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

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 general purpose 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

Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care

International audienceThis paper addresses a vehicle scheduling problem encountered in home health care logistics. It concerns the delivery of drugs and medical devices from the home care company's pharmacy to patients' homes, delivery of special drugs from a hospital to patients, pickup of bio samples and unused drugs and medical devices from patients. The problem can be considered as a special vehicle routing problem with simultaneous delivery and pickup and time windows, with four types of demands: delivery from depot to patient, delivery from a hospital to patient, pickup from a patient to depot and pickup from a patient to a medical lab. Each patient is visited by one vehicle and each vehicle visits each node at most once. Patients are associated with time windows and vehicles with capacity. Two mixed-integer programming models are proposed. We then propose a Genetic Algorithm (GA) and a Tabu Search (TS) method. The GA is based on a permutation chromosome, a split procedure and local search. The TS is based on route assignment attributes of patients, an augmented cost function, route re-optimization, and attribute-based aspiration levels. These approaches are tested on test instances derived from existing VRPTW benchmarks

Models for Reducing Deadheading through Carrier and Shipper Collaboration

The competitive nature in the trucking industry has forced trucking firms to develop innovative solutions to improve their operational efficiency and decrease marginal costs. There is also a great need to reduce deadheading miles of heavy trucks to help reduce the amount of air pollutants they emit. One way carriers and shippers are attempting to accomplish these goals is through various collaborative operational strategies. This work focuses on developing multiple collaboration frameworks and formulating optimization models for each framework that demonstrates the operations and reveals the potential cost savings of each framework.;The first collaboration framework focuses on how a medium level shipper or carrier can introduce collaboration in their operations by fulfilling a collaborative carrier\u27s or shipper\u27s delivery requests on its backhaul route. Two optimization models are developed to route the carrier of interest\u27s backhaul routes and select collaborative shipments to fulfill; one is formulated as an integer program and the other is formulated as a mixed integer program. Two solution methodologies, a greedy heuristic and tabu search, are used to solve the two problems, and numerical analysis is performed with a real world freight network. Numerical analysis on a real world freight network reveals that the percentage of cost savings for backhaul routes can be as high as 27%.;The second collaboration framework focuses on a group of shippers that collaborate their operations and form cycles between their long-haul shipping lanes. If the shippers provide the bundled lanes, as loops, to a common carrier they can realize cost savings from the carrier. The problem is formulated as a mixed integer program and forms least cost loops between the shipping lanes. A tabu search heuristic is used to solve the second collaboration framework and results using a real freight network reveal collaborative network costs savings between 7% to 12%. Three cost allocation mechanisms are proposed for the problem to distribute the costs to the shippers involved in the collaboration and computational results are provided for each of the allocation mechanisms

Algoritmos de solución para el problema multidepósito y multiobjetivo de ruteo de vehículos considerando recogida de productos y restricción de precedencia

En esta tesis se presenta la aplicación de diferentes técnicas heurísticas y metaheurísticas para la solución del problema de ruteo de vehículos con restricción de precedencia, heurísticas como el vecino más cercano y la del ahorro con inserción secuencial, y metaheurísticas como búsqueda tabú y optimización por colonia de hormigas son utilizadas y ajustadas para resolver eficientemente diferentes variantes del problema de ruteo de vehículos con entrega y recogida de paquetes con restricción de precedencia, considerando el caso monodepósito y multidepósito, mono y multiobjetivo. Cada ruta realizada consta de una sub-ruta en la que se realiza sólo la tarea de entrega y otra sub-ruta en la que se realiza sólo el proceso de recolección, esta última se inicia solo cuando el vehículo está vacío. Los algoritmos y metaheurísticas propuestas tratan de encontrar el mejor orden para visitar a los clientes en cada ruta realizada. Además, el enfoque propuesto determina la mejor conexión entre los sub-rutas de entrega y recogida, con el fin de obtener una solución global minimizando el número de vehículos, la distancia recorrida, el tiempo empleado y la cantidad de energía consumida por los vehículos. El estudio multiobjetivo permitió encontrar un conjunto de soluciones ordenadas en los frentes de Pareto considerando el concepto de dominancia. Adicionalmente, para el modelo multiobjetivo, se plantea la metodología de ponderaciones de los valores de cada función objetivo se selecciona una alternativa de solución con dominancia en el número de vehículos usados. La eficacia del enfoque propuesto se examina teniendo en cuenta un conjunto de casos adaptados de la literatura. También, se propone un modelo exacto, el cual es resuelto mediante la técnica de rutas abiertas con enlace óptimo. Los resultados computacionales muestran resultados de alta calidad en tiempos de procesamiento competitivos. Los resultados computacionales se comparan con los existentes en la literatura especializada y entre los diferentes algoritmos propuestos. Por último, se presentan las conclusiones y sugerencias para trabajos futuros

