On Saaty's and Koczkodaj's inconsistencies of pairwise comparison matrices

The aim of the paper is to obtain some theoretical and numerical properties of Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices (PRM). In the case of 3 × 3 PRM, a differentiable one-to-one correspondence is given between Saaty’s inconsistency ratio and Koczkodaj’s inconsistency index based on the elements of PRM. In order to make a comparison of Saaty’s and Koczkodaj’s inconsistencies for 4 × 4 pairwise comparison matrices, the average value of the maximal eigenvalues of randomly generated n × n PRM is formulated, the elements aij (i < j) of which were randomly chosen from the ratio scale ... ... with equal probability 1/(2M − 1) and a ji is defined as 1/a ij . By statistical analysis, the empirical distributions of the maximal eigenvalues of the PRM depending on the dimension number are obtained. As the dimension number increases, the shape of distributions gets similar to that of the normal ones. Finally, the inconsistency of asymmetry is dealt with, showing a different type of inconsistency

The state of the art development of AHP (1979-2017): A literature review with a social network analysis

Although many papers describe the evolution of the analytic hierarchy process (AHP), most adopt a subjective approach. This paper examines the pattern of development of the AHP research field using social network analysis and scientometrics, and identifies its intellectual structure. The objectives are: (i) to trace the pattern of development of AHP research; (ii) to identify the patterns of collaboration among authors; (iii) to identify the most important papers underpinning the development of AHP; and (iv) to discover recent areas of interest. We analyse two types of networks: social networks, that is, co-authorship networks, and cognitive mapping or the network of disciplines affected by AHP. Our analyses are based on 8441 papers published between 1979 and 2017, retrieved from the ISI Web of Science database. To provide a longitudinal perspective on the pattern of evolution of AHP, we analyse these two types of networks during the three periods 1979?1990, 1991?2001 and 2002?2017. We provide some basic statistics on AHP journals and researchers, review the main topics and applications of integrated AHPs and provide direction for future research by highlighting some open questions

Determining the items that structure bridge management components and their relative weights

2012 Spring.Includes bibliographical references.Ensuring the optimal allocation of available resources between competing bridges is difficult, especially when considering a combination of factors such as continual age related deterioration, ever-increasing traffic demands, and limited resources to address preservation and improvement needs. Optimally allocating funding is crucial since bridges are an essential and expensive component of transportation networks. Bridge Management Systems (BMSs) are commonly used tools that aid managers and decision makers in establishing methods for optimizing available resources and determining how to distribute funds between competing bridges. Recently, NCHRP Synthesis 397 Bridge Management Systems for Transportation Agency Decision Making investigated how transportation agencies are using BMSs and the current state of bridge management practices. The report identified concerns of inadequacy and ineffectiveness with bridge management practices that base decisions solely on single value assessments such as Pontis' Bridge Health Index or the Sufficiency Rating, as found in the federally mandated National Bridge Inspection Standards. Given the critiques in the NCHRP report and other literature related to bridge management, it is evident there exists a need to pursue and develop alternative bridge management practices and systems. The overall purpose of this research is to investigate the concept of isolating the items used to make up a single rating or index in an effort to categorize them under distinct bridge management components such as structural condition, impact on public, and hazard resistance. Each bridge management component has a defined objective as follows: • Structural Condition - accurately access the structural adequacy of a bridge. • Impact on Public - evaluate how bridge attributes affect the traveling public. • Hazard Resistance - evaluate how bridge attributes and external factors affect the vulnerability of a bridge concerning the probability of an extreme event as well as the probability of failure during that event. The specific objectives of this research are (i) to identify the appropriate items that make up each of the aforementioned components and (ii) to determine the relative importance of those items as represented by weighting factors. To achieve these objectives, the researcher conducted a two-part survey seeking input from key bridge management personnel from State DOTs, the Federal Highway Administration (FHWA), and other industry professionals and experts. The first part of the survey identified the appropriate items and the second part determined the relative importance of those items using a mathematical method called the Analytic Hierarchy Process (AHP). The primary contribution of this research is to provide bridge management engineers and decision-makers with effective bridge management components, with well-defined objectives and related items, which clearly identify and distinguish differences in bridge attributes that may go unnoticed when using a single rating or index. This will especially be useful for State DOTs and local agencies, like the Wyoming Department of Transportation, from which the motivation for this research was adapted, who are developing BMSs and methods customized to their particular needs. Upon establishing the bridge management components, by determining the items that make up the components and their relative weights, transportation agencies may utilize them in a variety of ways to conduct multi-criteria decision analyses that complement their current bridge management practices, which in turn may better illustrate the operation of bridges in their system. The total number of respondents was 47, of which 32 were from 29 different State transportation agencies. Of the 47 participants, only 27 contributed to the second part of the survey. A major finding of this research was a result of several participant remarks about with quantifying preservation and maintenance demands through the addition of a fourth bridge management component. The preservation and maintenance component encompasses items that are bridge elements, but may not contribute to the structural capacity of a bridge. Given the degree of influence of adding a fourth component, further research is recommend to confirm these findings and conclusions with a refined two-part survey similar to this research study and possibly interviews or focus groups

