The school bus routing problem: An analysis and algorithm

In this paper we analyse a flexible real world-based model for designing school bus transit systems and note a number of parallels between this and other well-known combinatorial optimisation problems including the vehicle routing problem, the set covering problem, and one-dimensional bin packing. We then describe an iterated local search algorithm for this problem and demonstrate the sort of solutions that we can expect with different types of problem instance

Industrial engineering applications in metrology: Job scheduling, calibration interval and average outgoing quality

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel UniversityThis research deals with the optimization of metrology and calibration problems. The optimization involved here is the application scientifically sound operations research techniques to help in solving the problem intended optimally or semi-optimally with a practical time frame. The research starts by exploring the subject of measurement science known as metrology. This involves defining all the constituents of metrology facilities along with their various components. The definitions include the SI units’ history and structure as well as their characteristics. After that, a comprehensive description of most of the operations and parameters encountered in metrology is presented. This involves all sources of uncertainties in most of the parameters that affect the measurements. From the background presented and using all the information within it; an identification of the most important and critical general problems is attempted. In this treatment a number of potential optimization problems are identified along with their description, problem statement definition, impact on the system and possible treatment method. After that, a detailed treatment of the scheduling problem, the calibration interval determination problem and the average outgoing quality problem is presented. The scheduling problem is formulated and modelled as a mixed integer program then solved using LINGO program. A heuristic algorithm is then developed to solve the problem near optimally but in much quicker time, and solution is packaged in a computer program. The calibration interval problem treatment deals with the determination of the optimal CI. Four methods are developed to deal with different cases. The cases considered are the reliability target case, the CI with call cost and failure cost of both first failure and all failures and the case of large number of similar TMDEs. The average out going quality (AOQ) treatment involves the development two methods to assess the AOQ of a calibration facility that uses a certain multistage inspection policy. The two methods are mathematically derived and verified using a simulation model that compares them with an actual failure rate of a virtual calibration facility

Models and heuristics for forest management with environmental restrictions

Tese de doutoramento, Estatística e Investigação Operacional (Otimização), Universidade de Lisboa, Faculdade de Ciências, 2018The main focus of this thesis was to develop mathematical models and methods in integer programming for solving harvest scheduling problems with environmental restrictions. Constraints on maximum clearcut area, minimum total habitat area, minimum total core area and inter-habitat connectivity were addressed for this purpose. The research was structured in a collection of three papers, each one describing the study of a different forest harvest scheduling problem with respect to the environmental constraints. Problems of papers 1 and 2 aim at maximizing the net present value. A bi objective problem is considered in paper 3. The objectives are the maximization of the net present value and the maximization of the inter-habitat connectivity. The tree search methods branch-and-bound and multiobjective Monte Carlo tree search were designed specifically to solve the problems. The methods could be used as heuristics, as a time limit of 2 hours was imposed. All harvest scheduling problems were based on the socalled cluster formulation. The proposed models and methods were tested with sixteen real and hypothetical instances ranging from small to large. The results obtained for branch-and-bound and Monte Carlo tree search show that these methods were able to find solutions for all instances. The results suggest that it is possible to address the environmental restrictions with small reductions of the net present value. With respect to the forestry fragmentation caused by harvestings, the results suggest that, although clearcut size constraints tend to disperse clearcuts across the forest, compromising the development of large habitats, close to each other, the proposed models, with the other environmental constraints, attempt to mitigate this effect

Optimum Allocation of Inspection Stations in Multistage Manufacturing Processes by Using Max-Min Ant System

