The Generalized Median Tour Problem: Modeling, Solving and an Application

Abstract

We introduce, formulate, and solve the Generalized Median Tour Problem, which is motivated in the health supplies distribution for urban and rural areas. A region comprises districts that must be served by a specialized vehicle visiting its health facilities. We propose a distribution strategy to serve these health facilities efficiently. A single tour is determined that visits a set of health facilities (nodes) composed of disjoint clusters. The tour must visit at least one facility within each cluster, and the unvisited facilities are assigned to the closest facility on the tour. We minimize the sum of the total tour distance and the access distance traveled by the unvisited facilities. Efficient formulations are proposed and several solution strategies are developed to avoid subtours based on branch & cut. We solve a set of test instances and a real-world instance to show the efficiency of our solution approaches.

Last mile delivery routing problem using autonomous electric vehicles

“…Moreover, if in MCP/RSP there exists an upper bound on the number of the nodes (or stops) on the cycle (tour), then MCP/RSP becomes Median Tour Problem (MTP) (Current & Schilling, 1994). There are several works on the MTP and its variants in the literature, such as heuristics on MTP (Current & Schilling, 1996), and recently introduced Generalized MTP (GMTP) (Obreque, Paredes-Belmar, Miranda, Campuzano & Gutiérrez-Jarpa, 2020). Also, if in MCP/RSP only some specific nodes (Steiner points) must be on the cycle (tour) and the customers must be assigned to these Steiner points, then MCP/RSP becomes Steiner RSP (SRSP), originally introduced by Lee, Chiu & Sanchez (1998).…”

Optimization of Humanitarian Aid Distribution in Case of an Earthquake and Tsunami in the City of Iquique, Chile

“…Recently, Ref. [13] presents the Generalized Median Tour Problem (GMTP). It consists of defining a main route that must visit a set of nodes grouped into disjoint clusters.…”

“…We also try an iterative method (similar to the applied in [13]) to deal with constraints (21). However, the results were not promising, since this method takes a lot of computational time to provide good feasible solutions.…”

“…Second, we determine efficient vehicle routes for humanitarian aid distribution. It should be noticed that the structure of this problem is a generalization of the Generalized Median Tour Problem (GMTP), introduced by [13], since they focus their study on a single tour visiting a set of clusters. Third, we model the problem using a mixed-integer linear programming (MILP) model.…”