A thermodynamical approach towards group multi-criteria decision making (GMCDM) and its application to human resource selection

Highlights

• A new model for group multi-criteria decision making (GMCDM) using thermodynamical indicators.

• TOPSIS used an indicator similar to energy while the current model uses exergy indicator for ranking of alternatives.

• The model incorporates a factor accounting for the quality of the ratings.

• The model is formulated for both crisp and fuzzy environment.

• Two case studies are carried out in human resource selection to demonstrate the application and the effectiveness of the proposed model.

Abstract

In group multi-criteria decision making (GMCDM) problems, ratings are assigned to the alternatives on different criteria by an expert group. In this paper, we propose a thermodynamically consistent model for GMCDM using the analogies for thermodynamical indicators – energy, exergy and entropy. The most commonly used method for analysing GMCDM problem is technique for order of preference by similarity to ideal solution (TOPSIS). The conventional TOPSIS method uses a measure similar to energy for the ranking of alternatives. We demonstrate that the ranking of the alternatives is more meaningful if we use exergy in place of energy. The use of exergy is superior due to the inclusion of a factor accounting for the quality of the ratings by the expert group. The unevenness in the ratings by the experts is measured by entropy. The procedure for the calculation of the thermodynamical indicators is explained in both crisp and fuzzy environments. Finally, the effectiveness of the proposed method is demonstrated by applying to human resource selection problem.

Introduction

Group multi-criteria decision making (GMCDM) is a process used for ranking of alternatives based on different criteria. The applications of GMCDM are numerous and it has been applied to human resource management [1], [2], transportation [3], portfolio optimization [4], product design [5], vendor selection [6], [7], energy efficient network selection [8], robot selection [9] and visual inspection [10].

Different methods have been used in the past to solve the complex MCDM problems. Multi-attribute utility theory (MAUT) [11], [12] was one among the first few methods developed for solving the MCDM problems. MAUT involves the representation of the preferences by means of a utility function to every possible consequence. MAUT takes into account the uncertainty and the preferences of the decision maker. However, its application requires extensive input at every step. On the similar lines of MAUT, analytic hierarchy process (AHP) [13] was developed. AHP uses pairwise comparison to estimate the criteria weights and also to compare the alternatives with respect to various criteria. Some of the advantages of AHP includes the ease of use, scalability and lesser data requirement compared to MAUT. AHP does not take into account the interdependence between the criteria and the alternatives. Pairwise comparisons in AHP lead to inconsistencies in judgement and rank reversal. AHP was later extended to analytic network process (ANP) [14] which is a nonlinear form of AHP, mostly suited for problems with network structure. ANP allows for the prioritization of the groups and handles interdependence of the alternatives better compared to AHP. However, ANP also ignores the interdependence among the groups. The ability of fuzzy set theory to deal with the imprecise and uncertain data has been utilized extensively by many researchers in MCDM [15], [16], [17], [18], [19], [20], [21]. Most of these methods were based on pairwise comparison. Fuzzy theory has also been used to develop consensus models in MCDM [22], [23], [24], [25], [26], [27]. Various mathematical programming models have also been developed for MCDM in which the multiple and conflicting objective functions are optimized over a feasible set of decisions. An optimization problem is then solved to find the feasible alternative. Data envelopment analysis (DEA) uses linear programming technique to calculate the relative efficiencies of the alternatives [28], [29], [30]. The disadvantage of DEA is that it cannot handle imprecise data and it assumes that all inputs and outputs are exactly known. Among mathematical programming models, goal programming is considered as one of the most effective methods for solving MCDM problems as they are able to handle large scale problems [31]. Outranking methods is another class of methods which have been widely used for. Outranking methods calculate the degree of dominance of one alternative over the other. These methods use outranking relations for modelling the decision maker's preferences. Two most commonly used outranking methods are ELimination Et Choix Traduisant la REalit (ELECTRE) (ELimination and Choice Expressing REality) [32], [33] and Preference Ranking Organization METHod for Enrichment Evaluations (PROMETHEE) [34]. The outranking methods have been popular for many decades because of their ease of use. Another method which has been quite popular for MCDM analysis is technique for order of preference by similarity to ideal solution (TOPSIS). The advantages of TOPSIS include [1] – scalar value accounting for both best and worst alternative; logical representation of human rationale and easy implementation. TOPSIS is based upon the concept that the chosen solution should be closest to positive ideal solution and farthest from negative ideal solution.

The motivation for the present study comes from the application of thermodynamics for bibliometric assessment by [35] who used the analogies of the energy, exergy and entropy associated with a bibliometric sequence to derive an indicator of scientist's performance. In the present study, we propose a model for GMCDM based on a novel approach within the paradigm of thermodynamics. We define analogies for thermodynamical indicators – energy, exergy and entropy with respect to GMCDM. It should be noted that the entropy defined in the present study is different from Shannon's entropy [36] which assumes a prior distribution. A natural definition of entropy derived from the first principles is used in the present study. It is observed that the conventional TOPSIS method uses a measure similar to what we define as energy indicator. We propose and also demonstrate, with the help of examples, that it is exergy indicator which makes better sense in the ranking of an alternative rather than energy indicator. The proposed model is quite simple to implement and is thermodynamically consistent. The proposed model is formulated for both crisp and fuzzy environments. The effectiveness of the proposed model is demonstrated by applying to human resource selection problem in both crisp and fuzzy environments.

The organization of the paper is as follows. The second section defines the preliminaries towards thermodynamics. In the third section, we define analogies for the energy, exergy and entropy in both crisp and fuzzy environments. The fourth section describes why using exergy indicator makes more sense than using an indicator based on energy. Fifth section lists out the procedure for GMCDM using thermodynamical indicators. In the sixth section, the method is applied to human resource selection. The results obtained from the proposed method are compared with those obtained from extended and fuzzy TOPSIS. The seventh section discusses the results obtained from the proposed method. The final section presents the conclusions drawn from the present study.