The　global　trend　of　increasing　resource　utilization　in　industry　has　drawn　great　attention　from　researchers　and　practitioners.　Industrial　managers　are　increasingly　optimizing　their　production　strategies　based　on　time-of-use　(TOU)　electricity　tariffs　to　reduce　energy　consumption　costs.　This　study　investigates　a　new　energy-efficient　single-machine　scheduling　problem　with　release　dates　under　TOU　electricity　tariffs.　It　consists　in　sequencing　a　set　of　jobs　with　release　dates　to　a　machine　under　TOU　pricing　to　minimize　the　total　energy　cost　given　a　bounded　maximum　completion　time.　We　first　formulate　the　problem　using　the　widely　used　time-indexed　mixed-integer　linear　programming　(T-MILP).　Due　to　its　time-consuming　disadvantage,　a　new　period-based　MILP　(P-MILP)　model　is　developed　based　on　the　characteristics　of　the　problem.　Given　the　NP-hardness　of　the　problem,　a　two-stage　heuristic　(TSH)　algorithm　is　proposed　to　solve　practical-sized　problems.　Specifically,　in　the　first　stage,　a　constructive　heuristic　is　designed　to　obtain　an　initial　solution,　and　in　the　second　one,　a　tailored　tabu　search　is　devised　to　yield　a　better　satisfactory　solution.　Numerical　experiments　are　conducted　on　a　real-life　case　and　1150　randomly　generated　instances　with　up　to　1000　jobs.　Computational　results　show　that　(i)　the　proposed　models　can　save　the　total　electricity　cost　by　about　30%　compared　with　an　existing　empirical　scheduling　method　when　solving　small-sized　instances;　(ii)　the　efficiency　of　P-MILP　is　about　140.94%　higher　than　that　of　T-MILP;　and　(iii)　the　proposed　TSH　algorithm　can　efficiently　obtain　high-quality　solutions　for　practical-sized　instances　with　gaps　of　less　than　7%　compared　to　the　lower　bounds,　which　can　effectively　support　production　managers　to　save　the　energy　costs　in　practical　production.　©　2023　Elsevier　Ltd