A social and environmental approach to microfinance credit scoring

Microfinance institutions provide loans to low-income individuals. Their credit scoring systems, if they exist, are strictly financial. Although many institutions consider the social and environmental impact of their loans, they do not incorporate formal systems to estimate these social and environmental impacts. This paper proposes that their creditworthiness evaluations should be coherent with their social mission and, accordingly, should estimate the social and environmental impact of microcredit. Thus, a decision support system to facilitate microcredit granting is proposed using a multicriteria evaluation. The assessment of social impact is performed by calculating the Social Net Present Value. The system captures credit officers'' experience and addresses incomplete and intangible information. The model has been tested in a microfinance institution. The paper shows how a small institution can include social and environmental issues in its decision-making systems to evaluate credit applications. A gap in the preferences was found between members of the board, who are socially driven, and managers and credit officers, who are financially drifted. This mission drift was corrected. The approach followed contributed to creating a culture of social and environmental assessment within the institution, especially among credit officers, thereby translating Microfinance institutions'' social mission into numbers

The state of the art development of AHP (1979-2017): a literature review with a social network analysis

Although many papers describe the evolution of the analytic hierarchy process (AHP), most adopt a subjective approach. This paper examines the pattern of development of the AHP research field using social network analysis and scientometrics, and identifies its intellectual structure. The objectives are: (i) to trace the pattern of development of AHP research; (ii) to identify the patterns of collaboration among authors; (iii) to identify the most important papers underpinning the development of AHP; and (iv) to discover recent areas of interest. We analyse two types of networks: social networks, that is, co-authorship networks, and cognitive mapping or the network of disciplines affected by AHP. Our analyses are based on 8441 papers published between 1979 and 2017, retrieved from the ISI Web of Science database. To provide a longitudinal perspective on the pattern of evolution of AHP, we analyse these two types of networks during the three periods 1979–1990, 1991–2001 and 2002–2017. We provide some basic statistics on AHP journals and researchers, review the main topics and applications of integrated AHPs and provide direction for future research by highlighting some open questions

Framework for evaluating water quality information system performance

1994 Fall.Includes bibliographic references (pages 280-308).Water resource and water quality managers are being held increasingly accountable for the programs they manage. Much progress has been made in applying total systems perspectives to the design and operation of water quality monitoring and information programs, and towards rationalizing those programs with respect to management objectives and information needs. A recent example of that progress is the development of data analysis protocols to enhance the information system design process. However, further work is necessary to develop approaches which can help managers confront the water quality management environment of the future, which will be characterized by: (1) fewer purely technical questions, (2) more complex problems with social, economic, political and legal ramifications, and (3) actively managed and continuously improved water quality information systems. This research concludes that the management of water quality information systems for continuous improvement requires: (1) a competent system design process, (2) comprehensive documentation of system design and operation, and (3) a routine and thorough performance measurement and evaluation process. The framework for evaluating water quality information system performance presented in this dissertation integrates the experience of several disciplines into an instrument to help water quality managers accomplish these requirements. The framework embodies four phases: (1) evaluation planning, (2) watershed and management system analyses, (3) information system analysis, and (4) information system performance evaluation. The application of the framework is demonstrated in the evaluation of water quality monitoring programs associated with a unique municipal water transfer project. Water quality professionals of the U.S. Environmental Protection Agency and the U.S. Geological Survey are surveyed as to its potential application to large (e.g., regional or national) systems. Those exercises indicate the framework to be a convenient, economic, and flexible instrument useful towards enhancing water quality information system performance. Recommendations for future research to refine the framework and to extend its scope and utility are also presented

Parameters of effects in decision making of automotive assembly line using the Analytical Hierarchy Process method

The automotive industry contributes high income to most of the countries. The assembly line is an essential part of the automotive industry because it combines all the components into a complete body unit. Assembly lines often experience delays in meeting production targets, requiring overtime to complete. Musculoskeletal Disorder (MSD) complaints among assembly workers predominantly lie in trimming, chassis, and finishing processes. Improvements are needed to reduce complaints according to the priority process. This study aims to prioritize the process on the assembly line with the parameters of work position, workload, work layout and equipment. This study implements the Analytical Hierarchy Process (AHP) method to achieve the objectives of the decision-making process. Preliminary weighting priorities for chassis, finishing and trimming are 0.6153, 0.2313 and 0.1533; respectively highest weight is in the chassis process and will be a priority for this study in optimizing solutions

Vendor Selection and Supply Quotas Determination by Using the Analytic Hierarchy Process and a New Multi-objective Programming Method

In this article, we propose a new methodology for solving the vendor selection and the supply quotas determination problem. The proposed methodology combines the Analytic Hierarchy Process (AHP) for determining the coefficients of the objective functions and a new multiple objective programming method based on the cooperative game theory for vendor selection and supply quotas determination. The proposed methodology is tested on the problem of flour purchase by a company that manufactures bakery products. For vendor selection and supply quotas determination we use three complex criteria: (1) purchasing costs, (2) product quality, and (3) vendor reliability

Transport policy and climate change: how to decide when experts disagree

Transport is the sector with the fastest growth of greenhouse gases emissions in many countries. Accumulation of these emissions may cause uncertain and irreversible adverse climate change impacts. In this context, we use the analytic hierarchy process (AHP) to face the question on how to select the best transport policy if the experts have different opinions and beliefs on the occurrence of these impacts. Thus, both the treatment of uncertainty and dissent are examined for the ranking of transport policies. The opinions of experts have been investigated by a means of a survey questionnaire. A sensitivity analysis of the experts’ weights and the criteria’ weights confirms the robustness of the results