The Multiple Trip Vehicle Routing Problem with Backhauls: Formulation and a Two-Level Variable Neighbourhood Search

In this paper a new VRP variant the Multiple Trip Vehicle Routing Problem with Backhauls (MT-VRPB) is investigated. The classical MT-VRP model is extended by including the backhauling aspect. An ILP formulation of the MT-VRPB is first presented and CPLEX results for small and medium size instances are reported. For large instances of the MT-VRPB a Two-Level VNS algorithm is developed. To gain a continuous balanced intensification and diversification during the search process VNS is embedded with the sequential VND and a multi-layer local search approach. The algorithm is tested on a set of new MT-VRPB data instances which we generated. Interesting computational results are presented. The Two-Level VNS produced excellent results when tested on the special variant of the VRPB

The Vehicle Routing Problem with Divisible Deliveries and Pickups

The vehicle routing problem with divisible deliveries and pickups is a new and interesting model within reverse logistics. Each customer may have a pickup and delivery demand that have to be served with capacitated vehicles. The pickup and the delivery quantities may be served, if beneficial, in two separate visits. The model is placed in the context of other delivery and pickup problems and formulated as a mixed-integer linear programming problem. In this paper, we study the savings that can be achieved by allowing the pickup and delivery quantities to be served separately with respect to the case where the quantities have to be served simultaneously. Both exact and heuristic results are analysed in depth for a better understanding of the problem structure and an average estimation of the savings due to the possibility of serving pickup and delivery quantities separately

Models and Heuristics for the Flow-Refuelling Location Problem

Purpose of this paper: Firstly, the paper serves as an overview of the emerging field of flow-refuelling location, which mainly occurs in the context of locating alternative-fuel (hydrogen, electric, liquefied natural gas and hybrid) vehicle refuelling stations. We aim to review and explain models and solution approaches, with a particular focus on mathematical programming formulations. Secondly, we propose a new heuristic for this problem and investigate its performance. Design/methodology/approach: The subject scope of this paper is the flow-refuelling location model (FRLM). While in most location problems demand arises at customer locations, in so-called flow-capturing models it is associated with journeys (origin-destination pairs). What makes the FRLM even more challenging is that due to the limited driving range of alternative-fuel vehicles, more than one facility may be required to satisfy the demand of a journey. There are currently very few such refuelling stations, but ambitious plans exist for massive development – making this an especially ripe time for researchers to investigate this problem. There already exists a body of work on this problem; however different authors make different model assumptions, making comparison difficult. For example, in some models facilities must lie on the shortest route from origin to destination, while in others detours are allowed. We aim to highlight difference in models in our review. Our proposed methodology is built on the idea of solving the relaxation of the mixed-integer linear programming formulation of the problem, identifying promising variables, fixing their values and solving the resulting (so-called restricted) problems optimally. It is somewhat similar to Kernel Search which has recently gained popularity. We also use a parallel computing strategy to simultaneously solve a number of restricted problems with less computation effort for large-sized instances. Findings: Our experimental results show that the proposed heuristic can find optimal solutions in a reasonable amount of time, outperforming other heuristics from the literature. Value: We believe the paper is of value to both academics and practitioners. The review should help researchers new to this field to orient themselves in the maze of different problem versions, while helping practitioners identify models and approaches applicable to their particular problem. The heuristic proposed can be directly used by practitioners; we hope it will spark further works on this area of logistics but also on other optimisation problems where Kernel Search type methods can be applied. Research limitations: This being the first paper applying a restricted-subproblem approach to this problem it is necessarily limited in scope. Applying a traditional Kernel Search method would be an interesting next step. The proposed heuristic should also be extended to cover for more than just one FRLM model: certainly the capacitated FRLM, the FRLM with deviation, the fixed-charge FRLM and the multi-period FRLM should be investigated. Practical implications: Our work adds to a body of research that can inform decisionmakers at governmental or international level on strategic decisions relating to the establishment or development of alternative-fuel refuelling station networks

An effective real time GRASP-based metaheuristic: Application to order consolidation and dynamic selection of transshipment points for time-critical freight logistics

Time-critical freight logistics is an area within logistics research where the shipper’s orders need to be received relatively urgently using a third party logistics (3PL) that provides a quote (bid) to the shipper within a very short period. We solved this 3PL problem by developing an effective meta-heuristic based on the Greedy Randomized Adaptive Search Procedure (GRASP). This is achieved by introducing novel attributes in the construction of the restricted candidate list while incorporating flexible and intelligent rules, some of which are inspired by expert knowledge. The approach performs order consolidation, locates transshipment points and performs an optimal assignment of shipments to the selected consolidation points dynamically and in real time. This intelligent system embeds expert knowledge within the design of neighbourhood reduction schemes and data structures to speed up the search. This is achieved by recording computed data that does not need to be recomputed again while avoiding unnecessary computations of the non-promising alternatives. The performance of this real time optimisation and scheduling tool is tested with a European 3PL company over a 13 weeks period in late 2017 resulting in a significant cost saving and a considerable reduction in CO2 emissions. This powerful decision support system assists the 3PL company in gaining competitive leadership advantage through producing promising quotes that turn customer requests into real customer orders

An efficient heuristic algorithm for the alternative-fuel station location problem

We have developed an efficient heuristic algorithm for location of alternative-fuel stations. The algorithm is constructed based on solving the sequence of subproblems restricted on a set of promising station candidates, and fixing a number of the best promising station locations. The set of candidates is initially determined by solving a relaxation model, and then modified by exchanging some stations between the promising candidate set and the remaining station set. A number of the best station candidates in the promising candidate set can be fixed to improve computation time. In addition, a parallel computing strategy is integrated into solving simultaneously the set of subproblems to speed up computation time. Experimental results carried out on the benchmark instances show that our algorithm outperforms genetic algorithm and greedy algorithm. As compared with CPLEX solver, our algorithm can obtain all the optimal solutions on the tested instances with less computation time

Vehicle routing problem with deliveries and pickups: Modelling issues and meta-heuristics solution approaches

The paper investigates a class of extensions to the vehicle routing problem. Different problem versions – some well-known, some more recent – are explained and placed in a taxonomy. A central focus of the paper is on the assumptions generally made in the literature and on the benefits of not making too restrictive assumptions. Research issues on novel problem classes are highlighted. An Integer Linear Programming (ILP) formulation is also presented. It is also shown how this formulation can be adapted to cater for other problem versions. This paper also discusses various solution methodologies including meta-heuristics to solve the models and what more is needed the vehicle routing problem