Group Decision Making with Dispersion in the Analytic Hierarchy Process

With group judgments in the context of the Analytic Hierarchy Process (AHP) one would hope for broad consensus among the decision makers. However, in practice this will not always be the case, and significant dispersion may exist among the judgments. Too much dispersion violates the principle of Pareto Optimality at the comparison level and/or matrix level, and if this happens, then the group may be homogenous in some comparisons and heterogeneous in others. The question then arises as to what would be an appropriate aggregation scheme when a consensus cannot be reached and the decision makers are either unwilling or unable to revise their judgments. In particular, the traditional aggregation via the geometric mean has been shown to be inappropriate in such situations. In this paper, we propose a new method for aggregating judgments when the raw geometric mean cannot be used. Our work is motivated by a supply chain problem of managing spare parts in the nuclear power generation sector and can be applied whenever the AHP is used with judgments from multiple decision makers. The method makes use of principal components analysis (PCA) to combine the judgments into one aggregated value for each pairwise comparison. We show that this approach is equivalent to using a weighted geometric mean with the weights obtained from the PCA.     

平衡记分卡与层次分析法

平衡记分卡是一种有效的企业绩效测评方法 ,它采用了内部测评的视角 ,有助于联系企业战略和短期行为。在引入了数学模型层次分析法后 ,不仅成功解决了各绩效测评指标的权重确定问题 ,而且也使平衡记分卡成为了一个决策工具     

Using the Analytic Hierarchy Process as a Two-phase Integrated Decision Approach for Large Nominal Groups

When decision makers who comprise a large nominal group face an unstructured decision problem and no simultaneous interactive communications are available, problem identification and consensus building are difficult, if not impossible. Few tools are available to assist decision makers in this situation. The Analytic Hierarchy Process (AHP) has typically been used to evaluate a set of alternatives after a decision problem has been structured as a hierarchy with various levels of criteria above the alternatives. With a group of decision makers, AHP has been used to evaluate those alternatives either by consensus building or by combining judgments or priorities using the geometric mean to aggregate their preferences. In this paper, we extend the use of AHP to a situation involving a large nominal group of dispersed decision makers where the entire hierarchy is not defined at the outset. In particular, we use the AHP as an integrative approach to identify the priorities of the various criteria and then use those priorities to screen and consolidate a large set of potential alternatives. This results in considering a reduced set of alternatives that will be affected by the more important criteria. The consolidated set of alternatives is evaluated by each individual in the group using AHP, combined using the geometric mean, and the results are synthesized to obtain the overall priorities of the alternatives. The approach is demonstrated and evaluated in a case study to select an alunmi anniversary gift to the U.S. Coast Guard Academy with a large nominal group of decision-makers dispersed throughout the United States.     

A Study on Aggregation of TOPSIS Ideal Solutions for Group Decision-Making

The technique for order preference by similarity to ideal solution (TOPSIS) has become a popular multi-criteria decision making (MCDM) technique, since it has a comprehensible theoretical structure and is able to provide an exact model for decision making. For the use of TOPSIS in group decisions, the common approaches in aggregating individual decision makers’ judgments are the geometric and the arithmetic mean methods, although these are too intuitive and do not consider either preference levels or preference priorities among alternatives for individual decision makers. In this paper, a TOPSIS group decision aggregation model is proposed in which the construction consists of three stages: (1) The weight differences are calculated first as the degrees of preferences among different alternatives for each decision maker; (2) The alternative priorities are then derived, and the highest one can be denoted as the degree to which a decision maker wants his most favorite alternative to be chosen; (3) The group ideal solutions approach in TOPSIS is used for the aggregation of similarities obtained from different decision makers. A comparative analysis is performed, and the proposed aggregation model seems to be more satisfactory than the traditional aggregation model for solving compromise-oriented decision problems.     

