The location routing problem with facility sizing decisions

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, we explore a realistic version in different capacities are considered, i.e., manager has consider not only but also size open. order tackle three mixed-integer linear formulations proposed and compared. As expected, they have been proved cost- time- inefficient. biased-randomized iterated local search algorithm proposed. Classical for homogeneous naturally extended test performance our approach.