New valid inequalities for the symmetric vehicle routing problem with simultaneous pickup and deliveries

Networks ◽  
2021 ◽  
Author(s):  
Yogesh Kumar Agarwal ◽  
Prahalad Venkateshan
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Valid Inequalities ◽  
Routing Problem

Valid inequalities for the fleet size and mix vehicle routing problem with fixed costs

Networks ◽  
2009 ◽  
Vol 54 (4) ◽  
pp. 178-189 ◽  
Author(s):  
Roberto Baldacci ◽  
Maria Battarra ◽  
Daniele Vigo
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Valid Inequalities ◽  
Fixed Costs ◽  
Routing Problem ◽  
Fleet Size ◽  
Fleet Size And Mix

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.

scholarly journals Mathematical models for the periodic vehicle routing problem with time windows and time spread constraints

2020 ◽  
Vol 11 (1) ◽  
pp. 10-23
Author(s):  
Hande Öztop ◽  
Damla Kizilay ◽  
Zeynel Abidin Çil
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Optimization Problems ◽  
Valid Inequalities ◽  
Time Windows ◽  
Mixed Integer ◽  
Routing Problem ◽  
Periodic Vehicle Routing Problem ◽  
Time Spread ◽  
Periodic Vehicle Routing

The periodic vehicle routing problem (PVRP) is an extension of the well-known vehicle routing problem. In this paper, the PVRP with time windows and time spread constraints (PVRP-TWTS) is addressed, which arises in the high-value shipment transportation area. In the PVRP-TWTS, period-specific demands of the customers must be delivered by a fleet of heterogeneous capacitated vehicles over the several planning periods. Additionally, the arrival times to a customer should be irregular within its time window over the planning periods, and the waiting time is not allowed for the vehicles due to the security concerns. This study, proposes novel mixed-integer linear programming (MILP) and constraint programming (CP) models for the PVRP-TWTS. Furthermore, we develop several valid inequalities to strengthen the proposed MILP and CP models as well as a lower bound. Even though CP has successful applications for various optimization problems, it is still not as well-known as MILP in the operations research field. This study aims to utilize the effectiveness of CP in solving the PVRP-TWTS. This study presents a CP model for PVRP-TWTS for the first time in the literature to the best of our knowledge. Having a comparison of the CP and MILP models can help in providing a baseline for the problem. We evaluate the performance of the proposed MILP and CP models by modifying the well-known benchmark set from the literature. The extensive computational results show that the CP model performs much better than the MILP model in terms of the solution quality.

scholarly journals Valid Inequalities for the Green Vehicle Routing Problem

2020 ◽  
Author(s):  
Matheus Diógenes Andrade ◽  
Fábio Luiz Usberti
Keyword(s):  
Vehicle Routing ◽  
Electric Vehicles ◽  
Vehicle Routing Problem ◽  
Valid Inequalities ◽  
Alternative Fuel ◽  
Hard Problem ◽  
Np Hard ◽  
Green Logistics ◽  
Routing Problem ◽  
Np Hard Problem

This work aims to investigate the Green Vehicle Routing Problem (G-VRP), which is an NP-Hard problem that generalizes the Vehicle Routing Problem (VRP) and integrates it with the green logistics. In the G-VRP, electric vehicles with limited autonomy can be recharged at Alternative Fuel Stations (AFSs) to keep visiting customers. This research proposes MILP formulations, valid inequalities, and preprocessing conditions.

A Branch-Price-and-Cut Algorithm for the Two-Echelon Vehicle Routing Problem with Time Windows

2021 ◽  
Author(s):  
Tayeb Mhamedi ◽  
Henrik Andersson ◽  
Marilène Cherkesly ◽  
Guy Desaulniers
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Time Window ◽  
Valid Inequalities ◽  
Time Windows ◽  
A Priori ◽  
Solution Process ◽  
High Capacity ◽  
Sensitivity Analyses ◽  
Routing Problem

In this paper, we propose an exact branch-price-and-cut (BPC) algorithm for the two-echelon vehicle routing problem with time windows. This problem arises in city logistics when high-capacity and low-capacity vehicles are used to transport items from depots to satellites (first echelon) and from satellites to customers (second echelon), respectively. The aim is to determine a set of least-cost first- and second-echelon routes such that the load on the routes respect the capacity of the vehicles, each second-echelon route is supplied by exactly one first-echelon route, and each customer is visited by exactly one second-echelon route within its time window. We model the problem with a route-based formulation where first-echelon routes are enumerated a priori, and second-echelon routes are generated using column generation. The problem is solved using BPC. To generate second-echelon routes, one pricing problem per satellite is solved using a labeling algorithm which keeps track of the first-echelon route associated with each (partial) second-echelon route considered. Furthermore, to speed up the solution process, we introduce effective deep dual-optimal inequalities and apply known valid inequalities. We perform extensive computational experiments on benchmark instances and show that our method outperforms a state-of-the-art algorithm. We also conduct sensitivity analyses on the different components of our algorithm and derive managerial insights related to the structure of the first-echelon routes.

Sign in / Sign up

Export Citation Format

Share Document