This paper presents a column generation algorithm for the Vehicle Routing Problem with Time Windows (VRPTW). Traditionally, column generation models of the VRPTW have consisted of a Set Partitioning master problem with each column representing a route, i.e., a resource feasible path starting and ending at the depot. Elementary routes (no customer visited more than once) have shown superior resu...

The Vehicle Routing Problem with Time Windows (VRPTW) is an important problem occurring in many logistics systems. The objective of VRPTW is to serve a set of customers within their predefined time windows at minimum cost. Ant Colony System algorithm (ACS) that is capable of searching multiple search areas simultaneously in the solution space is good in diversification. On the other hand, Simul...

The Vehicle Routing Problem with Time Windows (VRPTW) is an important problem in logistics, which is an extension of well known Vehicle Routing Problem (VRP), with a central depot. The Objective is to design an optimal set of routes for serving a number of customers without violating the customer’s time window constraints and vehicle capacity constraint. It has received considerable attention i...

At this time the effectiveness of COVID-19 vaccines has been proven, and it is crucial to carry out complete vaccination population. Therefore, imperative optimize vaccine distribution fleets. This paper discusses optimization routes for Pfizer in Portugal terms transportation time, total costs, CO2 emissions. To end, Vehicle Routing Problem with Time Windows (VRPTW) model a vehicle capacity re...

This paper presents a survey of the research on the Vehicle Routing Problem with Time Windows (VRPTW). The VRPTW can be described as the problem of designing least cost routes from one depot to a set of geographically scattered points. The routes must be designed in such a way that each point is visited only once by exactly one vehicle within a given time interval, all routes start and end at t...

In this paper we consider the vehicle routing problem with hard time windows and stochastic service times (VRPTW-ST); in this variant of the classic VRPTW the service times are random variables. In particular, given a set of vehicle routes, some of the actual service times might not lead to a feasible solution, given the customer time windows. We consider a chance-constrained program to model t...

The home care nurses routing and scheduling problem consists in determining the sequences of visits performed by home care nurses to patients. Very often public medical clinics are responsible for this planning. The problem shows similarities with the vehicle routing problem with time windows (VRPTW) but it also includes additional constraints related to medical restrictions and to the continui...

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...

In the vehicle routing problem with time window (VRPTW), the objective is to minimize the number of vehicles and then minimize the total time travelled. Each route starts at the depot and ends at a customer, visiting a number of customers, each once, en route, without returning to the depot. The demand of each customer must be completely fulfilled by a single vehicle. The total demand serviced ...

The Vehicle Routing Problem with Time Windows is an important task in logistic planning. The expenditure on employing labor force, i.e., drivers for vehicles, accounts for most of the costs in this domain. We propose an initialized Ant Colony approach, IACO-VRPTW, with the primary goal (f1) to reduce the number of vehicle needed to serve the customers and the second-priority goal (f2) of decrea...