The Minisum Multipurpose Trip Location Problem on Networks

We investigate multipurpose trip location problems on networks with two different types of facilities and three groups of customers, two of which need only one type of service, while the third group needs both types of service in a single trip. The objective is to minimize the total weighted travel distance of all trips. We prove that there exists a dominating location set for the problem on a general network, propose a general binary programming model, and analyze the properties of optimal solutions on networks with simple topologies and one facility per type. We also investigate several heuristic approaches to the problem on general networks and present extensive computational experiments.