This paper presents a three-level supply chain model which includes single supplier, several distribution centers and sets of retailers. For this purpose, by adopting the queuing approach, a mixed nonlinear integer programming model is formulated. The proposed model follows minimizing the total cost of the system by determining: 1) the number and location of distribution centers between candida...

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, ...