Combined route capacity and route length models for unit demand vehicle routing problems

Authors:
Maria Teresa Godinho;Luis Gouveia;Thomas L. Magnanti
Affiliations:
Departamento de Matemática, Escola Superior de Tecnologia e Gestão, Instituto Politécnico de Beja, Portugal;Faculdade de Ciências da Universidade de Lisboa, DEIO - CIO, Bloco C/2 - Campo Grande, CIDADE UNIVERSITARIA, 1749-016 Lisboa, Portugal;Department of Electrical Engineering and Computer Science and Sloan School of Management, MIT, Cambridge, MA 02139, USA
Venue:
Discrete Optimization
Year:
2008

Citing 12
Cited 2

The asymmetric assignment problem and some new facets of the traveling salesman polytope on a directed graph

SIAM Journal on Discrete Mathematics
Facets of the asymmetric traveling salesman polytope

Mathematics of Operations Research
A polyhedral intersection theorem for capacitated spanning trees

Mathematics of Operations Research
The fixed-outdegree 1-arborescence polytope

Mathematics of Operations Research
A polyhedral approach to the asymmetric traveling salesman problem

Management Science
The vehicle routing problem

The vehicle routing problem
The asymmetric travelling salesman problem: on generalizations of disaggregated Miller-Tucker-Zemlin contraints

Discrete Applied Mathematics - Special issue on the combinatorial optimization symposium
Using Variable Redefinition for Computing Lower Bounds for Minimum Spanning and Steiner Trees with Hop Constraints

INFORMS Journal on Computing
A new branch-and-cut algorithm for the capacitated vehicle routing problem

Mathematical Programming: Series A and B
Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem

Mathematical Programming: Series A and B
An Exact Algorithm for the Capacitated Vehicle Routing Problem Based on a Two-Commodity Network Flow Formulation

Operations Research
Classification of travelling salesman problem formulations

Operations Research Letters

Layered formulation for the robust vehicle routing problem with time windows

ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Natural and extended formulations for the Time-Dependent Traveling Salesman Problem

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider two types of hop-indexed models for the unit-demand asymmetric Capacitated Vehicle Routing Problem (CVRP): (a) capacitated models guaranteeing that the number of commodities (paths) traversing any given arc does not exceed a specified capacity; and (b) hop-constrained models guaranteeing that any route length (number of nodes) does not exceed a given value. The latter might, in turn, be divided into two classes: (b1) those restricting the length of the path from the depot to any node k, and (b2) those restricting the length of the circuit passing through any node k. Our results indicate that formulations based upon circuit lengths (b2) lead to models with a linear programming relaxation that is tighter than the linear programming relaxation of models based upon path lengths (b1), and that combining features from capacitated models with those of circuit lengths can lead to formulations for the CVRP with a tight linear programming bound. Computational results on a small number of problem instances with up to 41 nodes and 440 edges show that the combined model with capacities and circuit lengths produce average gaps of less than one percent. We also briefly examine the asymmetric travelling salesman problem (ATSP), showing the potential use of the ideas developed for the vehicle routing problem to derive models for the ATSP with a linear programming relaxation bound that is tighter than the linear programming relaxation bound of the standard Dantzig, Fulkerson and Johnson [G. Dantzig, D. Fulkerson, D. Johnson, Solution of large-scale travelling salesman problem, Operations Research 2 (1954) 393-410] formulation.