In this paper, we consider the classic stochastic (dynamic) knapsack problem, a fundamental mathematical model in revenue management, with general time-varying random demand. Our main goal is to study the optimal policies, which can be obtained by solving the dynamic programming formulated for the problem, both qualitatively and quantitatively. It is well-known that when the demand size is fixed and the demand distribution is stationary over time, the value function of the dynamic programming exhibits extremely useful first and second order monotonicity properties, which lead to monotonicity properties of the optimal policies. In this paper, we are able to verify that these results still hold even in the case that the price distributions are time-dependent. When we further relax the demand size distribution assumptions and allow them to be arbitrary, for example in random batches, we develop a scheme for using value function of alternative unit demand systems to provide bounds to the v 查看全文>>