A mixed integer linear programming formulation for the vehicle routing problem with backhauls

Abstract

The separate delivery and collection services of goods through different routes is an issue of current interest for some transportation companies by the need to avoid the reorganization of the loads inside the vehicles, to reduce the return of the vehicles with empty load and to give greater priority to the delivery customers. In the vehicle routing problem with backhauls (VRPB), the customers are partitioned into two subsets: linehaul (delivery) and backhaul (pickup) customers. Additionally, a precedence constraint is established: the backhaul customers in a route should be visited after all the linehaul customers. The VRPB is presented in the literature as an extension of the capacitated vehicle routing problem and is NP-hard in the strong sense. In this paper, we propose a mixed integer linear programming formulation for the VRPB, based on the generalization of the open vehicle routing problem; that eliminates the possibility of generating solutions formed by subtours using a set of new constraints focused on obtaining valid solutions formed by Hamiltonian paths and connected by tie-arcs. The proposed formulation is a generalpurpose model in the sense that it does not deserve specifically tailored algorithmic approaches for their effective solution. The computational results show that the proposed compact formulation is competitive against state-of-the-art exact methods for VRPB instances from the literature.

Multi-Objective Green Mixed Vehicle Routing Problem Under Rough Environment

“…Kancharla and Ramadurai (2018) developed a variety of G-VRP by introducing the concept of fuel consumption estimation based on driving cycle from the GPS's data. Granada-Echeverri et al (2019) publish a paper on VRP with backhauls. also develop a model on the open locationrouting problem.…”

A genetic algorithm for vehicle routing in logistic networks with practical constraints

“…The implementation of the problem we deal with in the form of an MIP, which is then solved with techniques such as branch and bound, cutting plane, etc., would require the introduction of many additional variables, like index binaries showing if any volume is shipped through a given edge for each stream or not, time-related variables, etc. (see Granada-Echeverri et al, 2019;Rieck & Zimmermann, 2010or Theurich et al (2021. Also, as shown by Boland et al (2017), in such a case the reformulation of the problem in the form of a timeextended graph is possible.…”

Optimizing Energy Consumption in Transportation: Literature Review, Insights, and Research Opportunities

“…Nevertheless, there are still some relevant works. For example, Granada-Echeverri et al [56] developed a mixed integer programming model. The idea is that the line-haul and back-haul routes are considered as two sub-problems.…”