A continuous approximation approach to the planar hub location-routing problem: Modeling and solution algorithms

The design of many-to-many parcel delivery networks is an important problem in freight transportation. To exploit economies of scale and provide a better service level, these networks usually have a hub-and-spoke architecture. We address a planar hub location-routing problem (HLRP) where the market demand is modeled as a uniform density function over a convex polygon service region. The continuous approximation (CA) technique is used for modeling the HLRP in such a way that it jointly decides on the location of hubs and the allocation of a service region to the hubs. The objective is to minimize the approximate total transportation cost, including local pickup and delivery costs, as well as line-haul transportation costs. Two solution algorithms are developed for the problem: an iterative Weiszfeld-type algorithm (IWA) and a particle swarm optimization (PSO) metaheuristic. The performance and solution quality of the proposed algorithms are compared with an adapted algorithm from the literature. Furthermore, extensive computational experiments are performed to study the effect of different input parameters such as the discount factor value, demand points density, and vehicle capacity on the total system cost and the final configuration of the network.