A Calibrated Group Decision Process

In practice most organisational decisions are made by groups that bring into the problem multiple perspectives, both complementary and contradictory. When having a group of decision makers, usually individuals’ preferences are either led to consensus or are aggregated with the use of some function like the median, the arithmetic or geometric mean. We focus in the second case, where individual’s preferences need to be aggregated. Our approach is based on the fact that when two decision makers are asked to give their preference between a pair of criteria using a specific scale, it is possible that they will give slightly different answers, even when they actually have the same opinion. This difference will not affect the case of a single decision maker, as it will be consistent throughout the whole process. However, it can affect a group decision when the values will be used as an input for the aggregation function. A novel approach is presented that enhances group decision making through a group calibration process. The proposed process adjusts individuals’ preferences based on their answers on a set of standardized questions prior to the aggregation phase. The method focuses The whole concept is applied to the group analytical network process method and it is illustrated through a telecommunications project case. The decision under examination concerns the selection of the right place for deploying a new telecom service of a multinational-based telecommunications company where a group of geographically dispersed decision makers form an ad-hoc virtual team in order to select the location for a new technical support centre.     

A New Linear Programming Method for Weights Generation and Group Decision Making in the Analytic Hierarchy Process

This paper proposes a new linear programming method entitled by LP-GW-AHP for weights generation in analytic hierarchy process (AHP) which employs concepts from data envelopment analysis. We propose four specially constructed linear programming (LP) models which are used to derive weight vector from a pair-wise comparison matrix or a group of them. We can use both interval and relative importance weights for each decision maker in LP-GW-AHP. In this method, solving only one LP model is enough for local weights derivation from pair-wise comparison matrices. Five numerical examples are examined to illustrate the potential applications of the LP-GW-AHP method. We show that not only derived weights of the new method have slight differences than Saaty’s eigenvector weights but sometimes they are better than eigenvector method weights in the fitting performance index as well. LP-GW-AHP is compared with a method which has been recently proposed for the weights derivation in the group AHP and it becomes obvious that LP-GW-AHP provides better weights. The simple additive weighting method is utilized to aggregate local weights without the need to normalize them.     

基于层次分析法的配送中心选址模糊综合研究述评

针对配送中心的选址评价具有层次性和模糊性的特点,本文对已有成果进行综述并引入改进的AHP(Analytic Hierarchy Process,层次分析法)方法确定评价指标的权重。在此基础上建立配送中心优化选址指标体系,进行两级模糊综合评价。     

An Application of the Analytical Hierarchy Process to International Marketing: Selection of a Foreign Distributor

Foreign distributors are often used by small and medium-sized firms for establishing an initial presence in overseas markets. While various selection criteria for foreign distributors have been noted in the international marketing literature, they are often subjective and judgemental in nature. In addition, the large number of variables as well as the consideration of both objective and subjective criteria suggest that a method which has the ability to quantify and synthesize both objective and subjective criteria is preferred. The recommended approach is the Analytical Hierachy Process (AHP). In this paper, the characteristics of the AHP are discussed and illustrated within the context of the foreign distribution selection process. For many small and medium-sized firms which lack sophisticated market research/decision analysis tools to assist them in the foreign distributor decision, the AHP is a highly flexible and versatile substitute.     

Information Technology Support for Corporate Bank Lending

Decision-making in corporate bank lending occurs at both strategic and individual proposition levels. In principle, these levels will require a different type of IT support for the decisions taken therein. This article discusses the concepts of decision support systems and management information systems, in the light of recent developments in information technology, particularly those in the field of expert systems. The conclusions drawn are that a decision support system will be needed at the strategic level, while an augmented management information system will be required for dealing with individual propositions. This augmentation is seen to come from an expert system front-end’ to the information system, providing an expert management information system.     

