An ACO-based heuristic approach for a route and speed optimization problem in home health care with synchronized visits and carbon emissions

The growing concern about the influences of anthropogenic pollutions has forced researchers and scholars to study the environmental concerns. This paper addresses a joint daily route and speed optimization problem in home health care (HHC) with the constraints of synchronized visits and carbon emissions. In this work, the aim is to design a reasonable logistics route with the objective of minimizing the carbon emissions, which has a linear relationship with fuel consumption. This goal can reduce environmental pollution while optimizing operating costs for the HHC company. This paper formulated the problem as a mixed-integer programming (MIP) model and used the Gurobi solver to solve the MIP model with a time limit of 1 h. However, the method based on the MIP model is difficult to solve large-scale instances. Therefore, this paper proposed an ant colony optimization (ACO)-based heuristic approach improved by local search for this problem with large-scale instances. The minimal carbon emissions of each route is calculated by a dynamic programming (DM) algorithm. We designed three kinds of experiments to test the proposed approach, including the basic vehicle routing problem with time window (VRPTW), the studied problem with one speed and the studied problem with two speeds. The experimental results highlight the effectiveness and efficiency of the proposed approach.