Combinatorial Challenges and Algorithms in New Energy Aware Scheduling Problems

Abstract

In this thesis, we study the theoretical approach on energy-efficient scheduling problems arising in demand response management in the modern electrical smart grid. Consumers send in power requests with flexible feasible timeslots during which their requests can be served. The grid controller, upon receiving power requests, schedules each request within the specified interval. The electricity cost is measured by a convex function of the load in each timeslot. The objective is to schedule all requests with the minimum total electricity cost. We study the smart grid scheduling problem in different models. For the offline model, we prove the problem is NP-hard for the general case. We propose a polynomial time algorithm for special input where jobs have unit power request and unit time duration. By adapting the polynomial time algorithm for unit-size jobs, we propose an approximation algorithm for more general input. On the other hand, we also present an exact algorithm to find the optimal schedule for the problem with general input. For the online model, we propose an online algorithm for jobs with jobs with arbitrary power request, arbitrary time duration, and arbitrary contiguous feasible intervals. We also show a lower bound of the competitive ratio for the smart grid scheduling problem with unit height and arbitrary width. For special cases, we design different online algorithms with better competitive ratios. Finally, we look at other optimization problems and show how to solve them by adapting our techniques. We prove that our online algorithm can solve the machine minimization problem with an asymptotically optimal competitive ratio. We also show that our exact algorithm can be adapted to solve other demand response management problems.