In this paper we introduce a robust optimization approach to solve the Vehicle Routing Problem (VRP) with demand uncertainty. This approach yields routes that minimize transportation costs while satisfying all demands in a given bounded uncertainty set. We show that for the Miller-Tucker-Zemlin formulation of the VRP and specific uncertainty sets, solving for the robust solution is no more diff...

The number of optimization techniques in the combinatorial domain is large and diversified. Nevertheless, there is still a lack of real benchmarks to validate optimization algorithms. In this work we introduce VRPBench, a tool to create instances and visualize solutions to the Vehicle Routing Problem (VRP) in a planar graph embedded in the Euclidean 2D space. We use VRPBench to model a real-wor...

It is well known that the Vehicle Routing Problem (VRP) becomes more difficult to solve as the problem size increases. However little is known about what makes a VRP difficult or easy to solve for problems of the same size. In this paper we investigate the effect of the formulation and data parameters on the efficiency with which we can obtain exact solutions to the VRP with a general IP solver...

Abstract In the classic Vehicle Routing Problem (VRP) a fleet of of vehicles has to visit a set of customers while minimising the operations’ costs. We study a rich variant of the VRP featuring split deliveries, an heterogeneous fleet, and vehiclecommodity incompatibility constraints. Our goal is twofold: define the cheapest routing and the most adequate fleet. To do so, we split the problem in...

In this paper, we address the Two-Echelon Vehicle Routing Problem (2E-VRP) in which freight is delivered from depots to intermediary satellites, from where it is delivered to customers. Different from other multi-level problems, the focus in 2E-VRP is on the global routing costs of the overall network. 2E-VRP has been recently introduced and, to our knowledge, there are no studies of the impact...

Vehicle Routing Problem (VRP) is a hot issue in the field of logistics. Furthermore, the Vehicle Routing Problem with Time-Windows (VRPTW) is an additional constraint of the customer access time windows based on the VRP. It becomes a noticeable problem with the development of logistics distribution and the just-intime distribution demand from customers, which increases a visiting window to trad...

The vehicle routing problem (VRP) is a family of problems whereby a fleet of vehicles must service the commodity demands of a set of geographically scattered customers from one or more depots, subject to a number of constraints. Early hyper-heuristic research focussed on selecting and applying a low-level heuristic at a given stage of an optimisation process. Recent trends have led to a number ...

The distribution of finished products from depots to customers is a practical and challenging problem in logistics management. Better routing and scheduling decisions can result in higher level of customer satisfaction because more customers can be served in a shorter time. The distribution problem is generally formulated as the vehicle routing problem (VRP). Nevertheless, there is a rigid assu...

The objective of vehicle routing problem (VRP) is to design a set of vehicle routes in which a fixed fleet of delivery vehicles from one or several depots to a number of customers have to be set with some constraints. To this date in the literature, many instances of VRP model have been introduced and applied for various types of scheduling problems. However, when implemented in a real life app...

Development of vaccines against cytomegalovirus (CMV) is an important public health priority. We used a propagation-defective, single-cycle RNA replicon vector system derived from an attenuated strain of an alphavirus, Venezuelan equine encephalitis virus, to produce virus-like replicon particles (VRP) expressing various combinations of pp65, IE1, or gB proteins of human CMV. Protein expression...