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The industrial sector is the largest consumer of the world’s total energy and most of its consumption is in form of electricity. In recent years, to strengthen the peak load regulation capability, time-of-use (TOU) pricing has been implemented in many countries to encourage consumers to shift their use from peak to mid-and off-peak periods such that their energy bills can be reduced. In this paper, we study a new single-machine batch scheduling problem with machine on/off switching under TOU tariffs, which aims to simultaneously minimize total electricity cost and makespan. For the problem, we first develop a bi-objective mixed-integer linear programming model. Based on optimal batch rule analysis, an improved model is further provided which greatly reduces Pareto optimal solution search space. To efficiently solve large-size problems, we propose a heuristic based ε-constraint method. The results from extensive …