Algoritmos de solución para el problema multidepósito y multiobjetivo de ruteo de vehículos considerando recogida de productos y restricción de precedencia

En esta tesis se presenta la aplicación de diferentes técnicas heurísticas y metaheurísticas para la solución del problema de ruteo de vehículos con restricción de precedencia, heurísticas como el vecino más cercano y la del ahorro con inserción secuencial, y metaheurísticas como búsqueda tabú y optimización por colonia de hormigas son utilizadas y ajustadas para resolver eficientemente diferentes variantes del problema de ruteo de vehículos con entrega y recogida de paquetes con restricción de precedencia, considerando el caso monodepósito y multidepósito, mono y multiobjetivo. Cada ruta realizada consta de una sub-ruta en la que se realiza sólo la tarea de entrega y otra sub-ruta en la que se realiza sólo el proceso de recolección, esta última se inicia solo cuando el vehículo está vacío. Los algoritmos y metaheurísticas propuestas tratan de encontrar el mejor orden para visitar a los clientes en cada ruta realizada. Además, el enfoque propuesto determina la mejor conexión entre los sub-rutas de entrega y recogida, con el fin de obtener una solución global minimizando el número de vehículos, la distancia recorrida, el tiempo empleado y la cantidad de energía consumida por los vehículos. El estudio multiobjetivo permitió encontrar un conjunto de soluciones ordenadas en los frentes de Pareto considerando el concepto de dominancia. Adicionalmente, para el modelo multiobjetivo, se plantea la metodología de ponderaciones de los valores de cada función objetivo se selecciona una alternativa de solución con dominancia en el número de vehículos usados. La eficacia del enfoque propuesto se examina teniendo en cuenta un conjunto de casos adaptados de la literatura. También, se propone un modelo exacto, el cual es resuelto mediante la técnica de rutas abiertas con enlace óptimo. Los resultados computacionales muestran resultados de alta calidad en tiempos de procesamiento competitivos. Los resultados computacionales se comparan con los existentes en la literatura especializada y entre los diferentes algoritmos propuestos. Por último, se presentan las conclusiones y sugerencias para trabajos futuros

