The location routing problem (LRP) integrates operational decisions on vehicle operations with strategic the of facilities or depots from which distribution will take place. In other words, it combines well-known (VRP) facility (FLP). Hence, LRP is an NP-hard combinatorial optimization problem, justifies use metaheuristic approaches whenever large-scale instances need to be solved. this paper, ...

In this paper we introduce a new facility location model, called backup multifacility location problem by considering the ideal radius for each customer. In this problem the location of clients are given in the plane. A radius is assigned to each client. We should find the location of new facilities, which some of them may fail with a given probability, such that the sum of weighted distances f...