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

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

Critical Analysis of English Language Teaching Skills, A Study of Primary School Teachers of Taluka Kotdiji, District Khairpur Mir’s

Abstract: English language teaching is very important because of the global status of English. English language teaching is a process that requires great efforts on the part of all the participants. Classroom interactions, activities, textbooks are the most important elements of teaching process for the aims and objectives of a course. Main objective of this study is to discover English language teaching skills in primary schools of union council Kumb Taluka Kotdiji, District Khairpur Mir’s. The Questionnaire was prepared for teachers to explore the different aspects of teaching English skills and teachers’ skills, (Training, teacher qualifications regarding English, English teaching methodologies). The questionnaire identifies teacher training and instructional materials. A sample of 20 teachers (both male and female) were selected from different schools of union council Kumb Taluka Kotdiji, District Khairpur Mir’s. The data obtained was tabulated and analyzed by the percentage

The Mixed Fleet Vehicle Routing Problem with overtime and light loads Formulation and Population Variable Neighbourhood search with Adaptive Memory

In this paper we consider a real-life Vehicle Routing Problem, characterized by heterogeneous vehicle fleet, demand-dependent service times, maximum allowable overtime and a special light load requirement. A new learning-based Population Variable Neighbourhood Search algorithm is designed to address this complex logistic problem. The computational experience suggests that savings up to 8% can be achieved when overtime and light load requirements are considered in advance. Moreover, accommodating for allowable overtime has shown to yield 12% better average utilization of the driver's working hours and 12.5% better average utilization of the vehicle load, without incurring extra running costs. The proposed metaheuristic method also shows some competitive results when applied to the special case of the real-life Vehicle Routing Problem, namely the Fleet Size and Mix Vehicle Routing Problem

Lithium in breast milk transiently affects the renal electrolytic balance of infants

Background: The use of lithium during breast-feeding has not been comprehensively investigated in humans due to concerns about lithium toxicity. Procedure: We analyzed lithium in the kidneys of nursed pups of lithium medicated mothers, using analytical spectroscopy in a novel rat model. The mothers were healthy rats administered lithium via gavage (1000 mg/day Li2CO3 per 50 kg body weight). Results: Lithium was detected in the breast milk, and in the blood of pups (0.08 mM), of lithium-exposed dams at post-natal day 18 (P18), during breast-feeding. No lithium was detected after breast-feeding, at P25 (4 days after cessation of nursing). The lithium pups blood had elevated urea nitrogen at P18 and reduced total T4 at P18 and P25, indicating a longer-term effect on the kidneys and the thyroid gland. Multivariate machine-learning analysis of spectroscopy data collected from the excised kidneys of pups showed elevated potassium in lithium-exposed animals both during- and after breast-feeding. The elevated renal potassium was associated with low nephrin expression in the kidneys measured immunohistochemically during breast-feeding. After lithium exposure is stopped, the filtration of lithium from the kidneys reverses these effects. Our study showed that breastfeeding during lithium use has an effect on the kidneys of the offspring in rats