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Climate change pushes the operation managers to take account of energy-saving issues in their decision-making of production scheduling and maintenance planning (PSMP). We address a PSMP problem for a single machine system under Time-of-Use electricity tariff. We consider two objectives including the makespan that measures the service level and the total energy cost that measures the energy sustainability. Both objectives are considered in a bi-objective mathematical model that is further solved using a novel heuristic algorithm consisting of two layers based on the problem decomposition. The inner layer problem, which is solved by a branch & bound algorithm, is to optimise the decision variables of preventive maintenance and machine's setup. The outer layer problem, which is solved by a hybrid NSGA-II algorithm, is to optimise the sequence of jobs and the amount of inserted buffer time. The effectiveness and efficiency of the algorithm are demonstrated by a series of numerical experiments. The Pareto frontier can serve as a tool for managers to consider energy cost explicitly in making decisions. It is observed in some scenarios that reducing energy cost will not increase the makespan.