The vehicle routing problem with backhauls integrates decisions on products delivery with decisions on collection of returnable items. In this paper we analyze the scenario in which collection is optional. Both transport costs and penalty costs for not collecting are considered. A mixed-integer linear model is proposed and solved for small instances. A metaheuristic algorithm combining biased randomization techniques with iterated local search is introduced for larger instances. This approach yields cost savings and is competitive compared to other state-ofthe-art approaches.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.