<p>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. </p><p>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. </p><p>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. </p><p>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. </p><p>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.</p>

<p>This thesis grew out of a problem encountered by a subsidiary of a Swedish multinational industrial corporation. This subsidiary is responsible for the corporation’s customer financing activities. In the thesis, we refer to these entities as the Division and the Corporation. The Division needed to find a new approach to finance its customer loan portfolio. Risk control and return maximization were important aspects of this need. The objective of this thesis is to devise and implement a method that allows the Division to make optimal funding decisions, given a certain risk limit. </p><p>We propose a funding approach based on stochastic programming. Our approach allows the Division’s portfolio manager to minimize the funding costs while hedging against market risk. We employ principal component analysis and Monte Carlo simulation to develop a multicurrency scenario generation model for interest and exchange rates. Market rate scenarios are used as input to three different optimization models. Each of the optimization models presents the optimal funding decision as positions in a unique set of financial instruments. By choosing between the optimization models, the portfolio manager can decide which financial instruments he wants to use to fund the loan portfolio. </p><p>To validate our models, we perform empirical tests on historical market data. Our results show that our optimization models have the potential to deliver sound and profitable funding decisions. In particular, we conclude that the utilization of one of our optimization models would have resulted in an increase in the Division’s net income over the past 3.5 years.</p>

This thesis grew out of a problem encountered by a subsidiary of a Swedish multinational industrial corporation. This subsidiary is responsible for the corporation’s customer financing activities. In the thesis, we refer to these entities as the Division and the Corporation. The Division needed to find a new approach to finance its customer loan portfolio. Risk control and return maximization were important aspects of this need. The objective of this thesis is to devise and implement a method that allows the Division to make optimal funding decisions, given a certain risk limit. We propose a funding approach based on stochastic programming. Our approach allows the Division’s portfolio manager to minimize the funding costs while hedging against market risk. We employ principal component analysis and Monte Carlo simulation to develop a multicurrency scenario generation model for interest and exchange rates. Market rate scenarios are used as input to three different optimization models. Each of the optimization models presents the optimal funding decision as positions in a unique set of financial instruments. By choosing between the optimization models, the portfolio manager can decide which financial instruments he wants to use to fund the loan portfolio. To validate our models, we perform empirical tests on historical market data. Our results show that our optimization models have the potential to deliver sound and profitable funding decisions. In particular, we conclude that the utilization of one of our optimization models would have resulted in an increase in the Division’s net income over the past 3.5 years.

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.

<p>Vid Onkologiska klinikens behandlingsmottagning ges cytostatika till de patienter som inte är inlagda vid kliniken. Arbetsförhållandena för sjuksköterskorna på mottagningen är ibland mycket påfrestande, genom att arbetsbelastningen kan vara mycket varierande, både mellan olika dagar och mellan olika sjuksköterskor. Vidare ger dagens bokningsrutiner inte någon samordning mellan sjuksköterskorna, vilket gör att mottagningen även har svårigheter att på ett bra sätt utnyttja sina behandlingsresurser.</p><p>Behandlingstiderna för patienterna bokas idag löpande. Examensarbetet syftar till att simulera förändringar i dagens verksamhet. Vi undersöker möjligheterna att genom samordnad bokning dels förbättra arbetsförhållandena för sjuksköterskorna och dels förbättra resursutnyttjandet vid mottagningen. Detta görs genom att konstruera dagsscheman för sjuksköterskorna. Arbetsförhållandena i dessa dagsschemana styrs av regler. Genom att utnyttja historisk statistik över utförda behandlingar genereras dagsscheman som uppfyller mottagningens behandlingsbehov på lång sikt. På så sätt kan även mottagningens maximala behandlingskapacitet undersökas. Dagsscheman skapas med hjälp av kolumngenerering, varvid kolumngenereringsproblemet löses med en girig heuristik.</p><p>Analyser visar att det finns stora möjligheter att med hjälp av samordnad bokning förbättra arbetsförhållandena för sjuksköterskorna, samtidigt som samma antal patienter, eller till och med fler, kan behandlas.</p>

