This thesis concerns the development of novel feasible direction type algorithms for constrained nonlinear optimization. The new algorithms are based upon enhancements of the search direction determination and the line search steps. The Frank-Wolfe method is popular for solving certain structured linearly constrained nonlinear problems, although its rate of convergence is often poor. We develop improved Frank--Wolfe type algorithms based on conjugate directions. In the conjugate direction Frank-Wolfe method a line search is performed along a direction which is conjugate to the previous one with respect to the Hessian matrix of the objective. A further refinement of this method is derived by applying conjugation with respect to the last two directions, instead of only the last one. The new methods are applied to the single-class user traffic equilibrium problem, the multi-class user traffic equilibrium problem under social marginal cost pricing, and the stochastic transportation problem. In a limited set of computational tests the algorithms turn out to be quite efficient. Additionally, a feasible direction method with multi-dimensional search for the stochastic transportation problem is developed. We also derive a novel sequential linear programming algorithm for general constrained nonlinear optimization problems, with the intention of being able to attack problems with large numbers of variables and constraints. The algorithm is based on inner approximations of both the primal and the dual spaces, which yields a method combining column and constraint generation in the primal space. / The articles are note published due to copyright rextrictions.

For most kind of analyses in the field of traffic planning, there is a need for origin--destination (OD) matrices, which specify the travel demands between the origin and destination nodes in the network. This thesis concerns the OD-matrix estimation problem, that is, the calculation of OD-matrices using observed link flows. Both time-independent and time-dependent models are considered, and we also study the placement of link flow detectors. Many methods have been suggested for OD-matrix estimation in time-independent models, which describe an average traffic situation. We assume a user equilibrium to hold for the link flows in the network and recognize a bilevel structure of the estimation problem. A descent heuristic is proposed, in which special attention is given to the issue of calculating the change of a link flow with respect to a change of the travel demand in a certain pair of origin and destination nodes. When a time-dimension is considered, the estimation problem becomes more complex. Besides the problem of distributing the travel demand onto routes, the flow propagation in time and space must also be handled. The time-dependent OD-matrix estimation problem is the subject for two studies. The first is a case study, where the conventional estimation technique is improved through introducing pre-adjustment schemes, which exploit the structure of the information contained in the OD-matrix and the link flow observations. In the second study, an algorithm for time-independent estimation is extended to the time-dependent case and tested for a network from Stockholm, Sweden. Finally, we study the underlying problem of finding those links where traffic flow observations are to be performed, in order to ensure the best possible quality of the estimated OD-matrix. There are different ways of quantifying a common goal to cover as much traffic as possible, and we create an experimental framework in which they can be evaluated. Presupposing that consistent flow observations from all the links in the network yields the best estimate of the OD-matrix, the lack of observations from some links results in a relaxation of the estimation problem, and a poorer estimate. We formulate the problem to place link flow detectors as to achieve the least relaxation with a limited number of detectors.

In the first part of our work we focus on the model of the optimal consumption with a random income. We provide the three dimensional equation for this model, demonstrate the reduction to the two dimensional case and provide for two different utility functions the full point-symmetries' analysis of the equations. We also demonstrate that for the logarithmic utility there exists a unique and smooth viscosity solution the existence of which as far as we know was never demonstrated before. In the second part of our work we develop the concept of the empirical liquidity measure. We provide the retrospective view of the works on this issue, discuss the proposed definitions and develop our own empirical measure based on the intuitive mathematical model and comprising several features of the definitions that existed before. Then we verify the measure provided on the real data from the market and demonstrate the advantages of the proposed value for measuring the illiquidity.

The problem of managing the portfolio provisions is of very high importance for any financial institution. In this paper we provide both static and dynamic models of provisions estimation for the case when the decision about provisions is made at the first moment of time subject to the absence of information and for the case of complete and incomplete information. Also the hedging strategy for the case of the defaultable market is presented in this work as another tool of reducing the risk of default. The default time is modelled as a first-passage time of a standard Brownian motion through a deterministic barrier. Some methods of numerical provision estimation are also presented.

