MCMC Analysis for Optimization of Stochastic Models

In any decision making under uncertainties, the goal is mostly to minimize the expected cost. The minimization of cost under uncertainties is usually done by optimization. For simple models, the optimization can easily be done using deterministic methods.However, many models practically contain some complex and varying parameters that can not easily be taken into account using usual deterministic methods of optimization. Thus, it is very important to look for other methods that can be used to get insight into such models. MCMC method is one of the practical methods that can be used for optimization of stochastic models under uncertainty. This method is based on simulation that provides a general methodology which can be applied in nonlinear and non-Gaussian state models. MCMC method is very important for practical applications because it is a uni ed estimation procedure which simultaneously estimates both parameters and state variables. MCMC computes the distribution of the state variables and parameters of the given data measurements. MCMC method is faster in terms of computing time when compared to other optimization methods. This thesis discusses the use of Markov chain Monte Carlo (MCMC) methods for optimization of Stochastic models under uncertainties .The thesis begins with a short discussion about Bayesian Inference, MCMC and Stochastic optimization methods. Then an example is given of how MCMC can be applied for maximizing production at a minimum cost in a chemical reaction process. It is observed that this method performs better in optimizing the given cost function with a very high certainty.

Epävarmuuden haltuunotosta Venäjälle suuntautuvissa hankkeissa - tapaustutkimus

Tämä tutkimus tarkastelee epävarmuutta Venäjälle suuntautuvissa hankkeissa. Tutkimuksessa analysoidaan Venäjän liiketoimintaympäristöön liittyvää epävarmuutta. Tutkimusongelman muodostaa näiden epävarmuuksien haltuunotto Venäjälle suuntautuvissa investoinneissa. Tutkimuksen teoreettisena viitekehyksenä käytetään 1970-luvulta lähtien kehitettyä reaalioptiolähestymistapaa. Tutkimusmenetelmänä käytetään tapaustutkimusta, jossa esimerkkiyritysten tekemiä valintoja pohditaan reaalioptioviitekehyksen lävitse. Tutkimuksen empiirisessä osassa on haastateltu esimerkkiyritysten edustajia sekämuita venäjänkaupan ammattilaisia ja tiedusteltu heidän näkemyksiään markkinoiden kehityksestä ja erityispiirteistä. Reaalioptiolähestymistapaa käytetään apuvälineenä hankkeisiin sisältyvää epävarmuutta jäsenneltäessä ja päätöksentekijöiden kommunikaatiovälineenä päätöstilanteissa. Sen sijaan Venäjälle suuntautuvien hankkeiden (reaalioptioiden) matemaattinen arvottaminen on hankalaa liiketoimintaympäristön ominaispiirteiden vuoksi.

Analyzing the Effects of the New Renewable Energy Policy in Russia on Investments into Wind, Solar and Small Hydro Power

This thesis presents an analysis of recently enacted Russian renewable energy policy based on capacity mechanism. Considering its novelty and poor coverage by academic literature, the aim of the thesis is to analyze capacity mechanism influence on investors’ decision-making process. The current research introduces a number of approaches to investment analysis. Firstly, classical financial model was built with Microsoft Excel® and crisp efficiency indicators such as net present value were determined. Secondly, sensitivity analysis was performed to understand different factors influence on project profitability. Thirdly, Datar-Mathews method was applied that by means of Monte Carlo simulation realized with Matlab Simulink®, disclosed all possible outcomes of investment project and enabled real option thinking. Fourthly, previous analysis was duplicated by fuzzy pay-off method with Microsoft Excel®. Finally, decision-making process under capacity mechanism was illustrated with decision tree. Capacity remuneration paid within 15 years is calculated individually for each RE project as variable annuity that guarantees a particular return on investment adjusted on changes in national interest rates. Analysis results indicate that capacity mechanism creates a real option to invest in renewable energy project by ensuring project profitability regardless of market conditions if project-internal factors are managed properly. The latter includes keeping capital expenditures within set limits, production performance higher than 75% of target indicators, and fulfilling localization requirement, implying producing equipment and services within the country. Occurrence of real option shapes decision-making process in the following way. Initially, investor should define appropriate location for a planned power plant where high production performance can be achieved, and lock in this location in case of competition. After, investor should wait until capital cost limit and localization requirement can be met, after that decision to invest can be made without any risk to project profitability. With respect to technology kind, investment into solar PV power plant is more attractive than into wind or small hydro power, since it has higher weighted net present value and lower standard deviation. However, it does not change decision-making strategy that remains the same for each technology type. Fuzzy pay-method proved its ability to disclose the same patterns of information as Monte Carlo simulation. Being effective in investment analysis under uncertainty and easy in use, it can be recommended as sufficient analytical tool to investors and researchers. Apart from described results, this thesis contributes to the academic literature by detailed description of capacity price calculation for renewable energy that was not available in English before. With respect to methodology novelty, such advanced approaches as Datar-Mathews method and fuzzy pay-off method are applied on the top of investment profitability model that incorporates capacity remuneration calculation as well. Comparison of effects of two different RE supporting schemes, namely Russian capacity mechanism and feed-in premium, contributes to policy comparative studies and exhibits useful inferences for researchers and policymakers. Limitations of this research are simplification of assumptions to country-average level that restricts our ability to analyze renewable energy investment region wise and existing limitation of the studying policy to the wholesale power market that leaves retail markets and remote areas without our attention, taking away medium and small investment into renewable energy from the research focus. Elimination of these limitations would allow creating the full picture of Russian renewable energy investment profile.

