Production and interplant batch delivery scheduling: Dominance and cooperation

In this paper, we consider scheduling problems in a supply chain with two agents, a manufacturer and a third-party logistics (3PL) provider. The manufacturer has to process a set of jobs at the upstream stage and at the downstream stage. The 3PL provider is in charge of transportation of semi-finished products from the upstream stage to the downstream stage. The manufacturer's objective is to minimize makespan Cmax and the 3PL provider's objective is to minimize transportation cost TC. We investigate three scenarios, corresponding to different types of contract: (i) decentralized scenario with strict responsiveness; (ii) decentralized scenario with flexible responsiveness; (iii) centralized (cooperative) scenario. We provide exact polynomial-time algorithms or prove the NP-completeness of the scheduling problems in these three scenarios. Moreover, we evaluate and compare various scenarios through a large set of computational experiments. The results show that cooperation may bring significant benefits to both actors. The benefit for the 3PL provider is particularly high if compared to situations in which the manufacturing sequence is fixed. Also the manufacturer can benefit from relaxing the job-by-job responsiveness constraint in favor of an integrated schedule which appropriately accounts for the role of the 3PL provider.