This paper illustrates Winograd's approach to computing the Discrete Fourier Transform (DFT). This new approach changes the DFT into a cyclic convolution of 2 sequences, and illustrates shortcuts for computing this cyclic convolution. This method is known to reduce the number of multiplies required to about 20% less than the number of multiplies used by the techniques of the Fast Fourier Transform. Three approaches are discussed, one for prime numbers, one for products of primes, and lastly one for powers of odd primes. For powers of 2 Winograd's algorithm is, in general, inefficient and best if it is not used. A computer simulation is illustrated for the 35 point transform and its execution time is compared with that of the Fast Fourier Transform algorithm for 32 points.

Hazardous waste site remediation cost estimation requires a good estimate of the contaminated soil volume. The United States Environmental Protection Agency (U.S. EPA) currently uses deterministic point values to estimate soil volumes but the literature suggests that probability bounds analysis (PBA) is the more accurate method to make estimates under uncertainty. The underlying statistical theory is that they are more accurate than deterministic estimates because probabilistic estimates account for data uncertainties. However, the literature does not address the problem of selecting an optimal decision point from the interval-valued PBA estimates. The purpose of this study was to identify the optimal PBA decision point estimator and use it to demonstrate that because the PBA method also accounts for data uncertainties, PBA estimates of remedial soil volumes are more accurate than the U.S. EPA deterministic estimates. The research questions focused on determining whether the mean or the 95th percentile decision point is the optimal PBA estimator. A convenience sample of seven sites was selected from the U.S. EPA Superfund Database. The PBA method was used to estimate the remedial soil volumes for the sites. Correlation analyses were performed between the mean and 95th percentile PBA estimates and the actual excavated soil volumes. The study results suggest that the lower bound 95th percentile PBA estimate, which had the best R2-value of 89%, is the optimal estimator. The R2-value for a similar correlation analysis using the U.S. EPA deterministic estimates was only 59%. This confirms that PBA is the better estimator. The PBA estimates are less contestable than the current U.S. EPA deterministic point estimates. Thus, the PBA method will reduce litigation and speed up cleanup activities to the benefit of the U.S. EPA, corporations, the health and safety of nearby residents, and society in general.

This 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.

The main subject matter of this thesis concerns radiotherapy patient scheduling subproblems formulated as four separate shop scheduling problem models (i.e. hybrid flowshop, flowshop, mixed shop and multiple identical parallel machine scheduling problems) based on the characteristics of the intricate real-life treatment processes observed at the Arden Cancer Centre in Coventry, UK. Insight into these processes was gained by developing and using a novel discrete-event simulation (DES) model of the four units of the radiotherapy department. By typifying the subproblems as well-known scheduling problem models, it was intended that methods amenable to them such as heuristics be used in the study. Four novel constructive heuristics based on priority dispatching rules and strategies adapted from some established algorithms have been developed and implemented using the C++ programming language. Further, these heuristics were incorporated into the DES model to create schedules of appointments for the patients generated daily. The effectiveness and efficiency of the constructive heuristics have been tested using the following performance criteria: minimising i) average waiting time to the start of treatment, and ii) average percentage of patients late for their treatment, and iii) the amount of overtime slots used for the patients received in a given period of time. The coordinated constructive heuristics and the DES model have also been tested using possible alternative pathways patients can follow in the treatment unit. The aim of these tests was to compare the efficiency of the radiotherapy department’s current pathway to other possible pathways. Further, strategies for using maximum allowed breaches of targeted due dates, reserved slots for critical treatments and overtime slots was also included in the heuristics. The results of several tests showed that the heuristics created schedules of appointments whose average waiting times for emergency, palliative and radical treatments improved by about 50%, 34% and 41%, respectively, compared to the historical data. However, their major slack was evidenced by the fact that about 13% of the patients needing palliative treatment were expected to be late for treatment compared to about 1% of those requiring radical treatment.

Gastro wastes, as a sort of biodegradable waste, has been established in legislation just quite recently, and its sorting is just in the beginning. However as a sort of waste it has a great potential like a secondary material. This work deals with gastro waste modelling and optimization of their cartage routes with purpose to decrease negative implications with them connected. For the model composition, the operational research was used, namely the transportation task or the circular transportation problem, further optimization (that includes the linear optimization and the index method.) The program ArcGIS and its extension Network Analyst from ERSI were used for delineation of transportation routes. Microsoft Excel, Visual Basic and Python were used for computation of optimization tasks. Final graphic output was carried out in the ArcGIS ArcMap. The results of this work are optimized trucking cartage routes, calculated values of minimal distances, quantity of cartage cars, calculated overall costs and other calculations. The part of this tasks is also time conversion of the model. Also, the attention was paid for minimization of trucking routes. The increase of the capacity of specific gastro waste processors was used for the minimization. These processors were chosen in accordance with required...

