This paper analyzes the fleet mixed vehicle-routing problem with backhauls, a rich and realistic variant of the popular vehicle-routing problem in which both delivery and pick-up customers are served from a central depot using a heterogeneous and configurable fleet of vehicles. After a literature review on the issue and a detailed description of the problem, a solution based on a multistart biased-randomized heuristic is proposed. Our algorithm uses an iterative method that relies on solving a series of smaller instances of the homogeneous-fleet version of the problem and then using these subsolutions as partial solutions for the original heterogeneous instance. In order to better guide the exploration of the solutions space, the algorithm employs several biased-randomized processes: a first one for selecting a vehicle type; a second one for sorting the savings list; and a third one to define the number of routes that must be selected from the homogenousfleet subsolution. The computational experiments show that our approach is competitive and able to provide 20 new best-known solutions for a 36-instance benchmark recently proposed in the literature.
This article analyzes the Vehicle Routing Problem with Backhauls, where delivery and pick-up customers are served from a central depot. Initially, we focus in the version with clustered backhauls (VRPCB), where all the customers in the delivery group of the same route have to be served before the first customer in the pick-up group can be visited. The article presents a relatively simpleto-implement yet efficient metaheuristic algorithm that integrates a biased-randomized version of the popular savings heuristic within a metaheuristic framework. A skewed probability distribution is used to induce a biased (oriented) randomization effect on the savings list of routing edges, and a penalty cost is assigned to those edges connecting delivery customers with pick-up customers in order to promote a sequential order in delivery and pick-up activities. In the proposed approach, the fleet size constraint is implicitly relaxed. This feature allows the perturbation process to explore unfeasible but promising regions in the solution space. Then, whenever the number of routes does not match the number of available vehicles, a "recursive corrective operator" is employed to transform the new solution into a feasible one. Some classical benchmark instances for the VRPCB selected in order to compare our approach with other state-of-the-art algorithms, and a new best-know solution for a classical benchmark set is obtained. Finally, we analyze the flexibility of our approach by employing it, after a minor adaptation, in the Vehicle Routing Problem with Mixed Backhauls, where linehaul and backhaul customers might appear in any order during a route.
Abstract. Underestimating facility location decisions may penalize business performance over the time. These penalties have usually been studied from the economic point of view, analyzing its impact on profitability. Additionally, the concern about obtaining sustainability is gaining importance, leading to a search for renewable energy sources to reduce greenhouse gas emissions. However, little attention has been paid to choosing a location considering environmental criteria. Thus, this work aims at determining a biorefinery location considering its impacts on natural resources. Therefore, a mixed integer linear programming (MILP) model has been developed, taking into account crop location and biomass production seasonality to obtain a proper location that minimizes environmental impact.
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