This paper examines consumer preferences and choice behavior in purchasing organic food products. Two studies investigate the role of organic food attributes in the consumer purchase decision and find the relative ranking of the attributes. Study I from 351 survey respondents in MTurk recognizes nine attributes for organic food purchase decisions. Study II surveys 298 MTurk participants to apply paired-choice analysis that reveals the relative preferences for attributes of organic food purchases on a ratio scale. Robustness and sensitivity analysis reveal the presence of a multi-segment organic food market. Segmentation analysis on the paired comparisons' results and validation on the clusters reveals three consumer segments: health-conscious, quality-conscious, and value-conscious. Notably, switching from organic to traditional foods is most likely from the value-conscious segment, whereas loyal behavior towards retailers can be expected from quality-conscious consumers.

Between the numerator and denominator, there is a fine line.Only a fraction appreciates the distinction of what is above or below that line.The denominator and the "of what" is the unit in a pairwise comparison and in priority vectors.Pairwise comparisons provide the unit conversions between the elements being compared.These relationships are key to the problem definition and representation.As we understand what is above and below the fine line we come to recognize, appreciate, and respect the unit.In AHP/ANP it is important to recognize the nature of the problem and how units are used to represent it.

Addressing the contingent dimensions (content and context) in multi-criteria decision-making is very important to ensure the validity of a study. While this approach is widely accepted in the strategic decision-making community, it is argued here that this practice is not properly addressed and/or reported in many cases and that it must be applied in all MCDM decisions to ensure the rigor and relevance of the outcome. To explore the extent to which contingent factors are addressed in the literature, a sample of 46 MCDM group decision-making papers from a single year of publication was examined with regard to a well-known contingent dimension: group decision-making. More specifically, the following four critical variables were examined: group membership, group process, aggregation of perspectives, and group engagement. The study found that the percentage of papers that addressed these variables in a reasonable way was 23.9%, 17.4%, 26.1%, and 19.6%, respectively. These results suggest that MCDM analysts are not, for the most part, properly addressing (or reporting) group decision-making and similar contingent dimensions. For this reason, this research is a call to authors and journal editors to include and properly address all MCDM applicable contingent dimensions to improve MCDM rigor and relevance; that is, the overall validity of MCDM studies.

The AHP can be referred to as a specific subset of decision models within the more general ANP.But ANP models are more complicated and perceived as difficult to understand.Viewing each column in an ANP supermatrix as a hierarchy provides clarity about how the priority vectors, clusters, and columns are combined in a supermatrix.Paying greater attention to the units of measurement and applying an AHP perspective provides answers to important questions that can significantly impact the quality of ANP decisions.

It has been more than 20 years since the appearance of the Analytic Network Process (ANP) in the scientific literature. Since that time, this method has been used to address complex decision-making situations and capture the dependency and feedback among the different elements in the decision model. Yet, a review of ANP studies published in 2015 shows that the reports of these studies are either deficient or incomplete in the analysis or reporting to the point that it casts a shadow on the validity of their conclusions. We propose, to our knowledge for the first time, a set of best practices to conduct, analyze and report ANP studies. (C) 2020 Elsevier Ltd. All rights reserved.

A review of more than 100 ANP studies published in 2015 shows that the report of these studies is either deficient or incomplete, to the point that it casts a shadow on the validity of their conclusions.In this study we identify key elements that must be present to ensure the validity, replicability and overall quality of the reported ANP study.

The Analytic Network Process (ANP) is a disruptive technology that has had significant impacts in the field of decision-making. By drawing on an analogy to the field of astronomy we can see that even with all that has been developed we must avoid the illusion of thinking that the field is mature and fully discovered. The ANP has many parallels to icebergs from what portion is visible to the value of providing relevant warning products. One of the most important contributions going forward will be the discovery of the more complex and hidden relationships and tests that ANP decision makers can use to test their models. These discoveries will improve both the reputation of the ANP and decision maker’s confidence in their models. Without these discoveries, the ANP runs the risk of becoming like a big box retail store.

