A new heuristic algorithm for the machine scheduling problem with job delivery coordination

In a rapidly changing environment, competition among enterprises has a tendency towards competing between supply chain systems instead of competing between individual companies. Traditional scheduling models which only address the sequence of jobs to be processed at the production stage under some criteria are no longer suitable and should be extended to cope with the distribution stage after production. Emphasizing on the coordination and integration among various members of a supply chain has become one of the vital strategies for the modern manufacturers to gain competitive advantages. This paper studies the NP-hard problem of the two-stage scheduling in which jobs are processed by two parallel machines and delivered to a customer with the objective of minimizing the makespan (P2→D,k=1|v=1,c=z|Cmax). The proposed heuristic algorithm is shown to have a worst-case ratio of 63/40, except for two particular cases.