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 \(P(z) = z^{\nu }\), the algorithm is \(\varTheta (\nu ^{\nu })\)-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 \(P(z) = z^{\nu }\). We present a \(2^{\nu }\)-approximation algorithm for this case.

我们考虑一个调度问题，它抽象了智能电网中的需求响应管理模型。我们用一组不相关的机器来研究这个问题，每个作业j（代表一个客户需求）的特征是它的发布日期，它的功率请求函数表达了它在特定时间的请求需求。每台机器都有能源动力功能，一次产生的能源成本取决于当时机器的负载。目标是找到一个最小化总能量的非迁移时间表。我们为在线设置中的问题提供了一种竞争算法，其中竞争比率（仅）取决于机器的幂函数。在具有典型能量函数\(P(z) = z^{\nu }\) 的设置中，算法为\(\varTheta (\nu ^{\nu })\) - 有竞争力的，这是一个常数因子的最佳选择。我们的算法是健壮的，因为保证适用于客户端的任意请求需求。这使得客户可以灵活地选择他们的需求——这是智能电网中的一个理想属性。我们还考虑了离线设置中的一种特殊情况，其中作业具有单位处理时间、恒定功率请求以及具有能量函数\(P(z) = z^{\nu }\) 的相同机器。对于这种情况，我们提出了一个\(2^{\nu }\) -近似算法。