Modeling and simulation in decision making under uncertainty

Abstract

The habilitation thesis is devoted to modeling and simulation in the decision making process. It deals with normative decision theory and emphasizes the role of modeling and simulations in the process of decision making in the presence of uncertainty. The presence of uncertainty in the contemporary practice of decision making is inevitable. One of the most important tasks facing the decision maker is to carry out an analysis of how the uncertainty connected with the input factor is propagated through the model to give uncertainty about the outputs. It is a problem of fundamental importance. However, in many realistic and practically important cases formal analysis of the uncertainty propagation is impossible because of the sophisticated probabilistic structure of the input-output relationship. In this thesis it is argued that in such situations the computer simulation is an irreplaceable research tool. In that context four important areas of contemporary decision making are examined in more details: the regression analysis, the optimal stopping theory, the multicriteria decision analysis and the stochastic programming. In the area of regression analysis various models of uncertainty of the prior information about the regression parameter are investigated. Based on computer simulation certain indices of uncertainty are introduced as well as related methods of incorporating prior information into regression analysis. In the area of optimal stopping the computer simulation is used to develop models relating the input factors with some characteristics of the risk connected with optimal stopping rules. In the area of multicriteria decision analysis the problem of priorizaion method selection is considered in detail. A new simulation framework to compare the existing methods for modeling the priorities is proposed. Based on the simulation experiments results new technique for deriving priority weights is proposed as well as a new approach to pairwise comparison matrices acceptance. Finally, the simulation studies are adopted for selection of the best possible meta-heuristic algorithm that can be used as a tool for solving chance constrained programming problems. As a whole, the thesis demonstrates the benefits resulting from decision making based on mathematical modeling combined with computer simulation. It is shown here that it is especially profitable in the following aspects of decision making practice: construction of decision rules, selection of optimal decision rule, analysis of the effects arising from the use of a given decision rule and analysis of the risk associated with the use of a given decision rule.