Currently,　customer　satisfaction　is　playing　an　increasingly　vital　role　in　both　manufacturing　and　service　industries.　Assuring　an　acceptable　waiting　time　to　customers　is　considered　as　an　effective　approach　to　improve　customer　satisfaction.　In　this　study,　an　identical　parallel　machine　scheduling　problem　assuring　the　maximum　waiting　time　for　an　emergency　job　which　arrives　at　any　time　is　investigated.　A　mixed　integer　programming　model　is　formulated,　based　on　which　a　variant　formulation　is　generated.　The　formulations　are　further　enhanced　by　various　techniques,　which　forms　two　formulation-based　methods.　Two　objectives,　makespan　and　total　completion　time,　are　considered　separately.　Regarding　the　makespan,　the　worst-case　approximation　ratios　of　the　classical　heuristic　rules　are　deduced.　For　the　total　completion　time,　efficient　bounds　are　provided　and　the　NP-hardness　of　the　problem　is　proved.　Heuristic　methods　based　on　the　classical　dispatch　rules　are　developed,　for　both　the　cases.　Extensive　computational　experiments　are　conducted,　based　on　which　the　performances　of　the　formulation-based　methods　and　heuristics　are　compared,　the　relationship　between　the　objective　values　and　the　assured　maximum　waiting　time　for　an　emergency　job　is　explored,　and　a　few　observations　and　managerial　insights　are　obtained.　©　2020　Elsevier　Ltd