Application of AHP in Decision-Making: Case Studies and Practical Implementation

Application of AHP, TOPSIS, and TFNs to plant selection for phytoremediation of petroleum-contaminated soils in shale gas and oil fields

This article aims to present a case study of a real decision problem, with the main objective of assisting an animal production company, on the installation of a new factory. When evaluating the various alternatives, organizations seek clear, objective and, if possible, mathematically represented criteria. However, decision-making involves a cognitive mental process resulting from the selection of the most appropriate course of action, based on various tangible and intangible criteria (Saaty, 2000) arbitrarily chosen by decision makers. In addition to the various criteria, we also have the participation of several decision makers with the common objective of choosing of the best place to guarantee the highest growth of the company. Several methods have been developed to aid decision-making in this scenario. In the described case, we used one of those methods, namely AHP (Analytic Hierarchy Process), to hierarchize the possible location for the installation of the new factory, being the alternatives the following: Carregado, Benavente and Covilha. In 1980, Professor L. Saaty of the University of Pittsburgh, created AHP, which allows using qualitative and/or quantitative criteria in the evaluation process. This method starts with the construction of a decision tree where the criteria, sub-criteria and the various alternatives are detailed. In a second step, those criteria are compared among the various elements at the same level of hierarchy, using a matrix created by the author - Fundamental Ratio Scale in pair-wise comparison of Saaty -, with values from 1 to 9, depending on their relevance, being 1 of equal importance and the 9 of absolute importance. The third step in the model is to calculate the relative priority of each criteria and to analyze the consistency of the judgments of the decision makers (i.e. the consistency of their responses/ comparisons). At final step, the composite priority matrix for the various alternatives is obtained, reflecting the alternatives hierarchy. According to Forman and Peniwati (1998), the behavior of a decision makers’ group is a factor that will determine how the information will be analyzed and aggregated. Should the group acts as a unit (when individuals in a group essentially desire the best for the organization they represent, regardless of their own preferences, values and goals, acting in tune and making their judgments so that the group behaves as a new individual), a variant of the AHP known as Individual Judgment Aggregation (IJA) is used. For groups that prefer to maintain individual analysis, there is Individual Priority Aggregation (IPA) alternative. In both cases it is possible to assign different weights to the decision makers in the process or to consider them with same degree of importance in terms of the decision. In both cases, the group decision is treated mathematically. In the application of the AHP to our case, two decision makers considered 3 criteria subdivided into several sub-criteria: implementation (sub-criteria: suppliers, cost of installation and distance to current clients), labor (sub-criteria: availability and qualification) and incentives (sub-criteria: social security, and taxes). In this case study, decision-makers' consensus was chosen, using IJA. The application of this method to this real case allowed us to create a model of analysis and support decision, contributing with another tool for this complex decision process.

The validity of the priority vector used in the analytic hierarchy process (AHP) relies on two factors: the selection of a numerical scale and the selection of a prioritization method. The traditional AHP selects only one numerical scale (e.g., the Saaty scale) and one prioritization method (e.g., the eigenvector method) for each particular problem. For this traditional selection approach, there is disagreement on which numerical scale and prioritization method is better in deriving a priority vector. In fact, the best numerical scale and the best prioritization method both rely on the content of the pairwise comparison data provided by the AHP decision makers. By defining a set of concepts regarding the scale function and the linguistic pairwise comparison matrices (LPCMs) of the priority vector and by using LPCMs to unify the format of the input and output of AHP, this paper extends the AHP prioritization process under the 2-tuple fuzzy linguistic model. Based on the extended AHP prioritization process, we present two performance measure criteria to evaluate the effect of the numerical scales and prioritization methods. We also use the performance measure criteria to develop a 2-tuple fuzzy linguistic multicriteria approach to select the best numerical scales and the best prioritization methods for different LPCMs. In this paper, we call this type of selection the individual selection of the numerical scale and prioritization method. We also compare this individual selection with traditional selection by using both random and real data and show better results with individual selection.

Service quality has gained significant attention in the last two decades. Various tools have been developed to measure service quality, the most prominent being the SERVQUAL survey instrument. It has been generally agreed that SERVQUAL and other instruments for measuring service quality are not entirely satisfactory. Recently, the Analytic Hierarchy Process (AHP) has also been applied for measuring service quality. Unfortuantely, applications of SERVQUAL and applications of AHP have not been compatible with each other since the former has traditionally been applied for measuring service quality of a single firm while the latter has usually been applied to compare service quality of more than one firm. In this paper, we have proposed a novel application of AHP so that it can be used to measure service quality of a single firm. The results and feedback received from the respondents indicate that AHP can be advantageously applied to measure service quality of an organization.

