The split heterogeneous vehicle routing problem with three-dimensional loading constraints on a large scale

This paper introduces a complex real-world problem on a large scale that combines the split delivery heterogeneous vehicle routing problem with three-dimensional loading and considers new routing and loading constraints. The problem aims to find a set of routes with minimum transportation cost by satisfying the demand of all customers and loading constraints. We propose a column generation-based heuristic algorithm that employs three heuristic algorithms to solve the subproblem and a hybrid algorithm for loading. Computational experiments on the literature instances indicate that the proposed algorithm can produce very near solutions to the literature algorithm's solutions in significantly shorter running times. This paper introduces real-world instances with 230 to 850 customers, several times larger than the existing benchmarks. The results of the proposed algorithm for real-world instances are effective, and compared to the current situation, it leads to a reduction of 20% in the average total cost of transportation. Also, the average number of vehicles is reduced by 36%.