The Effect of a Quantitative Decision Aid – Analytic Hierarchy Process – on Group Polarization

The objective of this paper is to examine group polarization in subjects who have access to a quantitative decision aid, comparing to subjects who do not. Group polarization indicates the opinion of a group involved in a decision process will tend to be more extreme in the direction of the norm than the initial opinions of its members. Most of previous studies were focused on the theoretical explanation of this effect. Two theories are generally proposed to explain it: social comparison (SC) and persuasive arguments (PA). As we know, no study has been worked on how it can be dealt with. In this study, we use Analytic Hierarchy Process (AHP) as a quantitative decision aid in a group process to examine the changes of this effect. Two hundred and forty undergraduate students participated in this study. Results show that persuasive argument was significantly reduced by the use of AHP, while no significant effect was found in group polarization and social comparison. The implications of the findings are further discussed.     

群体层次分析法的一种权重求解方法

针对群体层次分析法的权重计算问题,采用对数回归法求解。分析线性方程组,得到其系数矩阵的秩小于矩阵行数。通过修改系数矩阵的最后一行,使其为满秩,从而保证了解的唯一性。同时给出了稳定快速的基于LU分解的算法实现步骤。     

Aggregation of Individual Preference Structures in Ahp-Group Decision Making

This paper presents a new procedure, to which we have given the name Aggregation of Individual Preference Structures (AIPS), whose objective is to deal with multiactor decision making when using Analytic Hierarchy Process (AHP) as the methodological support. This procedure incorporates ideas similar to Borda count methods and transfers to the case of preference structures the principle of aggregation employed in the two approaches traditionally followed in AHP-group decision making (aggregation of individual judgments and aggregation of individual priorities). The new aggregation method allows us to capture: (i) the richness of uncertainty inherent to human beings; (ii) the vision of each decision maker within the context of the problem; (iii) the interdependencies between the alternatives being compared and (iv) the intensities of the preferences that each decision maker gives to these interdependencies. From the preference structure distribution associated to each decision maker, this new approach (AIPS) provides the holistic importance of each alternative and ranking, as well as the most representative preference structure distribution for the group. The knowledge derived from these could be employed as an initial step in the search for consensus, which characterises the negotiation processes followed by the actors involved in the resolution of decisional problems. An earlier version of this paper was presented at the GDN2005 Conference held at Vienna. The work has been partially funded under Research Projects “Electronic Government. Internet-based Complex Decision Making: e-democracy and e-cognocracy” (Ref. PM2004-052) and “Internet-based Complex Decision Making. Decisional Tools for e-cognocracy” (Ref. TSI2005-02511).     

Using fuzzy AHP and VIKOR for benchmarking analysis in the hotel industry

The present study is believed to be the first to apply the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) methodology to perform a benchmarking analysis in the hotel industry. This study used VIKOR to measure the performance of 26 international hotels to identify the benchmarking enterprise and to analyse strategies for performing a benchmark. During the calculation procedure, the fuzzy analytic hierarchy process (AHP) was applied to calculate the weights of the individual performance criteria using expert feedback. The findings suggest that the VIKOR technique integrating fuzzy AHP can be utilized to overcome the small shortcomings of stochastic frontier analysis and data envelopment analysis and that the technique is a feasible tool for benchmarking analysis.     

层次分析法在技术创新风险评估中的应用

在进行有效的技术创新风险评价之前,非常重要的一个环节就是每一层风险指标相对权重的确定,本文采用了层次分析法(AHP法)来确定风险指标权数(w).它将一个复杂的多指标评价问题作为一个系统,将总目标分解为多个分目标或准则,进而分解为多指标的若干层次,通过定性指标模糊量化方法算出层次单排序和总排序,以此确定多目标、多方案优化决策问题中各个指标的权重.     

Does management accounting play role in planning process?

This study examines the relationship between management accounting and planning profiles in Brazilian companies. The main goal is to understand the consequences of not including a fully structured management accounting scheme in the planning process. The authors conducted a field research among medium and large-sized companies, using a probabilistic sample from a population of 2281 companies. Using analytic hierarchy process (AHP) and statistical cluster analysis, the authors grouped the entities' strategic budget planning processes into five profiles, after which the authors applied statistical tests to assess the five clusters. The study concludes that poor or fully implemented strategic and budget-planning processes relate to the management accounting profiles of the Brazilian organizations studied.     

