Profitable mixed capacitated arc routing and related problems

Mixed capacitated arc routing problems aim to identify a set of vehicle tours that, starting and ending at a depot node, serve a given number of links at minimum cost, while satisfying the vehicles capacity. If both profits and costs on arcs are considered, we may define the profitable mixed capacitated arc routing problem (PMCARP). In this paper we present compact flow-based models for the PMCARP, where two types of services are tackled, mandatory and optional. Adaptations of the models to fit into some other related problems are also proposed. The models are evaluated, according to their bounds quality as well as to the CPU times, over large sets of test instances. New instances have been created for some variants that have been introduced here for the first time. Results show the new models performance within CPLEX and compare, whenever available, the proposed models against other resolution methods.