  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.
