Energy-Efficient Wireless Transmission Scheduling as an Inventory Control Problem with Stochastic Ordering Costs

We make a novel connection between an energy-efficient wireless transmission scheduling problem and a multi-period, multi-item inventory control problem with stochastic convex ordering costs, deterministic demands, and a joint budget constraint. In the special case of a single item, we show that a state-dependent modified base-stock policy is optimal when the stochastic ordering costs are linear, and a state-dependent finite generalized base-stock policy is optimal when the stochastic ordering costs are piecewise-linear convex. We also present an efficient method to compute the target stock-up levels characterizing these policies when certain technical conditions are satisfied. For the case of two items with a joint budget constraint, we state and prove the structure of the optimal policy, which is somewhat surprisingly not a base-stock policy. We show that due to the stochastic nature of the ordering costs, structural phenomena may arise that are not possible in a two-item inventory model with a joint budget constraint and the more classical configuration of stochastic demands and deterministic ordering costs.