Este trabalho detalha o problema de programação de atividades de desenvolvimento de poços marítimos (PPADPM), cujo objetivo é definir o uso de sondas e navios, de forma a otimizar a produção de óleo dos poços marítimos. São apresentados cinco modelos baseados em programação linear-inteira mista (MILP) e um modelo gerado via programação por restrições (PR) para este problema. Concluiu-se que, dentre os modelos MILP, aquele baseado em variáveis que definem a ordem de execução das atividades apresenta os melhores resultados, tanto em termos de qualidade de soluções quanto em termos de tamanho do modelo. O aumento do tamanho da instância (em número de poços e/ou em número de recursos) traz como consequência um menor número de nós analisados dentro de um tempo limite de execução do modelo, ao mesmo tempo em que se observa que as estratégias de escolha de variáveis, de escolha de nós e de uso de solução inicial nos modelos MILP tornam-se ineficientes. Na comparação entre modelos MILP e o modelo baseado em PR, constatou-se que este último obteve as melhores soluções em mais de 90% dos casos analisados e, consistentemente, obteve mais soluções viáveis para cada instância. Entretanto, por não fornecer informações sobre a qualidade da solução, o modelo baseado em PR somente obtém a solução ótima ao analisar todo o espaço de busca do modelo; desta forma, este apenas chegou à solução ótima em instâncias com até quatro poços, enquanto alguns dos modelos MILP obtiveram a solução ótima para instâncias com até treze poços. / This work details the offshore wells activities on specialized resources scheduling problem, focusing on the optimization of the total oil production. A Constraint Programming (CP) model and five Mixed-Integer Linear Programming (MILP) models were studied. Among the linear models, those based on activities order variables are smaller, and led to the better solutions for almost all of the instances analyzed. As far as the size of the instances (number of wells and/or number of resources) increases, the number of branched nodes in a limited time decreases and, consequently, the influence of B&B nodes and variable selection strategies and of the initial guesses on the MILP model solution gets less efficient. Comparing best solutions for each instance, the CP model outperformed MILP models in 90% of the studied cases. In addition, the CP based model consistently found more solutions per instance than the MILP based models did. However, because the CP model does not give information on the quality of a solution (gap), it was only able to obtain optimal solutions for instances with up to four wells, while MILP based models found optimal solutions for instances up to thirteen wells.

Essa tese tem como objetivo desenvolver um modelo matemático de programação mista para auxiliar na indicação das regiões ótimas para acréscimo da oferta de cana-de-açúcar no Brasil. Fazendo uso do ferramental desenvolvido almeja-se avaliar o comportamento espacial da produção de cana, dos fluxos de abastecimento e do consumo de açúcar e etanol mediante projeções futuras da demanda, e também mediante a incorporação dos novos projetos ferroviários, hidroviários e dutoviários na malha intermodal de transportes. Considerando as projeções do consumo doméstico e das exportações sucroalcooleiras para 2020/2021, o modelo matemático sugeriu as regiões ideais para aumentar a oferta de cana-de-açúcar, dentre as áreas com aptidão edafoclimática para o cultivo da cultura, visando a maximização da receita das indústrias do setor. As recomendações do modelo indicam acréscimo de 220 milhões de toneladas na produção dos canaviais do estado de São Paulo, 79 milhões em Mato Grosso do Sul, 70 milhões no Paraná, 65 milhões em Minas Gerais, 60 milhões na Bahia, 42 milhões em Goiás, 24 milhões no Tocantins, 15 milhões no Maranhão, 8 milhões no Mato Grosso e 7 milhões no estado do Piauí, nas condições do cenário com projeções de crescimento pessimista. Além disso, a alocação ótima dos fluxos de transporte de açúcar sugere uma participação de 45% do modal ferroviário, 52% do modal rodoviário e 3% de alternativas hidro-ferroviárias na produção total de serviços de transporte (TKU), considerando a demanda 2020/2021. No caso do etanol as proporções recomendadas indicam 61% para a modalidade rodoviária, 27% para a alternativa ferroviária e 12% para a combinação intermodal hidro-dutoviária. Os benefícios econômicos diretos proporcionados pela expansão da malha intermodal de transporte podem gerar economias com fretes próximas a R$ 444 milhões por safra, no escoamento da produção sucroalcooleira, baixando o frete unitário médio do setor de R$ 59,12 por tonelada para 54,12 por tonelada transportada. O método revelou-se uma ferramenta importante na análise da distribuição espacial da oferta de cana-de-açúcar, e os resultados geraram informações importantes para condução de políticas públicas e para organização do setor sucroenergético. / This thesis aims to construct a mathematical model of mix and integer programming for supporting the decisions about the best regions to increase the supply of sugar cane in Brazil. In addition is intended to use the model to provide inputs for analyzing the spatial sugar cane production and ethanol and sugar transport flows considering future supply and demand assumptions and different multimodal transportation network configuration. Supposing sugar and ethanol demand and exports projections to crop 2020/2021 the mathematical model recommended the optimum agricultural areas to increase the production of sugar cane in other to maximize the sector revenue. The model outputs recommended an increase of 220 million tons in sugarcane production at São Paulo state, 79 millions at Mato Grosso do Sul, 70 million at Paraná, 65 million at Minas Gerais, 60 millions at Bahia, 42 million at Goiás, 24 million at Tocantins, 15 million at Maranhão, 8 millions at Mato Grosso and 7 millions tons at Piauí. Regarding the sugar transportation flows the results proposed a share of 45% for rail mode, 52% for road and 3% for barge-rail alternatives in the total freight (Ton-Kilometer). In the case of ethanol the results indicated a share of 61% for road, 27% for rail, and 12% for barge-pipelines alternatives. The direct economic benefits provided by the expansion of multimodal transportation network implicates savings on freight near to R$ 444 million per crop, that involves a decrease from R$ 59.12 per ton to R$ 54,12 per ton in the unit freight cost. The mathematical model revealed be an important tool for spatial analysis of sugar cane supply in Brazil and the results provided important inputs for Federal Government policies and for planning the sugar and ethanol sector.