Offshoring and outsourcing under demand uncertainty -a supply chain management analysis

Outsourcing and offshoring or any combinations of these have not just become a popular phenomenon, but are viewed as one of the most important management strategies due to the new possibilities from globalization. They have been seen as a possibility to save costs and improve customer service. Executing offshoring and offshore outsourcing successfully can be more complex than initially expected. Potential cost savings resulting from of offshoring and offshore outsourcing are often based on lower manufacturing costs. However, these benefits might be conflicted by a more complex supply chain with service level challenges that can respectively increase costs. Therefore analyzing the total cost effects of offshoring and outsourcing is necessary. The aim of this Master´s Thesis was to to construct a total cost model using academic literature to calculate the total costs and analyze the reasonability of offshoring and offshore outsourcing production of a case company compared to insourcing production. The research data was mainly quantitative and collected mainly from the case company past sales and production records. In addition management level interviews from the case company were conducted. The information from these interviews was used for the qualification of the necessary quantitative data and adding supportive information that could not be gathered from the quantitative data. Both data collection and analysis were guided by a theoretical frame of reference that was based on academic literature concerning offshoring and outsourcing, statistical calculation of demand and total costs. The results confirm the theories that offshoring and offshore outsourcing would reduce total costs as both offshoring and offshore outsourcing options result in lower total annual costs than insourcing mainly due to lower manufacturing costs. However, increased demand uncertainty would make the alternative of offshore outsourcing more risky and difficult to manage. Therefore when assessing the overall impact of the alternatives, offshoring is the most preferable option. As the main cost savings in offshore outsourcing came from lower manufacturing costs, more specifically labour costs, the logistics costs in this case company did not have an essential effect in total costs. The management should therefore pay attention initially to manufacturing costs and then logistics costs when choosing the best production sourcing option for the company.

Analyzing Carbon Trade Permits in Optimization Framework

The threats caused by global warming motivate different stake holders to deal with and control them. This Master's thesis focuses on analyzing carbon trade permits in optimization framework. The studied model determines optimal emission and uncertainty levels which minimize the total cost. Research questions are formulated and answered by using different optimization tools. The model is developed and calibrated by using available consistent data in the area of carbon emission technology and control. Data and some basic modeling assumptions were extracted from reports and existing literatures. The data collected from the countries in the Kyoto treaty are used to estimate the cost functions. Theory and methods of constrained optimization are briefly presented. A two-level optimization problem (individual and between the parties) is analyzed by using several optimization methods. The combined cost optimization between the parties leads into multivariate model and calls for advanced techniques. Lagrangian, Sequential Quadratic Programming and Differential Evolution (DE) algorithm are referred to. The role of inherent measurement uncertainty in the monitoring of emissions is discussed. We briefly investigate an approach where emission uncertainty would be described in stochastic framework. MATLAB software has been used to provide visualizations including the relationship between decision variables and objective function values. Interpretations in the context of carbon trading were briefly presented. Suggestions for future work are given in stochastic modeling, emission trading and coupled analysis of energy prices and carbon permits.