Saaty recognized the value of research that would improve the quality of decision data. The Linking Coherency Index (LCI) is an innovative method to test for coherency in ANP Supermatrices. Coherent data can be defined as self-consistent and noncontradictory with respect to a particular system. Coherency can also be thought of as a “super consistency test” or a test for consistency at the level of the entire Supermatrix. Linking Estimates (LE) are an important component used to calculate the LCI and can also be used to reduce the number of comparisons that are required in ANP decisions. The value of testing the coherency of the Supermatrix and reducing comparisons will be demonstrated through a neat example.

When making decisions with the Analytic Network Process, coherency testing is an important step in the decision making process. Once an incoherent priority vector is identified it can either be costly or in some cases next to impossible to elicit new pairwise comparisons. Remarkably, there is useful information in the linking estimates that one may have already calculated and used in one of the approaches to measure the coherency of the Supermatrix. A dynamic clustering method is used to automatically identify a cluster of coherent linking estimates from which a new coherent priority vector can be calculated and used to replace the most incoherent priority vector. The decision maker can then accept or revise the proposed new and coherent priority vector. This process is repeated until the entire Supermatrix is coherent. This method can save decision makers valuable time and effort by using the information and relationships that already exist in a weighted Supermatrix that is sufficiently coherent. The method is initially motivated and demonstrated through a simple straightforward example. A group of conceptual charts and a figure provide a visual motivation and explanation of the method. A high level summary of the method is provided in a table before the method is presented in detail. Simulations demonstrate both the application and the robustness of the proposed method. Code is provided, as supplementary material, in the programming language R so the method can be easily applied by the decision maker.

Dr. Thomas Saaty developed the Analytic Hierarchy Process (AHP) with the underlying goal of making it simple and accessible to the lay user. In Saaty’s own words, the AHP is based on how “ordinary people process information” and “express the strength of their judgments” (Saaty, 1994, p. 37). Because he was successful in developing the AHP in accordance with these goals, when decision makers use the AHP their experience can feel magical as they find pairwise comparisons natural and can relate to the final priorities. Careful investigation of the axioms, theorems, and proofs shows that the AHP is more than just magic and provides scientific justification of the highest order. Five important components of the AHP and some background into the history of its development are summarized and highlighted from Saaty’s article, “How to Make a Decision: the Analytic Hierarchy Process” (Saaty, 1994). https://doi.org/10.13033/ijahp.v9i3.519

When designing an ANP model it is important to acknowledge and properly address whether the elements in the model are dependent on or independent of each other. The decision maker must perform criteria cluster weighting comparisons individually for the criteria clusters in each column of the Supermatrix to correctly model when the criteria and alternatives are dependent on one another to accurately capture the dependence. Failing to recognize that the criteria in a criteria cluster in one column of the Supermatrix is not necessarily equal in weight to the criteria in that same criteria cluster but in another column can lead to misrepresented rankings in the final priorities. In the extreme case, it can remove all dependence from an ANP model. Two models are used to demonstrate this unintended effect on the final priorities, and also demonstrate a crucial contribution that this effect is independent of the tangibility of the criteria considered. In the third model, the solution is discussed and implemented. A proof is provided in the appendix. This criteria cluster weighting approach further extends the applicability of the ANP to additional decisions when a decision maker wishes to represent a fully-dependent ANP decision.https://doi.org/10.13022/ijahp2017.v9.is1.450

The group Analytic Hierarchy Process (AHP) is an effective tool to collect experts' wisdom to evaluate complex decision making problems. Because judgments are always diverse in the real world, it is crucial to adequately support the consensus reaching process. In this paper, we develop a convergent group AHP consensus reaching model with a twofold feedback mechanism, which consists of both a judgment and a weighting feedback mechanism. In each round of this dynamic and interactive model, the most incompatible expert is asked to revise her judgment according to the judgment feedback mechanism. If the expert rejects the suggestion, her weight of importance will be adjusted downward based on the compatibility within the group by the weighting feedback mechanism. The proof of convergence of this consensus reaching model with the twofold mechanism is also provided and discussed. Hence this proposed consensus reaching process supports the leader or client in reaching a successful decision with a dispersed group of experts. The proposed consensus reaching model is applied to the brake pad supplier selection problem of Chery Automobile Co., Ltd. The empirical example demonstrates that the proposed methodology provides an operational decision framework for companies to select suitable suppliers in the supplier involvement under the environment of collaborative product development (SICPD) through its successful application in that context. (C) 2016 Elsevier Ltd. All rights reserved.

