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In this paper, a new version of the location-routing problem (LRP), named orienteering location-routing problem (OLRP) is investigated. The problem is composed of two-well known problems: team orienteering problem (TOP) and LRP. There are some challenging practical applications in logistics, tourism, military operations, and other fields, which can be modeled by OLRP. The problem is to consider the location and routing with a special objective function. In the OLRP, a set of nodes with specific scores is given, and some stations among candidate stations should be established. Moreover, there are some routes limited in length, which start from a station, visit some nodes and then return to the same station. Maximizing the sum of the collected scores is the goal of OLRP. To model the problem, an integer linear programming model is proposed. Against a commercial solver, a heuristic GRASP is developed for solving the standard test problems. Most test problems are found difficult to solve optimally with commercial software while the GRASP can find the best known or close to the best-known solution in a short time.

Formulation and a heuristic approach for the orienteering location-routing problem