This paper aims to compare a two-echelon and a single-echelon distribution system. A mathematical model for the Single-Echelon Capacitated Vehicle Routing Problem (SE-CVRP) is proposed. This SE-CVRP is the counterpart of Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP) introduced in the authors’ previous work. The proposed mathematical model is Mixed-Integer Non-Linear Programming (MIN...

We study the robust capacitated vehicle routing problem (CVRP) under demand uncertainty, which determines a minimum cost delivery of a product to geographically dispersed customers using capacity-constrained vehicles. Contrary to the deterministic CVRP, which postulates that the customer demands for the product are deterministic and known, the robust CVRP models the customer demands as random v...

In this paper, we present a branch-and-cut algorithm for the Vehicle Routing Problem with Two-dimensional Loading Constraints (2L-CVRP). The 2L-CVRP is a combination of the Capacitated Vehicle Routing Problem (CVRP) and the Two-dimensional Bin Packing Problem. We propose a strategy based on emphasizing cut generation using known families of valid inequalities for the CVRP. Checking packing feas...

The Vehicle Routing Problem (VRP) requires the determination of an optimal set of routes for a set of vehicles to serve a set of customers. We deal here with the Capacitated Vehicle Routing Problem (CVRP) where there is a maximum weight or volume that each vehicle can load. We developed an Ant Colony algorithm (ACO) for the CVRP based on the metaheuristic technique introduced by Colorni, Dorigo...

Vehicle Routing Problem (VRP) has become an integral part in logistic operations which determines optimal routes for several vehicles to serve customers. The basic version of VRP is Capacitated VRP (CVRP) which considers equal capacities for all vehicles. The objective of CVRP is to minimize the total traveling distance of all vehicles to serve all the customers. Various methods are used to sol...

Vehicle Routing Problem (VRP) is a popular combinatorial optimization problem which consists in finding an optimal set of routes for a fleet of vehicles in order to serve a specified collection of clients. Capacitated VRP (CVRP) is a version of VRP in which every vehicle has a capacity parameter assigned. The UCT (Upper Confidence bounds applied to Trees) is a heuristic simulation-based algorit...

This paper proposes a new transformation of arc routing problems into equivalents node routing problems, with emphasis on the transformation of Capacitated Arc Routing Problems (CARP) into Capacitated Vehicle Routing Problems (CVRP). For this last case, an analogue transformation has already been proposed in Pearn et al. [21], where each required CARP arc was mapped onto a triplet of CVRP nodes...

The Capacitated Vehicle Routing problem (CVRP) is a combinatorial optimization and nonlinear problem seeking to service a number of customers with a fleet of vehicles. CVRP isan important problem in the fields of transportation, distribution and logistics . Usually, the goal is delivering goods located at a central depot to customers who have placed orders. This transportation optimization prob...

This paper introduces the Pyramidal Capacitated Vehicle Routing Problem (PCVRP) as a restricted version of the Capacitated Vehicle Routing Problem (CVRP). In the PCVRP each route is required to be pyramidal in a sense generalized from the Pyramidal Traveling Salesman Problem (PTSP). A pyramidal route is defined as a route on which the vehicle first visits customers in increasing order of custom...

The Capacitated Vehicle Routing Problem (CVRP) is a combinatorial optimization and nonlinear problem seeking to service a number of customers with a fleet of vehicles. CVRP is an important problem in the fields of transportation, distribution and logistics. Usually, the goal is delivering goods located at a central depot to customers who have placed orders. This transportation optimization prob...