Two-stage parallel speed-scaling machine scheduling under time-of-use tariffs

Abstract

As one of the demand-side programs, time-of-use (TOU) tariffs brings opportunities of maintaining power grid stability for electricity providers and chances of energy conservation for manufacturers, but it also brings challenge for enterprises to optimize scheduling schemes. This paper studies a two-stage parallel machine scheduling problem under TOU to minimize total electricity costs. The two-stage parallel machine system is composed of identical parallel speed-scaling machines at stage 1 and unrelated parallel machines at stage 2. The key issues lie in assigning a group of jobs to a set of parallel machines at each stage and choosing the appropriate processing speed for all jobs at stage 1, and then determining the interval of processing time for jobs on each selected machine. To solve this problem, a new continuous-time mixed-integer linear programming model is formulated. According to the characteristics of this model, a tabu search-greedy insertion hybrid (TS-GIH) algorithm is designed, which realizes job-machine assignment based on load balancing principle, job insertion with greedy mechanism as well as movement and speed adjustment strategies to find more suitable positions for jobs. The effectiveness of the proposed TS-GIH is demonstrated by comparing with CLPEX and improved genetic algorithm (IGA) through real-life and randomly generated instances. The results show that TS-GIH can realize the trade-off between computation time and solution quality. Compared with CLPEX, the computation time of TS-GIH is significantly less, and the solution quality is much better than IGA.