Exact and Approximation Algorithms for the Multi-Depot Capacitated Arc Routing Problems

Abstract

In this work, we investigate a generalization of the classical capacitated arc routing problem, called the Multi-depot Capacitated Arc Routing Problem (MCARP). We give exact and approximation algorithms for different variants of the MCARP. First, we obtain the first constant-ratio approximation algorithms for the MCARP and its nonfixed destination version. Second, for the multi-depot rural postman problem, i.e., a special case of the MCARP where the vehicles have infinite capacity, we develop a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(2-\frac{1}{2k+1})$</tex> -approximation algorithm ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> denotes the number of depots). Third, we show the polynomial solvability of the equal-demand MCARP on a line and devise a 2-approximation algorithm for the multi-depot capacitated vehicle routing problem on a line. Lastly, we conduct extensive numerical experiments on the algorithms for the multi-depot rural postman problem to show their effectiveness.