Quantity discount with freight consolidation

We study an integrated quantity discount and vehicle routing problem where truck utilization is increased by building multi-stop routes and increasing order sizes through a purchase incentive. We model the problem and prove it to be NP-hard. Our experiments show that commercial solvers do not effectively solve instances with more than ten buyers. We propose the use of non-compromising route elimination rules and other improvement techniques for a route-based formulation. Our experimentation suggests that a cost savings of 18% can be realized by utilizing our model.