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>

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.

<p>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.</p><p>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.</p><p>Servera R&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.</p><p>Servera R&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.</p><p>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.</p><p>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.</p> / <p>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.</p><p>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.</p><p>Servera R&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.</p><p>Servera R&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.</p><p>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.</p><p>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.</p>

The main body of this thesis consists of six appended papers. In the  first two, different  cooperative surveillance problems are considered. The second two consider different aspects of the trajectory planning problem, while the last two deal with observer design for mobile robotic and Euler-Lagrange systems respectively.In Papers A and B,  a combinatorial optimization based framework to cooperative surveillance missions using multiple Unmanned Ground Vehicles (UGVs) is proposed. In particular, Paper A  considers the the Minimum Time UGV Surveillance Problem (MTUSP) while Paper B treats the Connectivity Constrained UGV Surveillance Problem (CUSP). The minimum time formulation is the following. Given a set of surveillance UGVs and a polyhedral area, find waypoint-paths for all UGVs such that every point of the area is visible from  a point on a waypoint-path and such that the time for executing the search in parallel is minimized.  The connectivity constrained formulation  extends the MTUSP by additionally requiring the induced information graph to be  kept recurrently connected  at the time instants when the UGVs  perform the surveillance mission.  In these two papers, the NP-hardness of  both these problems are shown and decomposition techniques are proposed that allow us to find an approximative solution efficiently in an algorithmic manner.Paper C addresses the problem of designing a real time, high performance trajectory planner for an aerial vehicle that uses information about terrain and enemy threats, to fly low and avoid radar exposure on the way to a given target. The high-level framework augments Receding Horizon Control (RHC) with a graph based terminal cost that captures the global characteristics of the environment.  An important issue with RHC is to make sure that the greedy, short term optimization does not lead to long term problems, which in our case boils down to two things: not getting into situations where a collision is unavoidable, and making sure that the destination is actually reached. Hence, the main contribution of this paper is to present a trajectory planner with provable safety and task completion properties. Direct methods for trajectory optimization are traditionally based on a priori temporal discretization and collocation methods. In Paper D, the problem of adaptive node distribution is formulated as a constrained optimization problem, which is to be included in the underlying nonlinear mathematical programming problem. The benefits of utilizing the suggested method for  online  trajectory optimization are illustrated by a missile guidance example.In Paper E, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotic systems, is considered. The set of feasible configurations and the set of output flow equivalent states are defined. It is shown that the inter-relation between these two sets may serve as the basis for design of active observers. The proposed observer design methodology is illustrated by considering a  unicycle robot model, equipped with a set of range-measuring sensors. Finally, in Paper F, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented  by  a proof  that the region of contraction is infinitely thin. Moreover, assuming a priori bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature. / QC 20100622 / TAIS, AURES

<p>The main body of this thesis consists of four appended papers. The first two consider different aspects of the trajectory planning problem, while the last two deal with observer design for mobile robotic and Euler-Lagrange systems respectively.</p><p>The first paper addresses the problem of designing a real time, high performance trajectory planner for aerial vehicles. The main contribution is two-fold. Firstly, by augmenting a novel safety maneuver at the end of the planned trajectory, this paper extends previous results by having provable safety properties in a 3D setting. Secondly, assuming initial feasibility, the planning method is shown to have finite time task completion. Moreover, in the second part of the paper, the problem of simultaneous arrival of multiple aerial vehicles is considered. By using a time-scale separation principle, one is able to adopt standard Laplacian control to this consensus problem, which is neither unconstrained, nor first order.</p><p>Direct methods for trajectory optimization are traditionally based on<i> a</i> <i>priori </i>temporal discretization and collocation methods. In the second paper, the problem of adaptive node distribution is formulated as a constrained optimization problem, which is to be included in the underlying nonlinear mathematical programming problem. The benefits of utilizing the suggested method for online trajectory optimization are illustrated by a missile guidance example.</p><p>In the third paper, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotics systems, is considered. The set of feasible configurations and the set of output flow equivalent states are defined. It is shown that the inter-relation between these two sets may serve as the basis for design of active observers. The proposed observer design methodology is illustrated by considering a unicycle robot model, equipped with a set of range-measuring sensors.</p><p>Finally, in the fourth paper, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer recently proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented by a proof that the region of contraction is infinitely thin. However, assuming <i>a</i> <i>priori </i>bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature.</p>