Robust identical parallel machine scheduling with two-stage time-of-use tariff and not-all-machine option

Time-of-use (TOU) tariff has been implemented in the manufacturing industry to improve energy efficiency by regulating the electricity imbalance between supply and demand. Besides, not-all-machine (NAM) option is another way of energy-saving by using only a subset of all the available machines. This study investigates a robust identical parallel machine scheduling problem with a two-stage TOU tariff and NAM option. Only interval bounds on job processing times are known. The problem is first formulated into a min–max regret model to maximise the robustness. Based on problem properties, both an iterative relaxation-based exact algorithm and a memetic differential evolution-based heuristic are developed to solve the problem. Computational experiments on 240 randomly generated instances with up to 20 jobs are conducted to evaluate the performance of the developed methods. Besides, 900 large-sized randomly generated instances with up to 150 jobs are tested for sensitivity analysis and to identify managerial insights for achieving energy-efficient schedules.