The integrated secondary route network design model in the hierarchical hub-and-spoke network for dual express services

The network industries design and operate physical distribution networks to provide services for spatial interactions. In the hierarchical hub-and-spoke network, each center is connected through a secondary route to its designated hub, while hubs are mutually connected by primary routes. It is a variation of pure hub-and-spoke networks that may eliminate center-hub partial loads with the result of higher load factor and lower cost. We study the integrated hierarchical hub-and-spoke network design problem for dual services. It integrates otherwise mutually exclusive secondary route networks for their respective services so that the total operating cost is minimized while meeting the service time and operations restrictions. Assuming symmetry in cost/time, it is equivalent to the integration of dual degree and time constrained trees. We propose a directed network configuration and formulate a link-based integer mathematical model. We also develop a link-based implicit enumeration with an embedded degree and time constrained spanning tree algorithm. The computational result showed that the integration provides a substantial cost reduction over the conventional exclusive secondary route networks for their respective services. In addition, the proper selection of number and location of hubs may achieve a higher cost-effectiveness as well as an increase in service territory at no additional operating cost.