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.