Standalone GUI Application for Game Theory Optimization Problem - Cerman, Otto (2013)
Occasionally, a part of the budget of a city, company or other entity has to be allocated among its parts in the form of subsidies or other contributions. The main objective of such an entity is to find such a set of criteria and such a set of their relative weights that estimate the expected cost best. The objective of a sub-entity is subsidy maximization by influencing the criteria and their weights. From this reason, the best budget splitting is a relative term. From the mathematical point of view, such a problem belongs to mathematical optimization or mathematical programming. In this thesis, five quantitative methods are presented. Two of them set the weights without the participation of decision makers. The first allocation method is based on multiple-criteria decision-making and the second one on data envelopment analysis. Together with them, a different mathematical model with maximum and minimum weights for the set of criteria is presented. Two its modifications are discussed too. As the only one presented multi-criteria mathematical model is based on maximization of the relative and absolute profit simultaneously. The aim of this work is to study the known mathematical models for subsidy allocation problem, to invent new ones, to choose suitable ones and subsequently to implement the suitable ones into a standalone GUI application created in the Matlab environment. The presented application proposes several allocation possibilities according to different selected models using mathematical functions taken from Matlab. This user-friendly application is executable on common computers and can be used at the Magistrate of the City of Prague as a support tool in voting decision. Moreover, this application can be extended to new methods or program functions. The selected quantitative methods are used for the budget allocation problem among the city districts for real data of the City of Prague. Experimental results are discussed.