In this paper we proposed a new variable neighborhood search (VNS) for solving the location- routing problem with considering capacitated depots and vehicles. A set of capacitated vehicles, a set of depots with restricted capacities, and associated opening costs, and a set of customers with deterministic demands are given. The problem aims to determine the depots to be opened, fleet assignment to each depot, and the routes to be performed to satisfy the demand of the customers. The objective is to minimize the total costs of the open depots, the setup cost associated with the used vehicles, and transportation cost. We proposed a new VNS which is augmented with a probabilistic acceptance criterion as well as a set of efficient local searches. The computational results implemented on four well-known data sets demonstrate that the proposed algorithm is competitive with other well- known algorithms while reaching many best-known solutions and updating six best new results with reasonable computational time. Conclusions and future research avenues close the paper.

In this paper we proposed a new variable neighborhood search (VNS) for solving the location- routing problem with considering capacitated depots and vehicles. A set of capacitated vehicles, a set of depots with restricted capacities, and associated opening costs, and a set of customers with deterministic demands are given. The problem aims to determine the depots to be opened, fleet assignment to each depot, and the routes to be performed to satisfy the demand of the customers. The objective is to minimize the total costs of the open depots, the setup cost associated with the used vehicles, and transportation cost. We proposed a new VNS which is augmented with a probabilistic acceptance criterion as well as a set of efficient local searches. The computational results implemented on four well-known data sets demonstrate that the proposed algorithm is competitive with other well- known algorithms while reaching many best-known solutions and updating six best new results with reasonable computational time. Conclusions and future research avenues close the paper.