Energy-efficient　scheduling　is　highly　necessary　for　energy-intensive　industries,　such　as　glass,　mould　or　chemical　production.　Inspired　by　a　real-world　glass-ceramics　production　process,　this　paper　investigates　a　bi-criteria　energy-efficient　two-stage　hybrid　flow　shop　scheduling　problem,　in　which　parallel　machines　with　eligibility　are　at　stage　1　and　a　batch　machine　is　at　stage　2.　The　performance　measures　considered　are　makespan　and　total　energy　consumption.　Time-of-use　(TOU)　electricity　prices　and　different　states　of　machines　(working,　idle　and　turnoff)　are　integrated.　To　tackle　this　problem,　a　mixed　integer　programming　(MIP)　is　formulated,　based　on　which　an　augmented　ε-constraint　(AUGMECON)　method　is　adopted　to　obtain　the　exact　Pareto　front.　A　problem-tailored　constructive　heuristic　method　with　local　search　strategy,　a　bi-objective　tabu　search　algorithm　and　a　bi-objective　ant　colony　optimisation　algorithm　are　developed　to　deal　with　medium-　and　large-scale　problems.　Extensive　computational　experiments　are　conducted,　and　a　real-world　case　is　solved.　The　results　show　effectiveness　of　the　proposed　methods,　in　particular　the　bi-objective　tabu　search.　©　2019,　©　2019　Informa　UK　Limited,　trading　as　Taylor　&　Francis　Group.