Inom vården utförs ofta schemaläggning av personal manuellt, vilket kräver mycket tid och resurser. Att planera arbetet för en grupp läkare, med dess ofta mycket komplexa sammansättning vad gäller exempelvis arbetsuppgifter och kompetenser, är ingen lätt uppgift. Detta examensarbete studerar huruvida en automatiserad taktisk bemanningsplanering med en tidshorisont på ett halvår till ett år, skulle kunna underlätta denna uppgift. I rapporten presenteras en måloptimeringsmodell som implementerats i AMPL för att med CPLEX som lösare generera förslag till bemanningsplaner. För att utveckla en matematisk modell som väl representerar de förutsättningar som råder vid bemanningsplanering av läkare har alternativa formuleringar provats och utvärderats. Den mest lovande av modellerna, som baseras på måloptimering, har i en pilotstudie testats på data från Onkologiska kliniken vid Linköpings universitetssjukhus. Flexibiliteten i modellen gjorde att den enkelt kunde användas på de data som erhölls därifrån. Resultatet från pilotstudien indikerar att den utvecklade modellen har kapacitet att ge förslag till rimliga bemanningsplaner. / Scheduling of staff in the health care industry is typically done by hand, thus consuming a lot of time and effort. To plan the work for a group of physicians is a complex task, having to take into account factors like individual preferences and competences among the physicians. This thesis studies whether an automated tactical workforce planning, with a time horizon of half a year to a year, could facilitate this task. This thesis presents a goal programming model for generating suggestions to workforce plans for physicians. The model has been implemented in AMPL and is solved using CPLEX. During the development of the mathematical model for workforce planning, alternative model formulations have been tested and evaluated, and some of these are presented in the report. The most promising of them is one based solely on goal programming, and it has been tested in a pilot study on data from the Oncology Clinic at the University Hospital in Linköping. The flexibility of the model made it easy to use on the data provided by the clinic. The result of the pilot study indicates that the developed model has the capacity to give reasonable suggestions for workforce plans.

<p>Many companies have traveling salesmen that market and sell their products.This results in much traveling by car due to the daily customer visits. Thiscauses costs for the company, in form of travel expenses compensation, and environmentaleffects, in form of carbon dioxide pollution. As many companies arecertified according to environmental management systems, such as ISO 14001,the environmental work becomes more and more important as the environmentalconsciousness increases every day for companies, authorities and public.The main task of this thesis is to compute reasonable limits on the mileage ofthe salesmen; these limits are based on specific conditions for each salesman’sdistrict. The objective is to implement a heuristic algorithm that optimizes thecustomer tours for an arbitrary chosen month, which will represent a “standard”month. The output of the algorithm, the computed distances, will constitute amileage limit for the salesman.The algorithm consists of a constructive heuristic that builds an initial solution,which is modified if infeasible. This solution is then improved by a local searchalgorithm preceding a genetic algorithm, which task is to improve the toursseparately.This method for computing mileage limits for traveling salesmen generates goodsolutions in form of realistic tours. The mileage limits could be improved if theinput data were more accurate and adjusted to each district, but the suggestedmethod does what it is supposed to do.</p>