Almost everywhere, routing plays an important role in everyday life. This thesis consists of three parts, each studying different applications where routing decisions are coordinated with other decisions. A common denominator in all applications is that an intelligent utilization of a fleet of vehicles is crucial for the performance of the system. In the first part, routing and inventorymanagement decisions are coordinated, in the second part, routing decisions concerning different modes of transportation are coordinated with inventory management, and in the third part, location decision and routing are coordinated. In the first part, an application concerning waste management is presented. Many industries generate garbage, and instead of handling the waste disposal themselves, other companies, specialized in garbage collection, handle the disposal. Each industry rents containers from a company to be used for waste, and the garbage collection companies handle the collection. The industries buy a service including one or more containers at the industry and the garbage collection companies are obliged to make sure that the containers never become overfull. The idea is that the industries buy this service and in return, the garbage collection company can plan the collection so that the overall cost and the number of overfull containers is minimized. Two models for the problem facing the garbage collection company are proposed. The first is solved using a Lagrangean relaxation approach on a flow based model, and the second is solved using Benders decomposition on a column based model. The second part investigates a distribution chain management problem taken from the Swedish pulp industry. Given fixed production plans at the mills, and fixed customer demands, the problem is to minimize the distribution cost. Unlike many other models for marine distribution chains, the customers are not located at the harbors. This means that the model proposed also incorporates the distribution planning from the harbors to the customers. All customers are not served from the harbors; some are served directly from the mills using trucks and trains to distribute the pulp, and these decisions are also included. The problem is modeled as a mixed integer linear program and solved using a branch and price scheme. Due to the complexity of the problem, the solution strategy is divided into two phases, where the first emphasizes the generation of schedules for the vessels operated by the company, while the second deals with the chartering of vessels on the spot market. In the third part, routing is combined with location decisions in the location-routing problem. Special emphasis is given to strategic management where decision makers must make location, capacity and routing decisions over a long planning period. The studied application comes fromstrategic schoolmanagement, where the location and capacity of the schools as well as their catchment areas are under consideration. The problem is modeled as a mixed integer linear program. The computational study shows the importance of incorporating a routing component allowing multiple visits, as well as the danger of having a too short planning period.

In this thesis, various control problems originating from the field of mobile robotics are considered. In particular, the thesis deals with problems that are related to the interaction and coordination of multiple mobile units. The scientific contributions are presented in five papers that together constitute the main part of the thesis. The papers are preceded by a longer introductory part, in which some important results from control theory, data processing and robotics are reviewed. In the first of the appended papers, two stabilizing tracking controls are proposed for a non-holonomic robot platform of unicycle type. Tolerance to errors and other properties of the controllers are discussed and a reactive obstacle avoidance control, that can easily be incorporated with the proposed tracking controls, is suggested. In Paper B, the results from Paper~A are extended to multi-agent systems. It is demonstrated how the tracking controls from Paper A can be used as building blocks when putting together formations of robots, in which each robot maintains a fixed position relative its neighbors during translation. In addition, switching between the different control functions is shown to be robust, implying that it is possible to change the shape of a formation on-line. In the first two papers, the tracking problem is facilitated by the assumption that the approximate velocity of the target/leader is known to the tracking robot. Paper C treats the the case where the target velocity is neither directly measurable with the available sensor setup, nor possible to obtain through communication with neighboring agents. Straight-forward computation of the target velocity from available sensor data unfortunately tend to enhance measurement errors and give unreliable estimates. To overcome the difficulties, an alternative approach to velocity estimation is proposed, motivated by the local observability of the given control system. Paper D deals with another problematic aspect of data acquisition. When using range sensors, one often obtains a mixed data set with measurements originating from many different sources. This problem would, for instance, be encountered by a robot moving in a formation, where it was surrounded by other agents. There exist established techniques for sorting mixed data sets off-line, but for time-depending systems where data need to be sorted on-line and only small time delays can be tolerated, established methods fail. The solution presented in the paper is a prediction-correction type algorithm, referred to as CCIA (Classification Correction and Identification algorithm). Finally, in Paper E, we consider the problem of maintaining connectivity in a multi-agent system. Often inter-agent communication abilities are associated with some proximity constraints, so when the robots move in relation to each other, communication links both break and form. In the paper we present a framework for analysis that makes it possible to compute a set of general constraints which, if satisfied, are sufficient to guarantee maintained communication for a given multi-agent system. Constraints are computed for two sorts of consensus-based systems and the results are verified in simulations. / QC 20100715

