The consistent vehicle routing problem considering driver equity and flexible route consistency

In this study, we address a new consistent vehicle routing problem (ConVRP) by considering driver equity and flexible route consistency. It aims to optimize the departure time and routes for a set of vehicles over a defined planning period, aiming to minimize the total travel time while considering the discounts for the route consistent segments. Previous studies on ConVRP have primarily focused on ensuring customer satisfaction through time consistency and driver consistency, while overlooking driver equity. In our ConVRP, we introduce a flexible strategy to attain route consistency, i.e., drivers are encouraged to traverse familiar routes as many as possible during the planning period by offering time discounts for routes crossed more than twice. Driver equity is addressed through the optimal allocation of delivery capacity. For this problem, we formulate it into a mixed-integer linear programming model. Given its strong NP-hardness, a tailored adaptive large neighborhood search algorithm (ALNS) is developed to solve practical-sized problems. Destroy and repair operators are adaptively applied to remove customers from the routes and reinsert them in better positions. A new repair operator that identifies suitable customer locations by considering vehicle load and an exchange operator that reverses part of the specified routes are proposed to obtain better solutions and increase search efficiency, respectively. Moreover, we enhance arrival time consistency by adjusting departure time. Extensive numerical experiments for instances of varying scales are conducted to evaluate the proposed algorithm. Results demonstrate that i) the proposed algorithm can obtain high-quality solutions (the average relative difference compared to the optimal solution is only 1.68%); ii) Our approach can also find better solutions (with an average improvement rate of 3.53% and 33.70%, respectively) in a short computation time, when compared to the basic ALNS without a new operator and the widely used variable neighborhood descent algorithm; and iii) setting a small discount allows decision-makers to significantly enhance consistent distance for drivers.