Scheduling and Pricing Non-Preemptive Electric Loads: A Convex Approach

This paper studies the problem of scheduling and pricing a large collection of non-preemptive electric loads. For the scheduling problem, we formulate the problem as a mixed integer program and propose an algorithm for solving it based on its convex relaxation. We establish that the admissible schedule produced by our algorithm is near optimal for any finite number of loads, and asymptotically optimal in a per-load cost sense when the number of loads grows to infinite. For the pricing problem, we analyze a natural marginal pricing policy defined for the convex relaxation. We show that the pricing policy is approximately budget adequate, and self-scheduling. Furthermore, we demonstrate that the pricing policy provides proper incentives for each flexible load to report its true flexibility window when the maximum duration of all loads is one. When there are some loads spanning multiple time slots, we show that this flexibility revealing property fails to hold. Our results suggest that while it is possible to achieve most of the aforementioned desirable properties by scheduling and pricing non-preemptive loads via convex relaxation, the marginal pricing rule needs to be adjusted to incentivize flexibility revealing for general non-preemptive loads.