An exact algorithm for the multi-trip vehicle routing and scheduling problem of pickup and delivery of customers to the airport

Door-to-Door service of Pickup and Delivery of Customers to the Airport (D2PDCA) is a new service provided by certain Airline Ticket Sales Agencies (ATSAs) in China. This new service provides an attractive alternative way by picking up customer at this/her specified position and at any time he/she preferred and delivering to the airport more conveniently than airport shuttle and thus earn high customer service quality. Compared with the single-trip mode, the multi-trip mode of D2PDCA (MTM-D2PDCA) service can reduce travel distances, the number of vehicles required and the operating cost. To obtain the exact solution of the MTM-D2PDCA problem, we propose a novel, exact algorithm based on the trip-chain-oriented set-partitioning (TCO-SP) model, where a trip-chain represents multiple trips made by a specific vehicle. In the exact algorithm, we propose an improved label-correcting method to remove infeasible trip-chains quickly and thus speed the search process. Based on the feasible trip-chains, the MTM-D2PDCA problem is formulated as the novel TCO-SP model, which can be solved exactly by the optimization software CPLEX. In addition, we present several mathematical insights into the relationship between the number of trip-chains and the number of local optimal trips that are applicable in both theory and practice. Extensive experiments are conducted to illustrate the application of the model and demonstrate the cost savings of the MTM-D2PDCA mode over the single-trip mode and provide managerial insights into successfully operating a MTM-D2PDCA service.