Development of some local search methods for solving the vehicle routing problem

Master'sMASTER OF ENGINEERIN

Evolutionary computing for routing and scheduling applications

Ph.DDOCTOR OF PHILOSOPH

Meta-Heuristics for the Multiple Trip Vehicle Routing Problem with Backhauls

With the growing and more accessible computational power, the demand for robust and sophisticated computerised optimisation is increasing for logistical problems. By making good use of computational technologies, the research in this thesis concentrates on efficient fleet management by studying a class of vehicle routing problems and developing efficient solution algorithms. The literature review in this thesis looks at VRPs from various development angles. The search reveals that from the problem modelling side clear efforts are made to bring the classical VRP models closer to reality by developing various variants. However, apart from the real VRP applications (termed as 'rich' VRPs), it is also noticeable that these classical VRP based variants address merely one or two additional characteristics from the real routing problem issues, concentrating on either operational (fleet management) or tactical (fleet acquisition) aspects. This thesis certainly hopes to add to one of those good efforts which have helped in bringing the VRPs closer to reality through addressing both the operational as well as the tactical aspects. On the solution methodologies development side, the proposed research noted some considerable and impressive developments. Although, it is well established that the VRPs belong to the NP-hard combinatorial class of problems, there are considerable efforts on the development of exact methods. However the literature is full of a variety of heuristic methodologies including the classical and the most modern hybrid approaches. Among the hybrid approaches, the most recent one noted is mat-heuristics that combine heuristics and mathematical programming techniques to solve combinatorial optimisation problems. The mat-heuristics approaches appear to be comparatively in its infant age at this point in time. However this is an exciting area of research which seeks more attention in the literature. Hence, a good part of this research is devoted to the development of a hybrid approach that combines heuristics and mathematical programming techniques. When reviewing the specific literature on the VRP problems focused in this thesis, the vehicle routing problem with backhauls (VRPB) and the multiple trip vehicle routing problem (MT-VRP), there is not sufficient development on the problem modelling side in terms of bringing these two problems closer to the reality. Hence, to fill the gap this thesis introduces and investigates a new variant, the multiple trip vehicle routing problem with backhauls (MT-VRPB) that combines the above two variants of the VRP. The problem is first described thoroughly and a new ILP (Integer Linear Programming) mathematical formulation of the MT-VRPB along with its possible variations is presented. The MT-VRPB is then solved optimally by using CPLEX along with providing an illustrative example showing the validation of the mathematical formulation. As part of the contribution, a large set of MT-VRPB data instances is created which is made available for future benchmarking. The CPLEX implementation produced optimal solutions for a good number of small and medium size data instances of the MT-VRPB and generated lower bounds for all instances. The CPLEX success may be considered as modest, but the produced results proved very important for the validation of the heuristic results produced in the thesis. To solve the larger instances of the MT-VRPB, a two level VNS algorithm called 'Two-Level VNS' is developed. It was noticed from the literature that the choice of using VNS for the VRPs has increased in recent literature due to its simplicity and speed. However our initial experiments with the classical VNS indicated that the algorithm is more inclined towards the intensification side. Hence, the Two-Level VNS is designed to obtain a maximum balance of the diversification and the intensification during the search process. It is achieved by incorporating a sub-set of neighbourhood structures and a sus-set of local search refinement routines and hence, a full set of neighbourhood structures and a full set of local search refinement routines at two levels of the algorithm respectively. The algorithm found very encouraging results when compared with the solutions found by CPLEX. These findings in this thesis demonstrate the power of VNS yet again in terms of its speed, simplicity and efficiency. To investigate this new variant further, we developed an algorithm belonging to the new class of the hybrid methodologies, i.e., mat-heuristics. A hybrid collaborative sequential mat-heuristic approach called the CSMH to solve the MT-VRPB is developed. The exact method approach produced in Chapter 4 is then hybridised with the Two-Level VNS algorithm developed in Chapter 5. The overall performance of the CSMH remained very encouraging in terms of the solution quality and the time taken on average compared with the CPLEX and the Two-Level VNS meta-heuristic. To demonstrate the power and effectiveness of our methodologies, we tested the designed algorithms on the two special versions of the VRP (i.e., VRPB and MT-VRP) to assess whether they are efficient and dynamic enough to solve a range of VRP variants. Hence the Two-Level VNS and the CSMH algorithms developed to solve the MT-VRPB are adapted accordingly and implemented to solve the two above variants separately. The algorithms produced very competitive results for the benchmark data sets when compared to the best known solutions from the literature. The successful implementations of these algorithms on the three VRP models with only minor amendments prove their generalizability and their robustness. The results in this research show that significant cost savings could be obtained by choosing the right fleet size and better vehicle utilisations with multiple trips and backhauling. Hence, the research proved the justification of studying this interesting combination. Moreover, the problem modelling, efficient algorithm design and implementation, and the research results reveal some vital information and implications from the managerial point of view in terms of making the tactical (fleet acquisition) and the operational (fleet management) decisions in a more informative manner