The classical Vehicle Routing Problem (VRP) is defined on a graph G = (V,A) where V = {111, v 2 . . . . , v,} is a set of vertices and A = {(vi,vj):i # j , v i, vj ~ V} is the arc set. Vertex v 1 represents a depot at which are based m identical vehicles, while the remaining vertices correspond to cities or customers. A matrix C = (ciy) is defined on A. The coefficients cgy represent distances,...

The Vehicle Routing Problem (VRP) has been extensively studied over the last twenty years, because it is an abstraction of many real-life logistics problems. In its multiple-depot variant (MDVRP), the routes of vehicles located at various depots must be optimized to serve a number of customers. In this paper, we investigate how to protect the privacy of delivery companies, when each depot is ow...

A train schedule defines each train’s arrival/departure time at a car depot. Between the arrival and departure times, every train has to have its designated works, such as inspection and cleaning of the cars, completed, which are predefined by a car operation schedule. The planner of car shuntings at a car depot must create a schedule that satisfies the above-mentioned conditions, while also ta...

This paper examines a practical transportation model known as the Open Vehicle Routing Problem (OVRP). OVRP aims at designing the minimum cost set of routes originating from a central depot for satisfying customer demand. Vehicles do not need to return to the depot after completing their delivery services. In methodological terms, we propose an innovative local search metaheuristic which examin...

In vehicle routing problems (VRPs) the decisions to be taken concern assignment of customers vehicles and sequencing assigned each vehicle. Additional may need jointly taken, depending on specific problem setting. this paper, after discussing different kinds in classes VRPs, class where decision about when routes start from depot has is considered related literature reviewed. This problems, tha...

In real-life logistics and distribution activities it is usual to face situations in which the distribution of goods has to be made from multiple warehouses or depots to the final customers. This problem is known as the Multi-Depot Vehicle Routing Problem (MDVRP), and it typically includes two sequential and correlated stages: (a) the assignment map of customers to depots, and (b) the correspon...

Vehicle Routing Problem (VRP) is addressed to a class of problems for determining a set of vehicle routes, in which each vehicle departs from a given depot, serves a given set of customers, and returns back to the same depot. On the other hand, simultaneous delivery and pickup problems have drawn much attention in the past few years due to its high usage in real world cases. This study, therefo...

in a logistic system, decisions on location of depot, vehicle routing and assignment of routes to vehicles should be considered simultaneously. the location-routing problems are defined to find the optimal number and locations of depots, and at the same time with the distribution routes for the vehicles. because of the complexity and the time consuming computation, this problem belongs to a cla...

In this paper, the fuzzy multi-depot vehicle routing problem with simultaneous pickup and delivery (FMDVRP-SPD) is investigated. The FMDVRP-SPD is the problem of allocating customers to several depots, so that the optimal set of routes is determined simultaneously to serve the pickup and the delivery demands of each customer within scattered depots. In the problem, both pickup and delivery dema...

This paper addresses the Vehicle Routing Problem with Delivery Time Cost. This problem aims to find a set of routes of minimal total costs including the travelling cost and delivery time cost, starting and ending at the depot, in such a way that each customer is visited by one vehicle given the capacity of the vehicle to satisfy a specific demand. In this research, a hybrid metaheuristic approa...