In the current business environment, both managers and researchers have realized that assessing and managing risk in a supply chain operation is crucial to business success. Furthermore, the traditional assessment methodologies are unable to deal with intangible criteria which are crucial factor in the analysis. Thus, we develop an orders-of-magnitude AHP (OM-AHP) based ex-ante supply chain risk assessment model, to enable the comparison of the tangible and intangible elements that influence supply chain risks. In the application of OM-AHP method to risk assessment it also became apparent a formal guiding structure of how to pivot using OM-AHP did not exist. A formal method is proposed that can significantly reduce the number of needed comparisons and improve the consistency with pairwise comparisons matrices under any AHP decision. The process of the proposed supply chain risk assessment framework consists of three phases: risk identification, risk assessment, and risk ranking and analysis. An illustrative example is provided to demonstrate the efficacy of the proposed risk assessment framework. The results are organized in a 2-way risk matrix based on their probability and consequence severity and tested for robustness via sensitivity analysis.

Consensus reaching models are widely applied in group decision making problems to improve the group's consensus level before making a common decision. Within the context of the group Analytic Hierarchy Process (AHP), a novel consensus reaching model in a dynamic decision environment is proposed. A Markov chain method can be used to determine the decision makers' weights of importance for the aggregation process with respect to the group members' opinion transition probabilities. The proposed group consensus reaching model facilitates a peer to peer opinion exchange process which relieves the group of the need for a moderator by using an automatic feedback mechanism. Moreover, as the elements in the group decision framework change in a dynamic decision making problem, this model provides feedback suggestions that adaptively adjust for each of the decision makers depending on his credibility in each round. The full process of the dynamic adaptive consensus reaching model is presented and its properties are discussed. Finally, a numerical example is given to demonstrate the effectiveness of our model. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.

An axiom of the Analytic Network Process (ANP) requires the elements being considered to be strongly connected in order to obtain a meaningful priority vector. A simple example demonstrates the issues that can arise when a decision contains disjoint clusters within the Supermatrix. From the example it can be observed that the necessary information to complete additional linking pin comparisons would have already been collected; and by performing linking pin comparisons a decision maker can convert a disjoint Supermatrix into a strongly connected Supermatrix. The linking process is summarized in five steps and provided in the general form. This linking comparison methodology exploits the fundamental advantages of pairwise comparisons and can also be used to weight the criteria clusters within a decision network. Linking pin comparisons performed at the level of a criterion of a single alternative with respect to another criterion of that same alternative can be used to obtain the criteria cluster weights. Linking pin comparisons at this level can reduce the decision maker's cognitive burden in comparison to totality comparisons. The ability to strongly connect an otherwise disjoint Supermatrix and reduce the decision maker's cognitive burden demonstrates the usefulness of linking pin comparisons in ANP decision models. Copyright (c) 2016 John Wiley & Sons, Ltd.

The consistency check within each pairwise comparison matrix is an important step in an Analytic Network Process (ANP) decision. In an ANP network there is both the ability and the need to test for additional levels of consistency or coherency among the priority vectors. Examples are used to highlight cases where a Supermatrix with priority vectors that were obtained from either perfect or nearly perfect consistent pairwise comparison matrices generates suboptimal decisions. Simulations are used to further demonstrate the frequency of these occurrences in general ANP networks. A form of cross validation within the Supermatrix called linking-validation is developed and demonstrated. The linking validation method allows decision makers to use the priority vectors within the Supermatrix to validate other priority vectors within the Supermatrix. The linking validation method involves generating linking estimates. The linking estimates are compared against each other to identify the most incoherent priority vector by calculating the Linking Coherency Index (LCI) scores. The decision maker can then update the specified priority vector and repeat this process until the LCI-score for every linking estimate is below the given threshold. The use of linking validation to test for coherency further improves the validity of ANP models. (C) 2015 Elsevier B.V. All rights reserved.