In multistage manufacturing processes it is common to locate inspection stations after some or all of the processing workstations. The purpose of the inspection is to reduce the total manufacturing cost, resulted from unidentified defective items being processed unnecessarily through subsequent manufacturing operations. This total cost is the sum of the costs of production, inspection and failures (during production and after shipment). Introducing inspection stations into a serial multistage manufacturing process, although constituting an additional cost, is expected to be a profitable course of action. Specifically, at some positions the associated inspection costs will be recovered from the benefits realised through the detection of defective items, before wasting additional cost by continuing to process them. In this research, a novel general cost modelling for allocating a limited number of inspection stations in serial multistage manufacturing processes is formulated. In allocation of inspection station (AOIS) problem, as the number of workstations increases, the number of inspection station allocation possibilities increases exponentially. To identify the appropriate approach for the AOIS problem, different optimisation methods are investigated. The MAX-MIN Ant System (MMAS) algorithm is proposed as a novel approach to explore AOIS in serial multistage manufacturing processes. MMAS is an ant colony optimisation algorithm that was designed originally to begin an explorative search phase and, subsequently, to make a slow transition to the intensive exploitation of the best solutions found during the search, by allowing only one ant to update the pheromone trails. Two novel heuristics information for the MMAS algorithm are created. The heuristic information for the MMAS algorithm is exploited as a novel means to guide ants to build reasonably good solutions from the very beginning of the search. To improve the performance of the MMAS algorithm, six local search methods which are well-known and suitable for the AOIS problem are used. Selecting relevant parameter values for the MMAS algorithm can have a great impact on the algorithm’s performance. As a result, a method for tuning the most influential parameter values for the MMAS algorithm is developed. The contribution of this research is, for the first time, a methodology using MMAS to solve the AOIS problem in serial multistage manufacturing processes has been developed. The methodology takes into account the constraints on inspection resources, in terms of a limited number of inspection stations. As a result, the total manufacturing cost of a product can be reduced, while maintaining the quality of the product. Four numerical experiments are conducted to assess the MMAS algorithm for the AOIS problem. The performance of the MMAS algorithm is compared with a number of other methods this includes the complete enumeration method (CEM), rule of thumb, a pure random search algorithm, particle swarm optimisation, simulated annealing and genetic algorithm. The experimental results show that the effectiveness of the MMAS algorithm lies in its considerably shorter execution time and robustness. Further, in certain conditions results obtained by the MMAS algorithm are identical to the CEM. In addition, the results show that applying local search to the MMAS algorithm has significantly improved the performance of the algorithm. Also the results demonstrate that it is essential to use heuristic information with the MMAS algorithm for the AOIS problem, in order to obtain a high quality solution. It was found that the main parameters of MMAS include the pheromone trail intensity, heuristic information and evaporation of pheromone are less sensitive within the specified range as the number of workstations is significantly increased

Mind the gap: a review of optimisation in mental healthcare service delivery

Well-planned care arrangements with effective distribution of available resources have the potential to address inefficiencies in mental health services. We begin by exploring the complexities associated with mental health and describe how these influence service delivery. We then conduct a scoping literature review of studies employing optimisation techniques that address service delivery issues in mental healthcare. Studies are classified based on criteria such as the type of planning decision addressed, the purpose of the study and care setting. We analyse the modelling methodologies used, objectives, constraints and model solutions. We find that the application of optimisation to mental healthcare is in its early stages compared to the rest of healthcare. Commonalities between mental healthcare service provision and other services are discussed, and the future research agenda is outlined. We find that the existing application of optimisation in specific healthcare settings can be transferred to mental healthcare. Also highlighted are opportunities for addressing specific issues faced by mental healthcare services

The Curricular Practical Training Rotation Problem Formulation and the Assessment of Rotation Strategies

This study addresses the curricular practical training rotation problem, which is a type of staff assignment problem. Many educational institutions require theoretical knowledge to be complemented by practical training. Although the details of the implementation differ from institution to institution, it is necessary to prepare a rotation plan that determines how long the trainees will practice in which unit in which training period. Because of the complexity of the problem and humanistic reasons, the manual rotation plan can not reach the optimal level that satisfies all stakeholders and takes time. This study defines a general Curricular Practical Training Rotation Planning Problem specific to the curriculum-based trainee assignment process carried out in a university department and proposes an integer mathematical model for its solution. It is one of the important contributions of this study. It also provides a methodological approach to identify the most appropriate rotation strategy that will satisfy stakeholders. The methodological approach followed is a structure that can be adapted to different perspectives. The study has the potential to guide practitioners and researchers in the field and to lead a rich literature that will be formed with different side constraints and purposes to the problem