Essa tese tem como objetivo desenvolver um modelo matemático de programação mista para auxiliar na indicação das regiões ótimas para acréscimo da oferta de cana-de-açúcar no Brasil. Fazendo uso do ferramental desenvolvido almeja-se avaliar o comportamento espacial da produção de cana, dos fluxos de abastecimento e do consumo de açúcar e etanol mediante projeções futuras da demanda, e também mediante a incorporação dos novos projetos ferroviários, hidroviários e dutoviários na malha intermodal de transportes. Considerando as projeções do consumo doméstico e das exportações sucroalcooleiras para 2020/2021, o modelo matemático sugeriu as regiões ideais para aumentar a oferta de cana-de-açúcar, dentre as áreas com aptidão edafoclimática para o cultivo da cultura, visando a maximização da receita das indústrias do setor. As recomendações do modelo indicam acréscimo de 220 milhões de toneladas na produção dos canaviais do estado de São Paulo, 79 milhões em Mato Grosso do Sul, 70 milhões no Paraná, 65 milhões em Minas Gerais, 60 milhões na Bahia, 42 milhões em Goiás, 24 milhões no Tocantins, 15 milhões no Maranhão, 8 milhões no Mato Grosso e 7 milhões no estado do Piauí, nas condições do cenário com projeções de crescimento pessimista. Além disso, a alocação ótima dos fluxos de transporte de açúcar sugere uma participação de 45% do modal ferroviário, 52% do modal rodoviário e 3% de alternativas hidro-ferroviárias na produção total de serviços de transporte (TKU), considerando a demanda 2020/2021. No caso do etanol as proporções recomendadas indicam 61% para a modalidade rodoviária, 27% para a alternativa ferroviária e 12% para a combinação intermodal hidro-dutoviária. Os benefícios econômicos diretos proporcionados pela expansão da malha intermodal de transporte podem gerar economias com fretes próximas a R$ 444 milhões por safra, no escoamento da produção sucroalcooleira, baixando o frete unitário médio do setor de R$ 59,12 por tonelada para 54,12 por tonelada transportada. O método revelou-se uma ferramenta importante na análise da distribuição espacial da oferta de cana-de-açúcar, e os resultados geraram informações importantes para condução de políticas públicas e para organização do setor sucroenergético. / This thesis aims to construct a mathematical model of mix and integer programming for supporting the decisions about the best regions to increase the supply of sugar cane in Brazil. In addition is intended to use the model to provide inputs for analyzing the spatial sugar cane production and ethanol and sugar transport flows considering future supply and demand assumptions and different multimodal transportation network configuration. Supposing sugar and ethanol demand and exports projections to crop 2020/2021 the mathematical model recommended the optimum agricultural areas to increase the production of sugar cane in other to maximize the sector revenue. The model outputs recommended an increase of 220 million tons in sugarcane production at São Paulo state, 79 millions at Mato Grosso do Sul, 70 million at Paraná, 65 million at Minas Gerais, 60 millions at Bahia, 42 million at Goiás, 24 million at Tocantins, 15 million at Maranhão, 8 millions at Mato Grosso and 7 millions tons at Piauí. Regarding the sugar transportation flows the results proposed a share of 45% for rail mode, 52% for road and 3% for barge-rail alternatives in the total freight (Ton-Kilometer). In the case of ethanol the results indicated a share of 61% for road, 27% for rail, and 12% for barge-pipelines alternatives. The direct economic benefits provided by the expansion of multimodal transportation network implicates savings on freight near to R$ 444 million per crop, that involves a decrease from R$ 59.12 per ton to R$ 54,12 per ton in the unit freight cost. The mathematical model revealed be an important tool for spatial analysis of sugar cane supply in Brazil and the results provided important inputs for Federal Government policies and for planning the sugar and ethanol sector.

