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To improve customer service in the reverse logistics, this article defines a new variant of the vehicle routing problem (VRP) by combining the consistent VRP (ConVRP) and the VRP with simultaneous distribution and collection (VRPSDC). This new variant is called the consistent vehicle routing problem with simultaneous distribution and collection, for which a mixed-integer programming model is formulated. To solve this problem, three heuristics are proposed on the basis of the record-to-record (RTR) travel algorithm, the local search with variable neighbourhood search (LSVNS), and the tabu search-based method. Numerical experiments are performed to validate the efficiency of our proposed solution methods and the effectiveness of the proposed model. The results show that the RTR-based heuristic has an advantage in small-scale instances. However, for medium-scale instances, the best option is the LSVNS-based heuristic, which can solve instances with 40 customers and 5 days within 10 s. Moreover, the LSVNS-based heuristic can solve large-scale instances with 200 customers and 5 days 3 hours. [ABSTRACT FROM AUTHOR]