Pricing and balancing of the sea–cargo service chain with empty equipment repositioning

• To study a sea-cargo supply chain through mathematical modeling
• Empty equipment repositioning and capacity pricing are considered
• To investigate pricing of capacity and balancing strategies of empty equipment
• Two bearing model are considered when studying empty equipment repositioning strategies
• Sensitivity analysis is conducted to assess influence of carrier’s and forwarders’ choices.

To sustain a business, firms have to reposition empty containers from a surplus port to a port with a shortage and incur repositioning costs if the realized demands are unbalanced in the sea–cargo service chain. In this paper, we study a sea cargo service chain with one carrier and two forwarders providing transportation service between two ports, and there are potential demands for transportation services in both directions. We built a mathematical model to study how the carrier and forwarders determine pricing and empty equipment repositioning (hereafter EER) decisions. We find that whether or not the carrier and forwarders use pricing policies to balance the cargo demands depends on the potential demand imbalance volume between two ports. We also investigate the EER sharing strategy on whether to share the EER cost or undertake it solely. It is found that there exists a threshold, and when the EER cost is beyond the threshold value, the carrier assumes all of the repositioning costs; otherwise, the forwarder assumes all of the repositioning costs. Lastly, we study a subsidy contract between both forwarders and expand to study an EER sharing mode between the carrier and both forwarders.