Machine Scheduling with a Maintenance Interval and Job Delivery Coordination

We investigate a scheduling problem with job delivery coordination in which the machine has a maintenance time interval. The goal is to minimize the makespan. In the problem, each job needs to be processed on the machine non-preemptively for a certain time, and then transported to a distribution center; transportation is by one vehicle with a limited physical capacity, and it takes constant time to deliver a shipment to the distribution center and return back to the machine. We present a \(2\)-approximation algorithm for the problem, and show that the performance ratio is tight.