Esta tese estuda a implementação de heurísticas e da metaheurística scatter search (SS) em um problema de roteirização de veículos com frota heterogênea, janelas de tempo e entregas fracionadas (Heterogeneous Fleet Vehicle Routing Problem with Time Windows and Split Deliveries – HFVRPTWSD). O HFVRPTWSD é uma combinação do problema de roteirização com frota heterogênea (HFVRP), problema de roteirização de veículos com janelas de tempo (VRPTW) e problema de roteirização com entregas fracionadas (VRPSD). O problema é baseado em um único depósito, a demanda dos clientes pode ser maior que a capacidade dos veículos e, além das restrições de janelas de tempo, há também restrições de capacidade dos veículos e restrições quanto ao tipo de veículo. O VRPSD foi introduzido na literatura por Dror e Trudeau em 1989. No problema de roteirização de veículos com entregas fracionadas, cada cliente pode ser abastecido por mais de um veículo, enquanto no problema clássico de roteirização de veículos (VRP), cada cliente é atendido por um único veículo. Desta forma, para o VRPSD, além dos roteiros de entrega, deve-se determinar a quantidade entregue a cada cliente em cada veículo. Todos os problemas de roteirização com entregas fracionadas encontrados na literatura (VRPSD e suas extensões) têm como característica frota homogênea. O problema estudado neste trabalho difere, portanto, de todos os problemas de roteirização com entregas fracionadas da literatura, pois tem, como característica, frota heterogênea. O mesmo raciocínio vale para problemas de roteirização de veículos com frota heterogênea. Os modelos são aplicados em uma rede de varejo no Brasil que é abastecida a partir de um centro de distribuição. A rede compõe um total de 519 lojas distribuídas em 12 estados do país. As heurísticas e a metaheurística scatter search também são aplicadas em três conjuntos de problemas encontrados na literatura (SOLOMON, 1987; HO E HAUGLAND, 2004; LIU E SHEN, 1999), com o objetivo de avaliar o desempenho dos algoritmos para cada problema. O problema consiste em determinar, a cada dia, como alocar os caminhões às lojas, a quantidade de carga em cada caminhão a ser entregue em cada uma das lojas, qual o melhor roteiro e o tempo de início de atendimento do primeiro cliente da rota, de forma a minimizar o custo total de distribuição, garantindo que a demanda das lojas seja atendida e as demais restrições do problema sejam respeitadas. Para a resolução do VRPSD e suas extensões, a única metaheurística encontrada na literatura foi busca tabu. Para o problema de roteirização com frota heterogênea e suas extensões, foram implementadas apenas as metaheurísticas busca tabu e BATA (Back-Tracking Adaptative Threshold Accepting). As estratégias de solução propostas no presente trabalho consistem na implementação de heurísticas construtivas e da metaheurística scatter search. As soluções iniciais de SS são obtidas através da implementação de quatro heurísticas construtivas: heurística de economias, heurística de inserção seqüencial baseada nas idéias de Solomon (1987), heurística de inserção seqüencial baseada nas idéias de Ho e Haugland (2004) e adaptação da heurística de inserção seqüencial de Dullaert et al. (2002). Para o caso real, foi possível uma redução no custo total da frota comparado com a solução atual da empresa. Para algumas instâncias dos três conjuntos de problemas da literatura, os algoritmos apresentaram resultados similares ou superiores às melhores soluções encontradas. / This thesis studies the implementation of heuristics and scatter search (SS) metaheuristic in a Heterogeneous Fleet Vehicle Routing Problem with Time Windows and Split Deliveries (HFVRPTWSD). The HFVRPTWSD is a combination of Heterogeneous Fleet Vehicle Routing Problem (HFVRP), Vehicle Routing Problem with Time Windows (VRPTW) and Vehicle Routing Problem with Split Deliveries (VRPSD). The problem is based in a single depot, the demand of each client can be greater than the vehicle’s capacity and beyond the time windows constraints, and there are also constraints on the vehicle capacity and vehicles type. The VRPSD was introduced in the literature by Dror e Trudeau in 1989. In the split deliveries vehicle routing problem, each client can be supplied by more than one vehicle; while in a classic vehicle routing problem (VRP) each client is supplied by only one vehicle. Thus, for the VRPSD, besides the delivery routes, the amount to be delivered to each client in each vehicle must also be determined. All the split delivery vehicle routing problems researched in the literature (VRPSD and its extensions) have as a characteristic the homogeneous fleet. Therefore, the problem studied differs from the split deliveries vehicle routing problems of the literature because it has a heterogeneous fleet. The same reasoning can be applied in heterogeneous fleet vehicle routing problem. The models will be applied in a retail market in Brazil that is supplied by a distribution center. The market has 519 stores distributed in 12 Brazilian states. The heuristics and the scatter search metaheuristic will also be applied in three benchmark problems (SOLOMON, 1987; HO AND HAUGLAND, 2004; LIU AND SHEN, 1999), aiming to evaluate the design of the algorithms for each problem. The problem consists in determining, each day, how to allocate the trucks to the stores, the amount to be delivered in each truck to each client, which one is the best route and the initial time for attending the first client, with the aim of minimizing the total distribution cost, attending the clients’ demand and respecting all the problem’s constraints. For the VRPSD and its extensions, the only metaheuristic implemented in the literature was tabu search. For the heterogeneous fleet vehicle routing problem and its extensions, only the tabu search and BATA (Back-Tracking Adaptative Threshold Accepting) metaheuristics have been implemented. The strategies proposed here consist in the implementation of constructive heuristics and the scatter search metaheuristic. The initial solutions of SS are obtained with the implementation of four constructive heuristics: saving heuristics, sequential insertion heuristic based on the ideas of Solomon (1987), sequential insertion heuristic based on the ideas of Ho e Haugland (2004) and adaptation of the sequential insertion heuristic of Dullaert et al. (2002). For the real case, it was possible to reduce the total fleet cost, when comparing to the actual solution. At some instances of the three benchmark problems, the algorithms presented similar or better results when compared to the best solutions in the literature.

