Parallel machine scheduling with job delivery coordination

We analyse a parallel (identical) machine scheduling problem with job delivery to a single customer. For this problem, each job needs to be processed on \(m\) parallel machines non-pre-emptively and then transported to a customer by one vehicle with a limited physical capacity. The optimization goal is to minimize the makespan, the time at which all the jobs are processed and delivered and the vehicle returns to the machine. We present an approximation algorithm with a tight worst-case performance ratio of \(7/3-1/m\) for the general case, \(m\ge 3\). doi:10.1017/S144618111700019