Inversion and assimilation methods with applications in geophysical remote sensing

Stratospheric ozone can be measured accurately using a limb scatter remote sensing technique at the UV-visible spectral region of solar light. The advantages of this technique includes a good vertical resolution and a good daytime coverage of the measurements. In addition to ozone, UV-visible limb scatter measurements contain information about NO2, NO3, OClO, BrO and aerosols. There are currently several satellite instruments continuously scanning the atmosphere and measuring the UVvisible region of the spectrum, e.g., the Optical Spectrograph and Infrared Imager System (OSIRIS) launched on the Odin satellite in February 2001, and the Scanning Imaging Absorption SpectroMeter for Atmospheric CartograpHY (SCIAMACHY) launched on Envisat in March 2002. Envisat also carries the Global Ozone Monitoring by Occultation of Stars (GOMOS) instrument, which also measures limb-scattered sunlight under bright limb occultation conditions. These conditions occur during daytime occultation measurements. The global coverage of the satellite measurements is far better than any other ozone measurement technique, but still the measurements are sparse in the spatial domain. Measurements are also repeated relatively rarely over a certain area, and the composition of the Earth’s atmosphere changes dynamically. Assimilation methods are therefore needed in order to combine the information of the measurements with the atmospheric model. In recent years, the focus of assimilation algorithm research has turned towards filtering methods. The traditional Extended Kalman filter (EKF) method takes into account not only the uncertainty of the measurements, but also the uncertainty of the evolution model of the system. However, the computational cost of full blown EKF increases rapidly as the number of the model parameters increases. Therefore the EKF method cannot be applied directly to the stratospheric ozone assimilation problem. The work in this thesis is devoted to the development of inversion methods for satellite instruments and the development of assimilation methods used with atmospheric models.

Bayesian methods for estimation, optimization and experimental design

Mathematical models often contain parameters that need to be calibrated from measured data. The emergence of efficient Markov Chain Monte Carlo (MCMC) methods has made the Bayesian approach a standard tool in quantifying the uncertainty in the parameters. With MCMC, the parameter estimation problem can be solved in a fully statistical manner, and the whole distribution of the parameters can be explored, instead of obtaining point estimates and using, e.g., Gaussian approximations. In this thesis, MCMC methods are applied to parameter estimation problems in chemical reaction engineering, population ecology, and climate modeling. Motivated by the climate model experiments, the methods are developed further to make them more suitable for problems where the model is computationally intensive. After the parameters are estimated, one can start to use the model for various tasks. Two such tasks are studied in this thesis: optimal design of experiments, where the task is to design the next measurements so that the parameter uncertainty is minimized, and model-based optimization, where a model-based quantity, such as the product yield in a chemical reaction model, is optimized. In this thesis, novel ways to perform these tasks are developed, based on the output of MCMC parameter estimation. A separate topic is dynamical state estimation, where the task is to estimate the dynamically changing model state, instead of static parameters. For example, in numerical weather prediction, an estimate of the state of the atmosphere must constantly be updated based on the recently obtained measurements. In this thesis, a novel hybrid state estimation method is developed, which combines elements from deterministic and random sampling methods.

Optimization of the refining and shoe press in board production

Optimointi on tavallinen toimenpide esimerkiksi prosessin muuttamisen tai uusimisen jälkeen. Optimoinnilla pyritään etsimään vaikkapa tiettyjen laatuominaisuuksien kannalta paras tapa ajaa prosessia tai erinäisiä prosessin osia. Tämän työn tarkoituksena oli investoinnin jälkeen optimoida neljä muuttujaa, erään runkoon menevän massan jauhatus ja määrä, märkäpuristus sekä spray –tärkin määrä, kolmen laatuominaisuuden, palstautumislujuuden, geometrisen taivutusjäykkyyden ja sileyden, suhteen. Työtä varten tehtiin viisi tehdasmittakaavaista koeajoa. Ensimmäisessä koeajossa oli tarkoitus lisätä vettä tai spray –tärkkiä kolmikerroskartongin toiseen kerrosten rajapintaan, toisessa koeajossa muutettiin, jo aiemmin mainitun runkoon menevän massan jauhatusta ja jauhinkombinaatioita. Ensimmäisessä koeajossa tutkittiin palstautumislujuuden, toisessa koeajossa muiden lujuusominaisuuksien kehittymistä. Kolmannessa koeajossa tutkittiin erään runkoon menevän massan jauhatuksen ja määrän sekä kenkäpuristimen viivapaineen muutoksen vaikutusta palstautumislujuuteen, geometriseen taivutusjäykkyyteen sekä sileyteen. Neljännessä koeajossa yritettiin toistaa edellisen koeajon paras piste ja parametreja hieman muuttamalla saada aikaan vieläkin paremmat laatuominaisuudet. Myös tässä kokeessa tutkittiin muuttujien vaikutusta palstautumislujuuteen, geometriseen taivutusjäykkyyteen ja sileyteen. Viimeisen kokeen tarkoituksena oli tutkia samaisen runkoon menevän massan vähentämisen vaikutusta palstautumislujuuteen. Erinäisistä vastoinkäymisistä johtuen, koeajoista saadut tulokset jäivät melko laihoiksi. Kokeista kävi kuitenkin ilmi, että lujuusominaisuudet eivät parantuneet, vaikka jauhatusta jatkettiin. Lujuusominaisuuksien kehittymisen kannalta turha jauhatus pystyttiin siis jättämään pois ja näin säästämään energiaa sekä säästymään pitkälle viedyn jauhatuksen mahdollisesti aiheuttamilta muilta ongelmilta. Vähemmällä jauhatuksella ominaissärmäkuorma saatiin myös pidettyä alle tehtaalla halutun tason. Puuttuvat lujuusominaisuudet täytyy saavuttaa muilla keinoin.

