optimizing a hub arc location problem with set-up cost and isolated hub nodes

Efficient flow management is critical in transportation and logistics, with hub networks playing a key role in optimizing these processes. the hub arc location problem has recently emerged as a new framework that emphasizes hub arcs while allowing for isolated hubs. this paper extends the hub arc location problem by incorporating set-up costs into the optimization model. a heuristic algorithm is developed to enhance hub network design, considering both the flow of goods and the associated hub set-up costs. additionally, a detailed sensitivity analysis is conducted to assess the impact of strategic adjustments on optimization outcomes. by reducing the discount factor for inter-hub flows and increasing the number of exogenous hub arcs, significant improvements in route optimization and cost reduction are achieved. this research challenges traditional approaches to hub network design and opens the door for further exploration of the dynamics within hub networks. a deeper understanding of these networks can lead to more efficient and resource-optimized transportation systems, potentially transforming flow management into a more cost-effective and sustainable process.