Made available in DSpace on 2016-12-23T14:37:33Z (GMT). No. of bitstreams: 1 Dissertacao Adriano.pdf: 704192 bytes, checksum: 7c33dc375052d165c08f082139c5cdab (MD5) Previous issue date: 2006-02-24 / This work had as general objective the evaluation of a methodology for estimate of the wood volume in the forest inventory, considering the profile of quality of the stem of the trees. A stand was used with area of 4,31 ha planted with Eucalyptus sp. with 16 year-old, originated from seminific propagation. The initial spacing used in the planting was 3 x 3 m and a selective thinning was done with 8,6 years. Firstly, it was evaluated four taper models to estimate the stem taper: Demaerschalk, Ormerod, Schöepfer and Hradetzky. These models were tested to estimate the volume and the height for the commercial diameters of 7 and 28 cm. It was used 32 tree-samples in equations fitting and 27 tree-samples for the validation tests. Based on the graphic analysis of the residuals, in the statistics (correlation coefficient, relative standard error, "bias" (B), in the average of the differences (MD) and standard deviation of the differences (DPD)) and in Leite and Oliveira (2002) test, it was verified that the model of Ormerod was what presented better volume estimate and the model of Schöepfer obtained better height results. The second part was dedicated in evaluating an inventory methodology to estimate the wood production for sawmill in relation to quality classes and assortment. Eight circular samples of 855 m² were located. In those samples were measured the diameter at 1,30 m (DAP) and total height (Ht) of the trees, and the stems with DAP larger than 28 cm were classified in agreement with a priori defined quality classes. The stems of the trees from 8 samples were submitted to the optimization process. After the crop xvi of all trees, the stems were marked by a trained team and they were sawed for subsequent comparison to the commercial volumes of the logs drawn with the volume obtained by the optimization method. The volume and the number of logs for quality classes and assortment, optimized and explored, have significantly difference by qui-square test, with 5% of probability. It was concluded that there is necessity of standardization of the exploration and inventory team training and the inventory methodology presented need to be improved before implementation. / Este trabalho teve como objetivo geral a avaliação de uma metodologia para estimativa do volume de madeira no inventário florestal, considerando o perfil de qualidade do fuste das árvores. Foi utilizado um talhão com área de 4,31 ha plantado com Eucalyptus sp. com idade de 16 anos, proveniente de propagação seminífera. O espaçamento inicial utilizado no plantio foi 3 x 3 m, sendo feito um desbaste seletivo aos 8,6 anos de idade. Primeiramente, foram avaliados quatro modelos que estimam o afilamento do tronco: Demaerschalk, Ormerod, Schöepfer e Hradetzky. Estes modelos foram testados para estimação do volume e da altura para os diâmetros comerciais de 7 e 28 cm. Foram utilizadas 32 árvores-amostra no ajuste das equações e 27 árvores-amostra para os testes de validação. Baseado na análise gráfica dos resíduos, nas estatísticas avaliadas (coeficiente de correlação, erro padrão relativo, bias (B), na média das diferenças (MD) e desvio padrão das diferenças (DPD)) e no teste de Leite e Oliveira (2002), verificou-se que o modelo de Ormerod foi o que apresentou melhores estimativas de volume e o modelo de Schöepfer obteve melhores resultados de altura. A segunda parte constitui-se na avaliação de uma metodologia de inventário para estimar a produção de madeira para serraria em relação a classes de qualidade e de sortimento. Foram lançadas oito parcelas circulares de 855 m². Nessas parcelas foram medidos o diâmetro na altura de 1,30 m (DAP) e altura total (Ht) das árvores, sendo os fustes com DAP xiv maior que 28 cm classificados de acordo com classes de qualidade definidas a priori. Os fustes das árvores das 8 parcelas foram submetidos ao processo de otimização. Após a colheita de todas as árvores das oito parcelas, os fustes foram marcados por uma equipe treinada e passaram pelo processo de traçamento para posterior comparação dos volumes comerciais das toras traçadas com o volume obtido pelo método de otimização. O volume e o número de toras por classes de qualidade e sortimento, otimizado e colhido, diferiram significativamente pelo teste qui-quadrado a 5% de probabilidade. Conclui-se que há necessidade de padronização do treinamento das equipes de colheita e inventário florestal e a metodologia de inventário apresentada necessita de ajustes antes de sua implementação.

