Scheduling Jobs with Precedence Constraints to Minimize Peak Demand

Abstract

Job scheduling to minimize peak demand occurs in the context of smart electric power grids. Some jobs (e.g. certain household appliances) may have flexibility in their start times and so can be shifted in order to lower the peak power demand of the schedule. In this work, we consider a version of peak-demand scheduling where jobs are non-preemptible and have precedence constraints (e.g. job j cannot begin until job i has finished). This problem occurs in the setting of industrial processes, where resource-consuming tasks may have completion dependencies. Our main contribution is the first polynomial time approximation algorithm for this problem. The algorithm is randomized and finds a $O(\varDelta \frac{\log n}{\log \log n})$-approximation with probability at least $1 - O(1/n)$, where n is the number of jobs to be scheduled and $\varDelta$ is the length of the input’s longest precedence chain. We demonstrate that the algorithm is practical on realistic inputs, finds solutions that are close to optimal, and improves over existing algorithms on the data sets tested.