Coordination of production and transportation in supply chain scheduling

This paper investigates a three-stage supply chain scheduling prob-lem in the application area of aluminium production. Particularly, the rst and the third stages involve two factories, i.e., the extrusion factory of the supplier and the aging factory of the manufacturer, where serial batching machine and parallel batching machine respectively process jobs in di erent ways. In the second stage, a single vehicle transports jobs between the two factories. In our research, both setup time and capacity constraints are explicitly considered. For the problem of minimizing the makespan, we formalize it as a mixed in-teger programming model and prove it to be strongly NP-hard. Considering the computational complexity, we develop two heuristic algorithms applied in two dierent cases of this problem. Accordingly, two lower bounds are derived, based on which the worst case performance is analyzed. Finally, dierent scales of random instances are generated to test the performance of the proposed al-gorithms. The computational results show the effectiveness of the proposed algorithms, especially for large-scale instances.