Coordinating scheduling with batch deliveries in a two-machine flow shop

In the demanding world of supply chain management, traditional scheduling models which only address the optimization of production sequence at certain stage are often not globally optimized. Rather, the extension, including the distribution stage following the production, can bring a more holistic view to the decision makers. This research focuses mainly on a class of two-machine flow shop problem in which jobs need to be delivered to customers by vehicles after their production stages. Two performance measures—the sum of job completion times (∑C _j ) and the makespan (C _max)—are investigated separately. For the objective of ∑C _j , this study shows that it is strongly NP-hard whether the job sizes are assumed to be equal or not. On the other hand, with regard to the C _max objective, this paper concentrates only on the problem of different job sizes and provides a proof of its NP-hardness. A heuristic method that guarantees to contain a worst-case performance ratio of 2 is developed for the C _max problem.