Equitable Workload Allocation in Vehicle Routing Problem With Heterogeneous Drivers

In the private logistics service sector, considerations of fairness among service agents are relatively new but are gaining importance due to public and governmental pressures to improve equity in workload allocation among internal stakeholders, such as the service personnel. Fairness becomes more complex in settings with a heterogeneous workforce due to inherent worker differences. In this study, we present an equitable workload allocation model for the vehicle routing problem with heterogeneous drivers. We adopt the Nash Social Welfare (NSW) solution as the focal point for coalition among the various drivers. In our setup, while the ultimate goal is to maximize the equity and efficiency of drivers, the company’s efficiency is guaranteed by putting a cap on the deviation of the company’s cost from the least-cost solution value. We formulate the problem of last-mile delivery of online orders from a store using a fleet of crowdshippers as a variant of the vehicle routing problem with a highly nonlinear objective function inspired by NSW’s objective function. To solve the proposed new formulation, a column generation method is developed and used to study the behavior of the model. Through a comprehensive computational study, we investigate the behavior of the system in terms of the company’s cost, drivers’ total profit, and the level of achieved equity among the drivers when the main parameters of the problem vary. Our study demonstrates that the proposed framework outperforms the classical max–min approach in balancing workload equity and efficiency. We show a median equity improvement of 18% with a 5% cost deviation and 30% with a 10% deviation from the least-cost solution.