scholarly journals Column Generation for a Multitrip Vehicle Routing Problem with Time Windows, Driver Work Hours, and Heterogeneous Fleet

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Michel Povlovitsch Seixas ◽  
André Bergsten Mendes
Keyword(s):  
Vehicle Routing ◽  
Column Generation ◽  
Vehicle Routing Problem ◽  
Resource Constraints ◽  
Time Windows ◽  
Planning Horizon ◽  
Work Hours ◽  
Start Time ◽  
Routing Problem ◽  
Multiple Routes

This study addresses a vehicle routing problem with time windows, accessibility restrictions on customers, and a fleet that is heterogeneous with regard to capacity and average speed. A vehicle can perform multiple routes per day, all starting and ending at a single depot, and it is assigned to a single driver whose total work hours are limited. A column generation algorithm is proposed. The column generation pricing subproblem requires a specific elementary shortest path problem with resource constraints algorithm to address the possibility for each vehicle performing multiple routes per day and to address the need to set the workday’s start time within the planning horizon. A constructive heuristic and a metaheuristic based on tabu search are also developed to find good solutions.

scholarly journals The last-mile vehicle routing problem with delivery options

OR Spectrum ◽  
2021 ◽  
Author(s):  
Christian Tilk ◽  
Katharina Olkis ◽  
Stefan Irnich
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Resource Constraints ◽  
Time Window ◽  
Time Windows ◽  
Service Level ◽  
Optimal Solutions ◽  
Routing Problem ◽  
Common Location ◽  
Delivery Options

AbstractThe ongoing rise in e-commerce comes along with an increasing number of first-time delivery failures due to the absence of the customer at the delivery location. Failed deliveries result in rework which in turn has a large impact on the carriers’ delivery cost. In the classical vehicle routing problem (VRP) with time windows, each customer request has only one location and one time window describing where and when shipments need to be delivered. In contrast, we introduce and analyze the vehicle routing problem with delivery options (VRPDO), in which some requests can be shipped to alternative locations with possibly different time windows. Furthermore, customers may prefer some delivery options. The carrier must then select, for each request, one delivery option such that the carriers’ overall cost is minimized and a given service level regarding customer preferences is achieved. Moreover, when delivery options share a common location, e.g., a locker, capacities must be respected when assigning shipments. To solve the VRPDO exactly, we present a new branch-price-and-cut algorithm. The associated pricing subproblem is a shortest-path problem with resource constraints that we solve with a bidirectional labeling algorithm on an auxiliary network. We focus on the comparison of two alternative modeling approaches for the auxiliary network and present optimal solutions for instances with up to 100 delivery options. Moreover, we provide 17 new optimal solutions for the benchmark set for the VRP with roaming delivery locations.

Solving the vehicle routing problem with time windows and multiple routes exactly using a pseudo-polynomial model

2011 ◽  
Vol 214 (3) ◽  
pp. 536-545 ◽  
Author(s):  
Rita Macedo ◽  
Cláudio Alves ◽  
J.M. Valério de Carvalho ◽  
François Clautiaux ◽  
Saïd Hanafi
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Time Windows ◽  
Polynomial Model ◽  
Routing Problem ◽  
Multiple Routes

scholarly journals A Bucket Graph–Based Labeling Algorithm with Application to Vehicle Routing

2020 ◽  
Author(s):  
Ruslan Sadykov ◽  
Eduardo Uchoa ◽  
Artur Pessoa
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Resource Constraints ◽  
Time Window ◽  
Time Windows ◽  
Routing Problem ◽  
Constrained Vehicle Routing ◽  
Time Window Constraints ◽  
Vehicle Capacity ◽  
First Time

We consider the shortest path problem with resource constraints arising as a subproblem in state-of-the-art branch-cut-and-price algorithms for vehicle routing problems. We propose a variant of the bidirectional label-correcting algorithm in which the labels are stored and extended according to the so-called bucket graph. This organization of labels helps to significantly decrease the number of dominance checks and the running time of the algorithm. We also show how the forward/backward route symmetry can be exploited and how to eliminate arcs from the bucket graph using reduced costs. The proposed algorithm can be especially beneficial for vehicle routing instances with large vehicle capacity and/or with time window constraints. Computational experiments were performed on instances from the distance-constrained vehicle routing problem, including multidepot and site-dependent variants, on the vehicle routing problem with time windows, and on the “nightmare” instances of the heterogeneous fleet vehicle routing problem. Significant improvements over the best algorithms in the literature were achieved, and many instances could be solved for the first time.

scholarly journals A Three-Stage Saving-Based Heuristic for Vehicle Routing Problem with Time Windows and Stochastic Travel Times

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Zheng Wang ◽  
Chunyue Zhou
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Time Windows ◽  
Travel Times ◽  
Start Time ◽  
Routing Problem ◽  
Problem Transformation ◽  
Basic Ideas ◽  
Two Stages ◽  
Stochastic Travel Times

This paper presents a saving-based heuristic for the vehicle routing problem with time windows and stochastic travel times (VRPTWSTT). One of the basic ideas of the heuristic is to advance the latest service start time of each customer by a certain period of time. In this way, the reserved time can be used to cope with unexpected travel time delay when necessary. Another important idea is to transform the VRPTWSTT to a set of vehicle routing problems with time windows (VRPTW), each of which is defined by a given percentage used to calculate the reserved time for customers. Based on the above two key ideas, a three-stage heuristic that includes the “problem transformation” stage, the “solution construction” stage, and the “solution improvement” stage is developed. After the problem transformation in the first stage, the work of the next two stages is to first construct an initial solution for each transformed VRPTW by improving the idea of the classical Clarke-Wright heuristic and then further improve the solution. Finally, a number of numerical experiments are conducted to evaluate the efficiency of the described methodology under different uncertainty levels.

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