When designing an ANP model it is important for decision makers to acknowledge and properly address whether the elements in the models are dependent or independent of each other. If it is determined that the criteria and alternatives are dependent then criteria cluster weights should be obtained individually for each column in the Supermatrix. If criteria weights are applied broadly across large clusters or rows of the Supermatrix a compromising or restricting effect on the relative influences of the alternatives termed the “pigeonholing effect” can occur. Pigeonholing compromises the ratio preservation in the final priority vector and can lead to unintended results in the Limit matrix. A final priority vector with ratios that represent alternatives which are dependent on the criteria are best obtained by performing cluster comparisons individually for each column.

The iron and steel industry of China has a wide distribution structure, which leads to low production efficiency, high resource use, and weak bargaining power among global competitors. A carefully planned and executed restructuring of the industry will provide the enterprise with a competitive advantage. Making the optimal restructuring decisions, however, is not easy because: 1) the decisions involve qualitative measures within a complex and uncertain environment, 2) the alternatives include up to 31 administrative regions, and 3) there are astounding differences in the economic development among the 31 alternatives. The orders-of-magnitude approach of the analytic hierarchy process (OM-AHP) could be a useful method to tackle the first and second challenges. However, this approach does not currently explain how to address the large differences between small items in a cluster and big items in a cluster when there are no medium items between them. A model of OM-AHP with a dummy pivot is proposed to tackle this particular challenge. This approach is then applied in a multicriteria decision making problem to both demonstrate how the proposed approach works and provide a solution for the restructuring of the steel industry in China.

The supplier involvement in collaborative product development (SICPD), a widely used supplier management mode in complex product development can improve product performance in terms of reducing costs and time to market while improving quality. In SICPD, selecting appropriate suppliers, by using collective intelligence of experts from different fields or departments, is vital to keep or develop the competitive advantage of a firm. The group Analytic Hierarchy Process (AHP) is a useful tool to help companies to make such a complex decision. However, judgments are always diverse in the real world. Thus supporting the process of consensus reaching is crucial. In this paper, we develop a convergent group AHP consensus reaching model with both an automated judgment and weight feedback mechanism to select the suitable suppliers in a SICPD environment. In each round of this dynamic and interactive model, the most incompatible expert is asked to revise his judgment according to the automatic judgment feedback mechanism. If the expert rejects this suggestion, his/her importance weight will be automatically adjusted downward based on the compatibility within the group by the automatic weight feedback mechanism. This process supports the leader or client to make a successful decision with a dispersed group of experts. The proposed consensus reaching model is applied to solve the brake pad supplier selection problem of Chery Company. The empirical example indicates that the proposed methodology provides a good decision framework for companies to select the suitable supplier in the supplier involvement in collaborative product development (SICPD) environment.

Improving relations between the People’s Republic of China (PRC) and the United States of America (US) and ensuring that they work together as allies rather than as competitors can serve as a stabilizing force against armed conflict, particularly with surrounding nations. The economic, social, and political relationships between the PRC and US have progressed along a hilly journey. As the second largest economy in the world, the PRC has continued to develop its military and is determined to climb the technological ladder. This growth has led the US and the PRC to be referred to as a G-2 of superpowers. As the US hegemony continues to weaken this G-2 relationship is becoming more important. With significant economic, political, and security issues at stake it is crucial that efforts to strengthen these relations are prioritized and implemented. A rigorous prioritization process, the Analytic Network Process (ANP) is used herein to prioritize the efforts and initiatives in the G-2 relationship. The model is presented with results and the extensive sensitivity analysis present additional insight into the suggested solutions.