Abstract Capacitated arc routing problem (CARP) is the determination of vehicle tours that serve all positive-demand edges (required edge) exactly once without exceeding vehicle capacity while minimizing sum of all tour costs. In CARP, total demand of a tour is calculated by means of all required edges on the tour. In this study, a new CARP variation is introduced, which considers not only required edges but also traversed edges while calculating total demand of the tour. The traversing demand occurs when the traversed edge is either servicing or non-servicing (deadheading). Since the new CARP formulation incurs deadheading edge demands it is called CARP with deadheading demands. An integer linear model is given for the problem which is used to solve small-sized instances, optimally. A constructive heuristic is presented to solve the problem which is a modified version of a well-known CARP heuristic. Furthermore, two post-optimization procedures are presented to improve the solution of the heuristic algorithm. The effectiveness of the proposed methods is shown on test problems, which are obtained by modifying CARP test instances.