Competitive algorithms for demand response management in a smart grid

We consider a scheduling problem that abstracts a model of demand response management in a smart grid. We investigate the problem with a set of unrelated machines, and each job j (representing a client demand) is characterized by its release date, and its power request function expressing its request demand at specific times. Each machine has an energy power function, and the energy cost incurred at a time depends on the load of the machine at that time. The goal is to find a non-migrative schedule that minimizes the total energy. We give a competitive algorithm for the problem in the online setting where the competitive ratio depends (only) on the power functions of machines. In the setting with typical energy function $$P(z) = z^{\nu }$$ P ( z ) = z ν , the algorithm is $$\varTheta (\nu ^{\nu })$$ Θ ( ν ν ) -competitive, which is optimal up to a constant factor. Our algorithm is robust in the sense that the guarantee holds for arbitrary request demands of clients. This enables flexibility on the choices of clients in shaping their demands—a desired property in a smart grid. We also consider a particular case in the offline setting in which jobs have unit processing time, constant power request, and identical machines with energy function $$P(z) = z^{\nu }$$ P ( z ) = z ν . We present a $$2^{\nu }$$ 2 ν -approximation algorithm for this case.