تعیین توابع سودمندی معیارهای مورد استفاده در ارزیابی املاک و مستغلات

This article presents an application of the UTA method and its variant UTA-CR to determining utility functions for the multicriteria evaluation of residential real estate. Data for the city of Volta Redonda, Brazil, were used in this study. Unlike UTA, UTA-CR makes use of the decision agents’ preferences in relation to a set of criteria to determine a ranking of the alternatives. It was concluded that UTA-CR manages to obtain utility functions closer to the preferences of the decision agents as compared to these that result from the use of UTA. This demonstrates an important advantage of UTA-CR over UTA.

This article deals with obtaining utility functions for criteria used in the evaluation of residential real estate. The UTA method (Jacquet-Lagrèze and Siskos, 1982; Siskos et al., 2004) and its variant UTA-CR (Rangel, 2002) were used in the study related here with the aim of evaluating a selected subset of residential properties which are available for rent in the Municipality of Volta Redonda in the south of the state of Rio de Janeiro, Brazil. In order to be implemented, the UTA method needs an a priori piece of information: the ranking of the alternatives or a subset of these alternatives present in the process. The ranking supplied by the decision agents is used as a restriction of a linear programming problem (LPP), which has its own objective function, the minimizing of the sum of the errors associated with the ranking of each alternative, that is, the value of the global utility of each alternative. The variant of the UTA method called UTA-CR is used in the same way as the original UTA method. This variant seeks to obtain utility functions as close as possible to the decision agents’ preferences. In order to obtain the new utility functions of the criteria it asks the decision agents to express their preferences in relation to the set of criteria, and not in relation to the alternatives as occurs when the original UTA method is used. A multicriteria decision support method of ranking is, thus, used and the ranking of the alternatives which will be used in the implementation of the UTA-CR method is determined, in the same way as when the original UTA method is used. In order to obtain utility functions as close as possible to the decision agents’ preferences a new mathematical model was developed, presenting a new objective function and new restrictions. In the study presented in this article, instead of asking a specialist for a subjective ranking of the properties present in the process to serve as input data in the implementation of the UTA method and its UTA-CR variant, a ranking of the properties obtained by using the TODIM method (Gomes and Lima, 1992; Gomes and Rangel, 2007) was employed. The implementation of the two methods was carried out with the aim of checking the differences between the utility functions obtained by the original UTA method and by its variant UTA-CR. The results of the two implementations are presented and discussed later in this article.

It was confirmed through the example implemented that the two methods present very different values for the utility functions of the six criteria used in this analysis. The criterion C1, for example, presents a weight of 0.187 using the original UTA method, while using the UTA-CR method this value is 0.294. The value determined by the UTA-CR variant is the same as supplied by the decision agent. In all the criteria, the variant of the UTA method presents values close to those supplied by the decision agents. The criterion C3 presents the greatest difference between the two methods: in the UTA method its value was 0.319, while in the UTA-CR method this value reached 0.118, extremely close to the value supplied by the decision agents, which was 0.117. The higher degree of closeness between criteria weights computed by the method and these that were originally estimated from consulting with professionals from the local real estate market validates the use of UTA-CR as compared against UTA. The fact that the solution of the linear programming problem of the UTA method [LPP1] (16) presents a zero value, meaning that the mathematical method succeeded in obtaining the preferences of the decision agents in terms of ranking, might not perfectly represent the preferences of the decision agents, as this solution is not unique, given that a large number of solutions manage to represent the decision agents’ preferences. Meanwhile, the UTA-CR method imposes restrictions to the criteria weights, restricting the search region for optimum solutions. Another important fact is that the objective function of the UTA-CR method [LPP4] (25) seeks to obtain values for the weights of the criteria with the smallest difference possible from the weights provided by the decision agents, whether more or less. The UTA method needs the a priori ranking of the alternatives provided by the decision makers to obtain the utility functions of the criteria. This information is not always precise, and often the mathematical model does not manage to obtain a solution without taking into consideration errors associated with the ranking of the alternatives. In this way, a change in the nature of the information required from the decision agents, from preferences concerning the alternatives to preferences in relation to the criteria, makes the utility functions of the criteria more faithfully represent these functions. Another criticism which can be made of the UTA method is the number of implementations necessary, two for each criterion, carried out in the post-optimization analysis. In addition to this, the average of the values of the variables must be calculated to obtain the utility functions of the criteria. As well as this, the average of the values of the variables must be calculated to obtain the utility functions of the criteria. In the UTA-CR method these values are determined by means of a single implementation, without the need for a post-optimization analysis to determine the values of the variables. The UTA-CR method, as a result of working with the decision agents’ preferences in relation to the set of criteria, and from this point determining a ranking of the alternatives, generally tends to lead to better forms of utility functions to represent the criteria present in the analysis. For the reasons demonstrated in this article, it is considered that the UTA-CR method deserves a place of prominence among the set of analytical methods designed to determine the utility functions of criteria.