The thesis consists of an introduction and four appended papers. In the introduction we give an overview of pulse-modulated systems and provide a few examples of such systems. Furthermore, we introduce the so-called dynamic phasor model which is used as a basis for analysis in two of the appended papers. We also introduce the harmonic transfer function and finally we provide a summary of the appended papers. The first paper considers stability analysis of a class of pulse-width modulated systems based on a discrete time model. The systems considered typically have periodic solutions. Stability of a periodic solution is equivalent to stability of a fixed point of a discrete time model of the system dynamics. Conditions for global and local exponential stability of the discrete time model are derived using quadratic and piecewise quadratic Lyapunov functions. A griding procedure is used to develop a systematic method to search for the Lyapunov functions. The second paper considers the dynamic phasor model as a tool for stability analysis of a general class of pulse-modulated systems. The analysis covers both linear time periodic systems and systems where the pulse modulation is controlled by feedback. The dynamic phasor model provides an $\textbf{L}_2$-equivalent description of the system dynamics in terms of an infinite dimensional dynamic system. The infinite dimensional phasor system is approximated via a skew truncation. The truncated system is used to derive a systematic method to compute time periodic quadratic Lyapunov functions. The third paper considers the dynamic phasor model as a tool for harmonic analysis of a class of pulse-width modulated systems. The analysis covers both linear time periodic systems and non-periodic systems where the switching is controlled by feedback. As in the second paper of the thesis, we represent the switching system using the L_2-equivalent infinite dimensional system provided by the phasor model. It is shown that there is a connection between the dynamic phasor model and the harmonic transfer function of a linear time periodic system and this connection is used to extend the notion of harmonic transfer function to describe periodic solutions of non-periodic systems. The infinite dimensional phasor system is approximated via a square truncation. We assume that the response of the truncated system to a periodic disturbance is also periodic and we consider the corresponding harmonic balance equations. An approximate solution of these equations is stated in terms of a harmonic transfer function which is analogous to the harmonic transfer function of a linear time periodic system. The aforementioned assumption is proved to hold for small disturbances by proving the existence of a solution to a fixed point equation. The proof implies that for small disturbances, the approximation is good. Finally, the fourth paper considers control synthesis for switched mode DC-DC converters. The synthesis is based on a sampled data model of the system dynamics. The sampled data model gives an exact description of the converter state at the switching instances, but also includes a lifted signal which represents the inter-sampling behavior. Within the sampled data framework we consider H-infinity control design to achieve robustness to disturbances and load variations. The suggested controller is applied to two benchmark examples; a step-down and a step-up converter. Performance is verified in both simulations and in experiments. / QC 20100628

