The fleet size and mix vehicle routing problem with synchronized visits

This paper introduces the Fleet Size and Mix Vehicle Routing Problem with Synchronized Visits (FSM-VRPS), an extension of the Vehicle Routing Problem with Synchronization (VRPS), where a mixed fleet composed of electric and conventional bikes, and passenger cars having different acquisition costs are considered. The problem consists of planning a set of different vehicle routes to serve a set of clients who may require more than one visit by different healthcare specialists, and some of these visits should be synchronized. Moreover, each client must be visited within a specified time window. In addition, the problem uses bikes to reduce Carbon Dioxide (CO2) emission for environmentally cleaner routing operations. This problem has many real-life applications, such as the scheduling of visits for homecare givers in the healthcare sector. We present a mixed integer linear-programming formulation and develop a Multi-Start Adaptive Large Neighborhood Search with Threshold Accepting algorithm. The results showed that our algorithm is highly effective on the FSM-VRPS, as well as on the heterogeneous VRPS. We also demonstrate the advantage of adopting different types of vehicles in terms of reducing the number of vehicles and costs. The analysis of the results also indicated that the new components added to the standard Adaptive Large Neighborhood Search algorithm enhanced intensification and diversification mechanisms during the search process.