A Note on Linguistic Hybrid Arithmetic Averaging Operator in Multiple Attribute Group Decision Making with Linguistic Information

In this paper, we propose a linguistic hybrid arithmetic averaging (LHAA) operator, which is based on linguistic weighted arithmetic averaging (LWAA) operator and extended ordered weighted averaging (EOWA) operator, and study some desirable properties of the LHAA operator. The LHAA operator can not only reflect the importance degrees of both the given argument and its ordered position, but also relieve the influence of unfair arguments on the decision results by weighting these arguments with small values. Based on the LWAA and LHAA operators, we develop a practical approach to multiple attribute group decision making under linguistic environment. The approach first aggregates the individual linguistic preference values into a collective linguistic preference value for each alternative by using the LWAA and LHAA operators (it is worth pointing out that the aggregation process does not produce any loss of linguistic information), and then orders the collective linguistic preference values to obtain the best alternative(s). Finally, an illustrative example is also given to verify the approach and to demonstrate its feasibility and practicality.     

Minimizing Group Discordance Optimization Model for Deriving Expert Weights

This paper focuses on the problem of how to determine expert weights in multiple attribute group decision making. We first aggregate all the individual decision matrices into the collective decision matrix by means of the weighted arithmetic averaging operator, and then from the angle of minimizing group discordance, we establish a general nonlinear optimization model based on deviation function, and employ a genetic algorithm to solve our model so as to find the optimal expert weights. Moreover, we extend our model to uncertain multiple attribute group decision making, where the attribute values are interval numbers, and finally, apply our model to the plan evaluation of new model of cars of an investment company.     

Non-numeric multi-criteria multi-person decision making

We describe a decision making technique, ME-MCDM, for the evaluation and selection of alternatives using a non-numeric scale. Using this procedure each alternative is evaluated by an expert for satisfaction to a multi-criteria selection function. Each criterion can have a different degree of importance. The individual expert evaluations can then be aggregated to obtain an overall evaluation function. We apply this technique to the problem of proposal selection in the funding environment. In this environment the technique is augmented by some textual information which can also be used to help in the decision process.     

Information Collection Strategic Design in Experts-assisted Decision Making Paradigm

In an experts-assisted decision making paradigm, the information collection design becomes a strategic variable under a weak assumption that the final decision is dependent on the design used to collect information as well. As a result, the same information of the experts and the decision maker about the problem can potentially produce different final decisions for different information collection designs. The implication is that a decision maker can strategically select a design which serves his/her objective. This paper uses a Bayesian estimation methodology for combining experts' information with the decision maker's prior. An information collection process is designed by setting constraints on this model. Several designs are developed here using such controlled factors as a one-stage versus a two-stage decision process, experts' rank ordering, and group versus individual lobbying/consultation. An example is provided to illustrate the applicability of the concept. It is shown that the information produced in the process of producing a decision can also give insights into the impacts of the decision maker and the experts on the decision.     

The Role of the DS/AHP in Identifying Inter-Group Alliances and Majority Rule Within Group Decision Making

DS/AHP is a nascent method of multi-criteria decision-making, based on the Dempster-Shafer theory of evidence and indirectly the Analytic Hierarchy Process. It is concerned with the identification of the levels of preference that decision makers have towards certain decision alternatives (DAs), through preference judgements made over a number of different criteria. The working result from a DS/AHP analysis is the body of evidence (BOE), which includes a series of mass values that represent the exact beliefs in the best DA(s) existing within certain subsets of DAs. This paper considers the role of DS/AHP as an aid to group decision-making, through the utilisation of a distance measure (between BOEs). Here, the distance measure enables the identification of the members of the decision-making group who are in most agreement, with respect to the judgements they have individually made. The utilisation of a single linkage dendrite approach to clustering elucidates an appropriate order to the aggregation of the judgements of the group members. This develops the DS/AHP method as a tool to identify inter-group alliances, as well as introduce a ‘majority rule’ approach to decision-making through consensus building.