We introduce the feeder-carrier routing problem with arc synchronization (FCRP-AS). The FCRP-AS encompasses multiple task nodes, a feeder base, and a carrier base housing multiple carriers. The synchronization locations for both the carrier and feeder flights are positioned along the flight arcs of the carriers, defining the arc synchronization mode. The arc synchronization mode aligns seamlessly with the RV foxtrot rendezvous procedure: the feeder initiates takeoff prior to the carrier(s), and the feeder can wait for the carrier(s) but not vice versa. The FCRP-AS must determine the coupling points as the initiation sites for refueling and the decoupling points as the refueling-termination sites. In the FCRP-AS network, there is a predetermined number of task nodes, each of which must be visited once by a carrier. The demand with the latest service-starting time characterizes each task node. At the task nodes, the service time is ignored. The feeder and carrier bases serve as distinct sources for various types of aircraft. Specifically, the feeder base is equipped with one feeder, whereas the carrier base is equipped with multiple carriers and cargo. Each carrier is restricted to at most one AAR along the route. The coupling and decoupling points located along the carrier route arcs must be determined. Solving the FCRP-AS model indicates the planning of the feeder route, carrier routes, and refueling segments (with determined coupling points and decoupling points) to minimize the total costs of the feeder and carriers. For each instance, the number of task nodes is denoted as TK. For small-scale instances, the TK ranged from 5 to 10 at intervals of 1. For each TK value, three small-scale instances were randomly generated, resulting in 18 small-scale instances. We referred to the practical data utilized by Hansknecht et al. (2023) for designing medium- and large-scale instances. We generated three instances for each TK value. For medium-scale instances, the TK value varied from 15 to 30 at intervals of five, resulting in 12 instances for each of the 16 sets of practical data. A total of 192 medium-scale instances were generated. Large-scale instances comprised 40 and 50 task nodes, leading to the generation of six instances for each of the 16 sets of practical data, resulting in 96 large-scale instances. The medium- and large-scale instances corresponding to each TK value are categorized into three series. For the medium- and large-scale instances, each instance is labeled as “the number of task nodes”-“index of location in the 2 regions”-“series number”.

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