Flow Shop Scheduling Problems with Transportation Constraints Revisited

In this paper, we study two flow shop scheduling problems with two machines A and B and a single transporter V. In the first problem, the transporter V is located at machine A initially, each job has to be processed on A first, then transported to machine B for further processing. While in the second problem, the transporter V is located at machine B initially, each job needs to be processed on A first, then on B, finally transported to the destination. In both problems, each machine has an unlimited buffer to store finished or unfinished jobs, and the transporter V can carry up to c jobs at a time where c >= 1. The objective of the former problem is to minimize the completion time on B, while that of the latter problem is to minimize the completion time when all jobs are transported to the destination. For each problem we design a polynomial-time approximation scheme (PTAS).