New directions in Stochastic Multicriteria Acceptability Analysis

Decisions taken in modern organizations are often multi-dimensional, involving multiple decision makers and several criteria measured on different scales. Multiple Criteria Decision Making (MCDM) methods are designed to analyze and to give recommendations in this kind of situations. Among the numerous MCDM methods, two large families of methods are the multi-attribute utility theory based methods and the outranking methods. Traditionally both method families require exact values for technical parameters and criteria measurements, as well as for preferences expressed as weights. Often it is hard, if not impossible, to obtain exact values. Stochastic Multicriteria Acceptability Analysis (SMAA) is a family of methods designed to help in this type of situations where exact values are not available. Different variants of SMAA allow handling all types of MCDM problems. They support defining the model through uncertain, imprecise, or completely missing values. The methods are based on simulation that is applied to obtain descriptive indices characterizing the problem. In this thesis we present new advances in the SMAA methodology. We present and analyze algorithms for the SMAA-2 method and its extension to handle ordinal preferences. We then present an application of SMAA-2 to an area where MCDM models have not been applied before: planning elevator groups for high-rise buildings. Following this, we introduce two new methods to the family: SMAA-TRI that extends ELECTRE TRI for sorting problems with uncertain parameter values, and SMAA-III that extends ELECTRE III in a similar way. An efficient software implementing these two methods has been developed in conjunction with this work, and is briefly presented in this thesis. The thesis is closed with a comprehensive survey of SMAA methodology including a definition of a unified framework.

Spatial multicriteria decision analysis for the siting of on-shore wind power in Kemiönsaari

Wind power is a low-carbon energy production form that reduces the dependence of society on fossil fuels. Finland has adopted wind energy production into its climate change mitigation policy, and that has lead to changes in legislation, guidelines, regional wind power areas allocation and establishing a feed-in tariff. Wind power production has indeed boosted in Finland after two decades of relatively slow growth, for instance from 2010 to 2011 wind energy production increased with 64 %, but there is still a long way to the national goal of 6 TWh by 2020. This thesis introduces a GIS-based decision-support methodology for the preliminary identification of suitable areas for wind energy production including estimation of their level of risk. The goal of this study was to define the least risky places for wind energy development within Kemiönsaari municipality in Southwest Finland. Spatial multicriteria decision analysis (SMCDA) has been used for searching suitable wind power areas along with many other location-allocation problems. SMCDA scrutinizes complex ill-structured decision problems in GIS environment using constraints and evaluation criteria, which are aggregated using weighted linear combination (WLC). Weights for the evaluation criteria were acquired using analytic hierarchy process (AHP) with nine expert interviews. Subsequently, feasible alternatives were ranked in order to provide a recommendation and finally, a sensitivity analysis was conducted for the determination of recommendation robustness. The first study aim was to scrutinize the suitability and necessity of existing data for this SMCDA study. Most of the available data sets were of sufficient resolution and quality. Input data necessity was evaluated qualitatively for each data set based on e.g. constraint coverage and attribute weights. Attribute quality was estimated mainly qualitatively by attribute comprehensiveness, operationality, measurability, completeness, decomposability, minimality and redundancy. The most significant quality issue was redundancy as interdependencies are not tolerated by WLC and AHP does not include measures to detect them. The third aim was to define the least risky areas for wind power development within the study area. The two highest ranking areas were Nordanå-Lövböle and Påvalsby followed by Helgeboda, Degerdal, Pungböle, Björkboda, and Östanå-Labböle. The fourth aim was to assess the recommendation reliability, and the top-ranking two areas proved robust whereas the other ones were more sensitive.

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.