A biased-randomized iterated local search for the vehicle routing problem with optional backhauls

The vehicle routing problem with backhauls integrates decisions on product delivery with decisions on the collection of returnable items. In this paper, we analyze a scenario in which collection of items is optional—but subject to a penalty cost. Both transportation costs and penalties associated with non-collecting decisions are considered. A mixed-integer linear model is proposed and solved for small instances. Also, a metaheuristic algorithm combining biased randomization techniques with iterated local search is introduced for larger instances. Our approach yields cost savings and is competitive when compared to other state-of-the-art approaches.