MATHEMATICAL MODELING FOR THE PROBLEM OF ALLOCATION OF HETEROGENEOUS LOADS IN VEHICLES WITH DIFFERENT OPERATIONAL CONSTRAINTS AND ADDITIONAL COSTS DUE TO THE FRAGMENTATION OF DELIVERIES BETWEEN VEHICLES PER CUSTOMER

This paper presents an Integer Programming model for the heterogeneous cargo allocation problem involving a fleet of different types of vehicles and customers distributed across multiple regions, with the objective of minimizing total operational costs. The model incorporates vehicle capacity and dimensional constraints, as well as penalties for unmet demand, unused capacity, and the splitting of a customer’s deliveries across multiple vehicles. Beyond the mathematical formulation, the study examines how penalizing delivery splitting affects the resulting solutions. Computational experiments are conducted on instances adapted from the literature and solved using the commercial optimizer Gurobi. The results show that setting fragmentation penalties is a key modeling decision. Poorly calibrated values can degrade solution quality by reducing the amount of demand served, which is the main objective of the problem, to be achieved at minimum cost.