Scheduling, pricing, and efficiency of non-preemptive flexible loads under direct load control

A market comprising a scheduler with a renewable generator and a pumped water storage system, a certain number of flexible and inflexible loads, and a non-renewable generator is considered. At the beginning of activity, the scheduler receives the following three information from each of the loads - consumption (in MW), duration (in hours) and start window. The start window of a load is the time interval in which the load must be started. A load is inflexible if its start window is singleton. The loads are assumed to be non-preemptive, that is, after a load is started, it cannot be interrupted or paused, and it must be served for its duration. The goal of the scheduler is to develop a scheduling policy that minimizes the aggregate cost of buying electricity from the non-renewable generator. We develop an understanding of the nature of optimal solutions to such an optimization problem and propose an approximately optimal scheduling policy for a sufficiently wide class of scheduling problems.