Formulations and Branch-and-Cut Algorithms for the Generalized Vehicle Routing Problem

• Published in: Transportation science Vol. 45; no. 3; pp. 299 - 316
• Main Authors: BEKTAS, Tolga, ERDOGAN, Güneş, RØPKE, Stefan
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01-08-2011; Transportation Science & Logistic Society of the Institute for Operations Research and Management Sciences; Institute for Operations Research and the Management Sciences
• Subjects: Algorithms; Applied sciences; Branch & bound algorithms; branch-and-cut; Branch-and-cut algorithms; Cluster analysis; Comparative analysis; Computational methods; Demand analysis; Exact sciences and technology; Formulae; Generalized vehicle routing; Ground, air and sea transportation, marine construction; Heuristics; Inequality; Integer programming; Integers; Linear programming; Logistics; Mathematics; Methods; Multicommodity flow; Optimal solutions; Preprocessing; Road transport; Routing; Studies; Transport costs; Transport planning; Transportation; Transportation demand; Transportation planning, management and economics; Transportation problem (Operations research); Travel; Vehicles; Vertices; United States; Integer programming; branch-and-cut; Branch and cut method; Formulation; Vehicle routing problem; Transportation; generalized vehicle routing; Algorithm; Modeling; Comparative study; Result
• ISSN: 0041-1655; 1526-5447
• DOI: 10.1287/trsc.1100.0352

The generalized vehicle routing problem (GVRP) consists of finding a set of routes for a number of capacitated vehicles on a graph where the vertices are partitioned into clusters with given demands, such that the total cost of travel is minimized and all demands are met. This paper describes and compares four new integer linear programming formulations for the GVRP, two based on multicommodity flow and the other two based on exponential-size sets of inequalities. Branch-and-cut algorithms are proposed for the latter two. Computational results on a large set of instances are presented.