A nonlinear optimization model for the balanced vehicle routing problem with loading constraints.

The vehicle routing problem with loading constraints (VRPLC) is related to real‐life transportation problems and integrates two of the most important activities in distribution logistics: packing of items inside vehicles and planning of delivery routes. In spite of its relevance, literature on VRPLCs is still limited. The majority of the solution approaches have concentrated on heuristic solution methods, and few have presented mathematical optimization models to help characterize the problem. Furthermore, few studies have considered several practical loading and routing constraints that could be used to approximate the problem toward more realistic situations. To help fill this gap in the literature, this article extends an existing VRPLC optimization model to a nonlinear optimization model that considers weight‐bearing strength of three‐dimensional items, vehicle weight capacity, weight distribution inside vehicles, delivery time windows, and a balanced fleet of vehicles. The model is solved by applying a simple procedure that isolates the nonlinearity of the model. Computational experiments show that the new proposed model gives a more streamlined formulation than the model it extended on, and that the addition of practical loading constraints can improve the solutions of the original model by reducing the measure of tardiness due to late deliveries and by producing cargo patterns with better weight distribution. [ABSTRACT FROM AUTHOR]