Flow shop scheduling problems with transportation and capacities constraints

In most manufacturing and distribution systems, semi-finished jobs are transferred from one processing facillity to another and finished jobs are delivered to customers or warehouse by vehicles such as trucks. This paper investigates flow shop scheduling problems that explicitly consider constraints on both transportation and buffer capacities. These elements enable the Flexible Manufacturing Systems (FMS) to process different types of parts. The finished jobs leave the processing facility to be delivered to customers or sent to warehouses by vehicles such as trucks. The objective function that is considered is makespan C-max. We prove that this problem is strongly NP-hard when the capacity of truck is equal to two with unlimited buffer behind each machine. This problem with additional constraints, such as blocking; is also proved to be NP-hard.