Integrated Planning of Feeder Route Selection, Schedule Design, and Fleet Allocation with Multimodal Transport Path Selection Considered

In the shipping network optimization, the feeder liner companies not only need to decrease the operation cost by comprehensively optimizing the route, schedule, and fleet but also try to increase the operation income by attracting more shippers, with multimodal transport-path selection considered. Therefore, this paper proposes the integrated planning of feeder route selection, schedule design, and fleet allocation with shippers’ transport-path selection considered. We utilize the nested Logit model to analyze the shipper selection behavior for the multimodal transport path and then formulate a mixed-integer nonlinear programming model of integrated optimization for route, schedule, and fleet. To solve our nonlinear model, we propose a particle swarm optimization (PSO) framework embedded with CPLEX solver by combining the constraint relaxations and the linearization techniques with the heuristic rules. Based on the multimodal transport system in Northern China, computational experiments were conducted to verify the effectiveness of our model and algorithm. The sensitivity analyses of model parameters show that with the increase in ship rent, feeder liner companies should reduce the ship capacity or try to increase the number of port call. With the increase in fuel price, feeder liner companies should reduce the ship speed under the constraints of the arrival-time window and schedule interval. If shippers’ time utility coefficient is high, feeder liner companies should shorten the sailing time of ships by decreasing the number of port calls or shorten the at-port time of ships by increasing the service frequency. If the multimodal transport paths are cost-advantaged or if the waterway transport time has a small impact on multimodal transport time, feeder liner companies should weigh the increase in income and cost when using the measures of time saving. These management insights provide decision support for the operation practice of liner shipping network optimization.