A Column Generation Algorithm for a Rich Vehicle-Routing Problem

2009 ◽  
Vol 43 (1) ◽  
pp. 56-69 ◽  
Author(s):  
Alberto Ceselli ◽  
Giovanni Righini ◽  
Matteo Salani
Keyword(s):  
Vehicle Routing ◽  
Column Generation ◽  
Vehicle Routing Problem ◽  
Routing Problem ◽  
Generation Algorithm

A column generation algorithm for the vehicle routing problem with soft time windows

4OR ◽  
2010 ◽  
Vol 9 (1) ◽  
pp. 49-82 ◽  
Author(s):  
Federico Liberatore ◽  
Giovanni Righini ◽  
Matteo Salani
Keyword(s):  
Vehicle Routing ◽  
Column Generation ◽  
Vehicle Routing Problem ◽  
Time Windows ◽  
Routing Problem ◽  
Generation Algorithm ◽  
Soft Time Windows

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 Joint Network Vehicle Routing Game

2020 ◽  
Author(s):  
Mathijs van Zon ◽  
Remy Spliet ◽  
Wilco van den Heuvel
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Cost Allocation ◽  
Allocation Problem ◽  
Routing Problem ◽  
Generation Algorithm ◽  
Core Allocation ◽  
New Variant ◽  
Delivery Routes ◽  
The Cost

Collaborative transportation can significantly reduce transportation costs as well as greenhouse gas emissions. However, allocating the cost to the collaborating companies remains difficult. We consider the cost-allocation problem, which arises when companies, each with multiple delivery locations, collaborate by consolidating demand and combining delivery routes. We model the corresponding cost-allocation problem as a cooperative game: the joint network vehicle routing game (JNVRG). We propose a row generation algorithm to either determine a core allocation for the JNVRG or show that no such allocation exists. In this approach, we encounter a row generation subproblem, which we model as a new variant of a vehicle routing problem with profits. Moreover, we propose two main acceleration strategies for the row generation algorithm. First, we generate rows by relaxing the row generation subproblem, exploiting the tight linear programming (LP) bounds for our formulation of the row generation subproblem. Secondly, we propose to also solve the row generation subproblem heuristically and to only solve it to optimality when the heuristic fails. We demonstrate the effectiveness of the proposed row generation algorithm and the acceleration strategies by means of numerical experiments for both the JNVRG as well as the traditional vehicle routing game, which is a special case of the JNVRG. We create instances based on benchmark instances of the capacitated vehicle routing problem from the literature. We are able to either determine a core allocation or show that no core allocation exists, for instances ranging from 5 companies with a total of 79 delivery locations to 53 companies with a total of 53 delivery locations.

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