Inom grossistbranschen associeras distributionen med svårigheter så som många kunder, små godsvolymer per kund och krav på korta ledtider. Många kunder kräver dessutom leveranser inom vissa tidsfönster. Dessa faktorer ställer höga krav på logistiken och skapar behov om hög leveransservice. Inom transportbranschen råder idag generellt en relativt låg datormognad. Sedan tidigare finns avancerade digitala informationssystem tillgängliga för inköp, ordermottagning och lagerkontroll. Utvecklingen går dock mot att även logistik- och transportavdelningarna i större utsträckning börjar använda sig av mer avancerade transporttekniska hjälpmedel. Exempel på sådana är ruttoptimeringsprogram som kan användas för att beräkna optimala körvägar. Servera R&amp;S är en restauranggrossist som har ett antal lager utspridda i Sverige. Då deras kundkrets i stockholmsområdet under senare år blivit allt större har även antalet lossningsplatser ökat drastiskt. Godset till dessa förses från lager placerade i Norrköping och Västerås. Godset från Norrköping samlas och packas om i en terminal i Årsta innan det transporteras vidare till kunderna i Stockholm. Servera R&amp;S efterfrågade en analys av deras distribution i Stockholm. Detta för att undersöka om nuvarande distributionsstrategier är kostnadseffektiva. Syftet var att finna möjliga förändringar i verksamheten som skulle kunna medföra förbättringar för distributionen till kunder i Stockholm. Målet innefattade att finna förbättringsförslag som skulle innebära ett bättre användande av distributionsnätverkets resurser, minskade transportkostnader och ökad leveransservice. Inledningsvis genomfördes en nulägesanalys för att kartlägga arbetsmetoder och tillvägagångssätt vid distributionen. Utifrån intervjuer och enkätundersökningar skapades sedan en modell av distributionen i vilken det verkliga trafikarbetet efterliknades. Denna användes vid simuleringar i ett ruttoptimeringsprogram med syftet att påvisa förbättringsmöjligheter. Under analysfasen studerades distributionsprocessen och simuleringsresultaten med målet att ta fram förslag på förbättringar och annorlunda tillvägagångssätt vid terminalhantering och transport. Studien visar att det i distributionsprocessen finns stora möjligheter för förbättringar gällande terminalhantering och godstransporter. Ruttoptimeringen påvisar stora besparingsmöjligheter gällande transporttid, antalet körda kilometer och antalet använda fordon i distributionsarbetet. Simuleringsresultaten visar exempelvis en minskning av den totala transportsträckan med upp till 30 procent. Då transportsträckan står i direkt relation till transportkostnaderna skulle en sådan minskning innebära reducerade kostnader för distributionen. / Within the wholesale sector, the distribution is often associated with difficulties, such as many customers and a requirement for short lead times. A lot of customers also demand delivery within certain time windows. These factors all contribute to a high level of strain on the logistics. In general, the amount of computer usage within the transportation industry is relatively low. However, advanced information systems are available for order handling and inventory management, and a lot of software for distribution planning and vehicle routing have surfaced as of recently. These often combine digital maps and optimization algorithms, and can be used for calculating optimized routes within the distribution. Servera R&amp;S is a wholesale company with a number of warehouses in different parts of Sweden. As of lately, their clientele in Stockholm has expanded, and the number of delivery points have increased drastically. The customers in Stockholm are provided with goods from warehouses in Norrköping and Västerås. The goods from Norrköping passes through a transfer terminal in Årsta before it is delivered to the customer in Stockholm. Servera R&amp;S is requesting an analysis of their distribution in Stockholm. They want to determine whether their distribution strategies are economically effective or not. Within this study, we aim to analyze different distribution strategies, which may or may not result in improvements of the efficiency of the distribution process. The purpose is to find solutions that better use the recourses of the distribution network (i.e. vehicles and personnel etc.), increase the level of delivery service and reduce the transportation costs. A survey analysis was carried out to map work methods and procedures within the distribution process. Interviews and surveys were used in the process of creating a basis for the optimization tool. Simulations were performed in an attempt to demonstrate the possibilities for decreasing distribution costs through the use of a vehicle routing program. During the analysis, the distribution process and the results from the simulations were studied with an aim to find possible improvements in the way that goods and information are handled within the warehouses and during the transports. The study shows a lot of possibilities for improvements within the distribution process. The route optimization prove a potential for decreasing costs regarding transportation time, distances and the number of vehicles used within the distribution. For example, the simulations show that the distances can be decreased with as much as 30 percent.

The Swedish National Debt Office (SNDO) is the Swedish Government’s financial administration. It has several tasks and the main one is to manage the central government’s debt in a way that minimizes the cost with due regard to risk. The debt management problem is to choose currency composition and maturity profile - a problem made difficult because of the many stochastic factors involved. The SNDO has created a simulation model to quantitatively analyze different aspects of this problem by evaluating a set of static strategies in a great number of simulated futures. This approach has a number of drawbacks, which might be handled by using a financial optimization approach based on Stochastic Programming. The objective of this master’s thesis is thus to apply financial optimization on the Swedish government’s strategic debt management problem, using the SNDO’s simulation model to generate scenarios, and to evaluate this approach against a set of static strategies in fictitious future macroeconomic developments. In this report we describe how the SNDO’s simulation model is used along with a clustering algorithm to form future scenarios, which are then used by an optimization model to find an optimal decision regarding the debt management problem. Results of the evaluations show that our optimization approach is expected to have a lower average annual real cost, but with somewhat higher risk, than a set of static comparison strategies in a simulated future. These evaluation results are based on a risk preference set by ourselves, since the government has not expressed its risk preference quantitatively. We also conclude that financial optimization is applicable on the government debt management problem, although some work remains before the method can be incorporated into the strategic work of the SNDO.