A Modified Weighted Sum Method Based on the Decision-
maker’s Preferred Levels of Performances
Dragisa STANUJKIC1,*, Edmundas Kazimieras ZAVADSKAS2
1 Faculty of Management Zajecar, Megatrend University Belgrade,
Park Suma “Kraljevica” bb, 19000 Zajecar, Serbia
2 Research Institute of Smart Building Technologies,
Vilnius Gediminas, Technical University,
Sauletekio al. 11, 10223, Vilnius, Lithuania
* Corresponding author
Abstract: This paper proposes a modified version of the Weighted Sum method that takes into account decision-maker preferences and provides a possibility of higher interactivity in the selection of the most suitable alternative. The proposed approach uses a specific normalization procedure, which takes into account decision-maker preferences and also introduces a compensation coefficient that enables the decision-maker to make choices between alternatives with higher overall performance ratings and alternatives that better match the decision-maker preferences.
Keywords: MCDM, Multiple Criteria Decision Making, preferred performance ratings, Weighted Sum Method, normalization procedures, ideal point approach.
CITE THIS PAPER AS:
Dragisa STANUJKIC, Edmundas Kazimieras ZAVADSKAS, A Modified Weighted Sum Method Based on the Decision-maker’s Preferred Levels of Performances, Studies in Informatics and Control, ISSN 1220-1766, vol. 24 (4), pp. 461-470, 2015.
Multiple Criteria Decision Making (MCDM) is one of the most important and the fastest growing subfields of the management science. As a result of its rapid development, many MCDM methods have also been proposed, such as: SAW [1, 2] or WS , AHP , TOPSIS , PROMETHEE , ELECTRE , COPRAS  and VIKOR .
In order to ensure their usage for solving various complex decision-making problems, these methods are often adapted or extended to apply fuzzy or grey numbers. For example, the ELECTRE method has several variants, namely ELECTRE I, ELECTRE II, ELECTRE III, ELECTRE TRE and ELCTRE IV [10, 11].
In addition, the introduction and the usage of new MCDM methods, such as ARAS , MULTIMOORA  and WASPAS [14, 15], as well as their extensions, are also noticeable.
The proposed MCDM methods are used to solve a wide variety of decision-making problems, such as: evaluation of environmental impact , selecting software and hardware infrastructure for cyber security centre , evaluating performances of a fish farm , selecting a contractor [15, 19].
A great number of papers considered the use of different MCDM methods for solving decision-making problems, such as [19, 20, 21].
The Weighted Sum (WS) method, more often referred to as the Simple Additive Weighted (SAW) method, is probably the best-known and the earlier, widely used, MADM method [5, 14].
Although the use of the WS method is significantly substituted by other MCMD methods, it is still topical, as has been evidenced in some recent researches, such as the following ones: Chou et all.  used the fuzzy SAW for solving the facility location selection problem; Zavadskas et al.  applied grey extensions of the SAW and the TOPSIS methods for solving the contractor selection problem; Rădulescu and Rahoveanu  used framework based on SAW and AHP method for evaluating performances of a fish farm; Cheng  conducted a comparative study about the use of interval-valued fuzzy extensions of the SAW and the TOPSIS methods and noticed that significant similarities existed between the interval-valued fuzzy SAW and TOPSIS rankings; Rikhtegar et al.  used fuzzy SAW to evaluate environmental impacts of construction projects; Dogan et al.  combined the SAW method and a mixture design to determine the optimum cocoa combination of hot chocolate beverage; Wang  applied a fuzzy extension of the SAW method for solving the distribution centre location selection problem, and Stejskal et al.  used the WS method to evaluate the effects arising from the existence of the regional innovation system of the regions of the Czech Republic.
Based on the WS method and the new normalization procedure, Stanujkic et al.  suggested an approach that to a greater extent takes into account decision-maker preferences. In the above mentioned approach for each criterion, target levels of performances, called preferred performance ratings, were introduced. The aim of the decision maker is to obtain a range of alternatives that takes into account the preferred performance ratings.
In this paper, this approach is further improved, thus providing decision-makers with a possibility of higher interactivity in the selection of the most suitable alternative. The rest of this paper is, therefore, structured as follows: In Section 2 of the paper, the Weighted Sum method is presented, while in Section 3, the normalization procedure based on distances from decision-maker’s preferences is considered. Section 4 proposes a new approach. An illustrative example is discussed, with the aim to explain the proposed approach, in Section 5. Finally, the conclusions are given.
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