Stability Analysis in Multicriteria Discrete Portfolio Optimization.

Almost every problem of design, planning and management in the technical and organizational systems has several conflicting goals or interests. Nowadays, multicriteria decision models represent a rapidly developing area of operation research. While solving practical optimization problems, it is necessary to take into account various kinds of uncertainty due to lack of data, inadequacy of mathematical models to real-time processes, calculation errors, etc. In practice, this uncertainty usually leads to undesirable outcomes where the solutions are very sensitive to any changes in the input parameters. An example is the investment managing. Stability analysis of multicriteria discrete optimization problems investigates how the found solutions behave in response to changes in the initial data (input parameters). This thesis is devoted to the stability analysis in the problem of selecting investment project portfolios, which are optimized by considering different types of risk and efficiency of the investment projects. The stability analysis is carried out in two approaches: qualitative and quantitative. The qualitative approach describes the behavior of solutions in conditions with small perturbations in the initial data. The stability of solutions is defined in terms of existence a neighborhood in the initial data space. Any perturbed problem from this neighborhood has stability with respect to the set of efficient solutions of the initial problem. The other approach in the stability analysis studies quantitative measures such as stability radius. This approach gives information about the limits of perturbations in the input parameters, which do not lead to changes in the set of efficient solutions. In present thesis several results were obtained including attainable bounds for the stability radii of Pareto optimal and lexicographically optimal portfolios of the investment problem with Savage's, Wald's criteria and criteria of extreme optimism. In addition, special classes of the problem when the stability radii are expressed by the formulae were indicated. Investigations were completed using different combinations of Chebyshev's, Manhattan and Hölder's metrics, which allowed monitoring input parameters perturbations differently.

Foreign direct investment motives and location decision factors under economic recession: Three cases of Finnish FDI in Portugal

The purpose of this thesis was to study how uncertainty in economic conditions of the FDI host country affects location decision of an investment, and what kinds of motives are behind the investment decision to a country in economic recession, in this case Portugal. The country has attracted foreign direct investment steadily, but it is evident that most multinational firms and investors tend to be more interested in emerging economies in general. The aim was to find out also which host country specific advantages are important in this kind of cross-border investment and which factors are important for an FDI to succeed under economic uncertainty at the host country. The study was done by analyzing three Finnish case companies: a private equity and real estate investment firm Pontos Group, A wave energy technology research and development company AW Energy and NSN, Nokia Solutions and Networks, a global telecommunications company. The research was done empirically, by interviewing experts on the subject, mainly persons representing these companies. In addition relevant articles, journals and content from case companies’ web-pages is used for the desk research regarding the topic. The results of this thesis showed that the FDIs with strategic asset-seeking investments seem most profitable FDI types under uncertain economic conditions. This kind of investments aim to strengthen the company’s long-term strategy, including the time after recession. Firm-specific ownership advantages that bring competitive advantage proved out to be important under these circumstances, as well as first-mover advantages and externally created assets such as government promotional policies regarding FDI incentives. Also the location was considered suitable for resource- or efficiency seeking motives, based on the lowered price level at the host country. Problems were related mainly to financing, but as foreign companies receive financing usually from their home countries, the economic recession of the host country does not have significant effect for FDI decision, according to this study