In this paper I propose a Branch-and-Price algorithm for the solution of the Vehicle Routing Problem with Time Windows where the pricing subproblem, the resource constrained elementary shortest path problem (RCESPP), is solved to optimality. 1. Problem formulation The Vehicle Routing Problem with Time Windows (VRPTW) is defined over a graph G = (V, A) where V = {0, . . . , n} is the node set in...

the inventory routing problem (irp) arises in the context of vendor-managed systems. this problem addresses jointly solving an inventory management problem and a vehicle routing problem. in this paper, we consider a multi-depot multi-vehicle inventory routing problem in which suppliers produce one type of product to be delivered to customers during a finite time horizon. we propose a two-phase ...

Vehicle routing problem is a kind of common problem in logistics distribution center, in order to solve the high delivery cost of VRP and time constraint problem, the VRP model with the object level and constraints by semi-soft time window is built. Aiming to the semi-soft time window constraints the optimization of the model is discussed. Finally the numerical examples prove the superiority of...

In this thesis, we consider ow formulations for the Time Window Assignment Vehicle Routing Problem (TWAVRP), the problem of assigning time windows for delivery before demand volume becomes known. Using commercial solver CPLEX as a basis, we develop a branch-and-cut algorithm that is able to solve all test-instances of Spliet and Gabor (2014) to optimality and is highly competitive with the stat...

One of the important extensions of the classical resource allocation problem is integrated resource allocation and routing problem with time window (IRARPTW). IRARPTW problem focuses on the time window for the service at the demanding node with the consideration of travel time of vehicle for a varying demand-oriented multi echelon supply chain with the consideration of limitation on the number ...

This paper formulates a mathematical model for the Green Vehicle Routing Problem (GVRP), incorporating bi-fuel (natural gas and gasoline) pickup trucks in a mixed vehicle fleet. The objective is to minimize overall costs relating to service (earliness and tardiness), transportation (fixed, variable and fuel), and carbon emissions. To reflect a real-world situation, the study considers: (1) a co...

the vehicle routing problem with backhauls (vrpb) as an extension of the classical vehicle routing prob-lem (vrp) attempts to define a set of routes which services both linehaul customers whom product are to be delivered and backhaul customers whom goods need to be collected. a primary objective for the problem usually is minimizing the total distribution cost. most real-life problems have othe...