Branch-and-Cut-and-Price for the Vehicle Routing Problem with Time Windows and Convex Node Costs

2019 ◽  
Vol 53 (5) ◽  
pp. 1409-1426 ◽  
Author(s):  
Qie He ◽  
Stefan Irnich ◽  
Yongjia Song
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Time Windows ◽  
Branch And Cut ◽  
Routing Problem

scholarly journals The Robust Vehicle Routing Problem with Time Windows: Compact Formulation and Branch-Price-and-Cut Method

2019 ◽  
Vol 53 (4) ◽  
pp. 1043-1066 ◽  
Author(s):  
Pedro Munari ◽  
Alfredo Moreno ◽  
Jonathan De La Vega ◽  
Douglas Alem ◽  
Jacek Gondzio ◽  
...  
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Time Windows ◽  
Real Life ◽  
Set Partitioning ◽  
Branch And Cut ◽  
Small Scale ◽  
Routing Problem ◽  
Compact Formulation ◽  
Cut Method

We address the robust vehicle routing problem with time windows (RVRPTW) under customer demand and travel time uncertainties. As presented thus far in the literature, robust counterparts of standard formulations have challenged general-purpose optimization solvers and specialized branch-and-cut methods. Hence, optimal solutions have been reported for small-scale instances only. Additionally, although the most successful methods for solving many variants of vehicle routing problems are based on the column generation technique, the RVRPTW has never been addressed by this type of method. In this paper, we introduce a novel robust counterpart model based on the well-known budgeted uncertainty set, which has advantageous features in comparison with other formulations and presents better overall performance when solved by commercial solvers. This model results from incorporating dynamic programming recursive equations into a standard deterministic formulation and does not require the classical dualization scheme typically used in robust optimization. In addition, we propose a branch-price-and-cut method based on a set partitioning formulation of the problem, which relies on a robust resource-constrained elementary shortest path problem to generate routes that are robust regarding both vehicle capacity and customer time windows. Computational experiments using Solomon’s instances show that the proposed approach is effective and able to obtain robust solutions within a reasonable running time. The results of an extensive Monte Carlo simulation indicate the relevance of obtaining robust routes for a more reliable decision-making process in real-life settings.

The Robust Vehicle Routing Problem with Time Window Assignments

2021 ◽  
Vol 55 (2) ◽  
pp. 395-413
Author(s):  
Maaike Hoogeboom ◽  
Yossiri Adulyasak ◽  
Wout Dullaert ◽  
Patrick Jaillet
Keyword(s):  
Travel Time ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Service Providers ◽  
Time Window ◽  
Time Windows ◽  
Branch And Cut ◽  
Optimal Time ◽  
Routing Problem ◽  
Solution Approach

In practice, there are several applications in which logistics service providers determine the service time windows at the customers, for example, in parcel delivery, retail, and repair services. These companies face uncertain travel times and service times that have to be taken into account when determining the time windows and routes prior to departure. The objective of the proposed robust vehicle routing problem with time window assignments (RVRP-TWA) is to simultaneously determine routes and time window assignments such that the expected travel time and the risk of violating the time windows are minimized. We assume that the travel time probability distributions are not completely known but that some statistics, such as the mean, minimum, and maximum, can be estimated. We extend the robust framework based on the requirements’ violation index, which was originally developed for the case where the specific requirements (time windows) are given as inputs, to the case where they are also part of the decisions. The subproblem of finding the optimal time window assignment for the customers in a given route is shown to be convex, and the subgradients can be derived. The RVRP-TWA is solved by iteratively generating subgradient cuts from the subproblem that are added in a branch-and-cut fashion. Experiments address the performance of the proposed solution approach and examine the trade-off between expected travel time and risk of violating the time windows.

scholarly journals Cover Inequalities for a Vehicle Routing Problem with Time Windows and Shifts

2019 ◽  
Vol 53 (5) ◽  
pp. 1354-1371 ◽  
Author(s):  
Said Dabia ◽  
Stefan Ropke ◽  
Tom van Woensel
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Valid Inequalities ◽  
Time Windows ◽  
Branch And Cut ◽  
Master Problem ◽  
Loading Capacity ◽  
Routing Problem ◽  
Cover Inequalities ◽  
And Shifts

This paper introduces the vehicle routing problem with time windows and shifts (VRPTWS). At the depot, several shifts with nonoverlapping operating periods are available to load the planned trucks. Each shift has a limited loading capacity. We solve the VRPTWS exactly by a branch-and-cut-and-price algorithm. The master problem is a set partitioning with an additional constraint for every shift. Each constraint requires the total quantity loaded in a shift to be less than its loading capacity. For every shift, a pricing subproblem is solved by a label-setting algorithm. Shift capacity constraints define knapsack inequalities; hence we use valid inequalities inspired from knapsack inequalities to strengthen the linear programming relaxation of the master problem when solved by column generation. In particular, we use a family of tailored robust cover inequalities and a family of new nonrobust cover inequalities. Numerical results show that nonrobust cover inequalities significantly improve the algorithm.

A Branch-and-Cut Procedure for the Vehicle Routing Problem with Time Windows

2002 ◽  
Vol 36 (2) ◽  
pp. 250-269 ◽  
Author(s):  
Jonathan F. Bard ◽  
George Kontoravdis ◽  
Gang Yu
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Time Windows ◽  
Branch And Cut ◽  
Routing Problem

scholarly journals A hybrid ant colony algorithm based on multiple strategies for the vehicle routing problem with time windows

2021 ◽  
Author(s):  
Hongguang Wu ◽  
Yuelin Gao ◽  
Wanting Wang ◽  
Ziyu Zhang
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Ant Colony Algorithm ◽  
Time Window ◽  
Time Windows ◽  
Ant Colony ◽  
Routing Problem ◽  
Multiple Strategies ◽  
Hard Time ◽  
Mutation Operation

AbstractIn this paper, we propose a vehicle routing problem with time windows (TWVRP). In this problem, we consider a hard time constraint that the fleet can only serve customers within a specific time window. To solve this problem, a hybrid ant colony (HACO) algorithm is proposed based on ant colony algorithm and mutation operation. The HACO algorithm proposed has three innovations: the first is to update pheromones with a new method; the second is the introduction of adaptive parameters; and the third is to add the mutation operation. A famous Solomon instance is used to evaluate the performance of the proposed algorithm. Experimental results show that HACO algorithm is effective against solving the problem of vehicle routing with time windows. Besides, the proposed algorithm also has practical implications for vehicle routing problem and the results show that it is applicable and effective in practical problems.

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.

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