Modeling and Solving the Capacitated Vehicle Routing Problem on Trees

Capacitated vehicle routing problems (CVRPs) form the core of logistics planning and are hence of great practical and theoretical interest. This chapter considers the CVRP on trees (TCVRP), a problem that often naturally arises in railway, river, and rural road networks. Our objective is to build high-quality models that exploit the tree structure of the problem that can also be easily implemented within the framework of a modeling language (a feature desired by practitioners) like AMPL, GAMS, or OPL. We present two new integer programming models for the TCVRP that explicitly take advantage of the tree structure of the graph. The two models are implemented using the AMPL model building language, and compared along several metrics—computation time, quality of the linear programming relaxation, and scalability—to examine their relative strengths.