Over the last decade considerable interest has been generated into the use of analytical methods in organisations. Along with this, many have reported a significant gap between organisational demand for analytical-trained staff, and the number of potential recruits qualified for such roles. This interest is of high relevance to the operational research discipline, both in terms of raising the profile of the field, as well as in the teaching and training of graduates to fill these roles. However, what is less clear, is the extent to which operational research teaching in universities, or indeed teaching on the various courses labelled as analytics , are offering a curriculum that can prepare graduates for these roles. It is within this space that this research is positioned, specifically seeking to analyse the suitability of current provisions, limited to master s education in UK universities, and to make recommendations on how curricula may be developed. To do so, a mixed methods research design, in the pragmatic tradition, is presented. This includes a variety of research instruments. Firstly, a computational literature review is presented on analytics, assessing (amongst other things) the amount of research into analytics from a range of disciplines. Secondly, a historical analysis is performed of the literature regarding elements that can be seen as the pre-cursor of analytics, such as management information systems, decision support systems and business intelligence. Thirdly, an analysis of job adverts is included, utilising an online topic model and correlations analyses. Fourthly, online materials from UK universities concerning relevant degrees are analysed using a bagged support vector classifier and a bespoke module analysis algorithm. Finally, interviews with both potential employers of graduates, and also academics involved in analytics courses, are presented. The results of these separate analyses are synthesised and contrasted. The outcome of this is an assessment of the current state of the market, some reflections on the role operational research make have, and a framework for the development of analytics curricula. The principal contribution of this work is practical; providing tangible recommendations on curricula design and development, as well as to the operational research community in general in respect to how it may react to the growth of analytics. Additional contributions are made in respect to methodology, with a novel, mixed-method approach employed, and to theory, with insights as to the nature of how trends develop in both the jobs market and in academia. It is hoped that the insights here, may be of value to course designers seeking to react to similar trends in a wide range of disciplines and fields.