochastic partial differential equation are shown to be the limit of the process that following the optimal solution of the stochastic knapsack problem.

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