Flowshop scheduling with interstage job transportation

There are a variety of joint job production and transportation scheduling problems that arise in modern manufacturing systems. In this paper, we study two such problems that arise in a flowshop environment where there are two processing stages and a single transporter that is available to deliver the finished jobs from the first stage to the second. In the first problem, there is a single machine in each of the two flowshop stages and jobs have different sizes when loaded onto the transporter. In the second problem, there are two parallel machines in the first stage and a single machine in the second stage, and the transporter can carry only one job in each shipment. The objective of both problems is to minimize the makespan, i.e., the completion time of the last job in the second stage. The two problems are both strongly NP-hard. For each problem, we propose a fast heuristic and show that the heuristic has a tight worst-case bound of 2.