This thesis consists of an introduction and seven appended papers. The purpose of the introduction is to give an overview of the field of topology optimization of discretized load carrying continuum structures. It is assumed that the design domain has been discretized by the finite element method and that the design variable vector is a binary vector indicating presence or absence of material in the various finite elements. Common to all papers is the incorporation of von Mises stresses in the problem formulations. In the first paper the design variables are binary but it is assumed that the void structure can actually take some load. This is equivalent to adding a small positive value, epsilon, to all design variables, both those that are void and those that are filled with material. With this small positive lower bound the stiffness matrix becomes positive definite for all designs. If only one element is changed (from material to void or from void to material) the new global stiffness matrix is just a low rank modification of the old one and thus the Sherman-Morrison-Woodbury formula can be used to compute the displacements in the neighbouring designs efficiently. These efficient sensitivity calculations can then be applied in the context of a neighbourhood search method. Since the computed displacements are exact in the 1-neighbourhood (when one design variable is changed) the neighbourhood search method will find a local optimum with respect to the 1-neighbourhood. The second paper presents globally optimal zero-one solutions to some small scale topology optimization problems defined on discretized continuum design domains. The idea is that these solutions can be used as benchmarks when testing new algorithms for finding pure zero-one solutions to topology optimization problems. In the third paper the results from the first paper are extended to include also the case where there is no epsilon&gt;0. In this case the stiffness matrix will no longer be positive definite which means that the Sherman-Morrison-Woodbury formula can no longer be applied. The changing of one or two binary design variables to their opposite binary values will still result in a low rank change, but the size of the reduced stiffness matrix will change with the design. It turns out, however, that it is possible to compute the effect of these low rank changes efficiently also without the positive lower bound. These efficient sensitivity calculations can then be used in the framework of a neighbourhood search method. In this case the complete 1-neighbourhood and a subset of the 2-neighbourhood is investigated in the search for a locally optimal solution. In the fourth paper the sensitivity calculations developed in the third paper are used to generate first and partial second order approximations of the nonlinear functions usually present in topology optimization problems. These approximations are then used to generate subproblems in two different sequential integer programming methods (SLIP and SQIP, respectively). Both these methods generate a sequence of iteration points that can be proven to converge to a local optimum with respect to the 1-neighbourhood. The methods are tested on some different topology optimization problems. The fifth paper demonstrates that the SLIP method developed in the previous paper can be applied also to the mechanism design problem with stress constraints. In order to generate the subproblems in a fast way small displacements are assumed, which implies that the efficient sensitivity calculations derived in the third paper can be used. The numerical results indicate that the method can be used to lower the stresses and still get a functional mechanism. In the sixth paper the SLIP method developed in the fourth paper is used as a post processor to obtain locally optimal zero-one solutions starting from a rounded solution to the corresponding continuous problem. The numerical results indicate that the method can perform well as a post processor. The seventh paper is a theoretical paper that investigates the validity of the commonly used positive lower bound epsilon on the design variables when stating and solving topology optimization problems defined on discretized load carrying continuum structures. The main result presented here is that an optimal "epsilon-1" solution to an "epsilon-perturbed" discrete minimum weight problem with constraints on compliance, von Mises stresses and strain energy densities, is optimal, after rounding to zero-one, to the corresponding "unperturbed" discrete problem. This holds if the constraints in the perturbed problem are carefully defined and epsilon&gt;0 is sufficiently small. / QC 20100917

Vid Onkologiska klinikens behandlingsmottagning ges cytostatika till de patienter som inte är inlagda vid kliniken. Arbetsförhållandena för sjuksköterskorna på mottagningen är ibland mycket påfrestande, genom att arbetsbelastningen kan vara mycket varierande, både mellan olika dagar och mellan olika sjuksköterskor. Vidare ger dagens bokningsrutiner inte någon samordning mellan sjuksköterskorna, vilket gör att mottagningen även har svårigheter att på ett bra sätt utnyttja sina behandlingsresurser. Behandlingstiderna för patienterna bokas idag löpande. Examensarbetet syftar till att simulera förändringar i dagens verksamhet. Vi undersöker möjligheterna att genom samordnad bokning dels förbättra arbetsförhållandena för sjuksköterskorna och dels förbättra resursutnyttjandet vid mottagningen. Detta görs genom att konstruera dagsscheman för sjuksköterskorna. Arbetsförhållandena i dessa dagsschemana styrs av regler. Genom att utnyttja historisk statistik över utförda behandlingar genereras dagsscheman som uppfyller mottagningens behandlingsbehov på lång sikt. På så sätt kan även mottagningens maximala behandlingskapacitet undersökas. Dagsscheman skapas med hjälp av kolumngenerering, varvid kolumngenereringsproblemet löses med en girig heuristik. Analyser visar att det finns stora möjligheter att med hjälp av samordnad bokning förbättra arbetsförhållandena för sjuksköterskorna, samtidigt som samma antal patienter, eller till och med fler, kan behandlas.

The well-known Dijkstra's algorithm uses weights to determine the shortest path. The focus here is instead on the opposite problem, does there exist weights for a certain set of shortest paths? OSPF (Open Shortest Path First) is one of several possible protocols that determines how routers will send data in a network like the internet. Network operators would however like to have some control of how the traffic is routed, and being able to determine the weights, which would lead to the desired shortest paths to be used, would be a help in this task.The first part of this thesis is a mathematical explanation of the problem with a lot of examples to make it easier to understand. The focus here is on trying to combine several routing patterns into one, so that the result will be fewer, but more fully spanned, routing patterns, and it can e.g. be shown that there can't exist a common set of weights if two routing patterns can't be combined.The second part is a program that can be used to make several tests and changes to a set of routing patterns. It has a polynomial implementation of a function that can combine routing patterns. The examples that I used to combine routing patterns, showed that this will increase the likelihood of finding and significantly speed up the computation of a “valid cycle”. / Egentligen 30p/45hp, men det fanns inte som alternativ.