This study discusses the application of Analytic Hierarchy Process (AHP) to support the decision-making regarding the destination of a batch of defective products. The alternatives of destination are rework or discard. Six criteria of analysis and comparison were used. The mathematical development of the model was performed in Excel, which allowed several interactions and simulations, giving greater reliability to its application. The study was developed in a Brazilian plant of a Japanese auto parts industry which supplies a world-renowned Japanese motorcycle manufacturer. The defective product is the steering column of one of the models that presented the weld bead displaced from the correct position. From a flow of analysis of quality problems, the AHP method was adapted and applied in this case study, using evaluation questions to establish the criteria for comparison. The evidence generated by the problem analysis promotes answers and determination of criteria weights according to the influences of the answers on the cost and the quality of the product in case of rework or disposal. The AHP method assisted the systematization of the decision process, allowing the developed system to be used in other quality problems involving the destination of defective products. The contribution of this work is the adaptation of the AHP method to the application of problems of this type, using questions and answers (information already existent in the analysis of quality problems). In continuation of this specific application, the format can be adapted to the reality of other companies with inclusion or exclusion of criteria and weightings as necessary, justified, either by the characteristic of the problem or by internal policies. The applied method assisted in the decision to discard the parts of the study.

A multi-criteria problem involves the consideration of two or more criteria in the prioritization of alternative solutions. The Analytic Hierarchy Process (AHP) is a leading multi-criteria method. Consistency checking is a great advantage of AHP. Since in AHP priorities come from pairwise comparisons, it is possible to check the consistency of these comparisons. However, a problem occurs when comparisons fail the consistency check. Then, the excluding options are to review some comparisons (Option 1) or to keep the comparisons (Option 2). This paper presents an AHP application in the maintenance management of an industrial plant. Industrial maintenance is not in the core business of an organization. However, maintenance costs can account over 50% of production costs. One of the first maintenance management decisions is on the maintenance strategy. Shall maintenance anticipate the occurrence of failure? Or shall maintenance be performed after an equipment breakdown? Answering those questions with classical AHP resulted in inconsistent comparison matrices. In that case, Fuzzy AHP (FAHP) were applied, avoiding this situation. Therefore, the purpose of this paper is to present the applications of four AHP models: Classical AHP and three models of FAHP, including hesitant fuzzy sets and intuitionistic fuzzy sets. The application of Hesitant FAHP (HFAHP) and Intuitionistic FAHP (IFAHP) are the novelty of this paper. The four AHP models were also applied in the same case of maintenance management of an industrial plant. Results were very similar, but experts could express their preferred model.

Latinos in the United States represent a disproportionate burden of illness and disease and face barriers to accessing health care and related resources. Culturally tailored, evidence‐based interventions hold promise in addressing many of these challenges. Yet, ensuring patient voice is vital in the successful development and implementation of such interventions. Thus, this paper examines the application of analytic hierarchy process (AHP) to inform the augmentation and implementation of an evidence‐based chronic disease self‐management programme for underserved Latinos living with both minor depression and chronic illness. The process of AHP allows for direct input from the individuals that would utilize such a programme, including afflicted individuals, their family members and the health educators/promotores that would be responsible for implementation. Specifically, 45 participants, including 15 individuals with chronic disease, 15 family members/caregivers and 15 promotores, partook in the Stakeholder Values Questionnaire, which elicited preferences and values regarding major goals, processes and content for the intervention. AHP was employed to analyse pairwise comparison ratings and to determine differences and similarities across stakeholder groups. This analytical technique allowed for the adaptation of the EBI to stakeholders' specific priorities and preferences and facilitated complex decision‐making. Findings not only shed light on similarities and differences between stakeholder groups, but also the magnitude of these priorities and preferences and allowed the intervention to be driven by the participants, themselves. Applying AHP was a unique opportunity to optimize the decision‐making process to inform cultural adaptation of an EBI while considering multiple viewpoints systematically.

Frequently, management decision making problems involve multiple criteria/objectives/attributes. Over the years, many quantitative methods have been developed to facilitate making rational decisions involving multiple criteria. The Analytic Hierarchy Process (AHP) is, in general, regarded as one of the most successful techniques to solve decision making problems involving multiple criteria. In AHP, the decision maker starts by constructing the overall hierarchy of the decision problem. The hierarchy consists of criteria, subcriteria and alternatives of the decision making problem. A number of pairwise comparison matrices are formed in order to derive weights of the criteria and the local weights of the alternatives. Subsequently, the principle of hierarchical composition is used to determine the global weights of the alternatives. The alternative with the highest global weight is selected as the best alternative. The drawback of the traditional AHP is that it requires a large number of pairwaise comparisons, especially in the presence of a large number of criteria. The present empirical study attempts to investigate the possibility of eliminating insignificant criteria in order to reduce AHP computational time. Using the Expert Choice software, findings confirm that criteria that carry comparatively lesser weights can be excluded from the hierarchy and thereby the total time required for making the pairwise comparisons can be reduced drastically. To solve large-scale enterprise multi-criteria decision making problems (that involve large number of criteria) by AHP, it is proposed that at the very outset, decision makers can apply nominal group technique to identify the insignificant criteria. These criteria can be dropped from subsequent analysis and this exclusion will not affect the final decision significantly. This proposed methodology is expected to enhance the applicability of AHP in solving various kinds of larger sized multi-criteria decision making problems in any enterprise.

When comparing and evaluating two or more scheduling methods the need to use a multiple criteria decisionmaking technique arises. Instead of just employing a qualitative approach of evaluating the methods, one can integrate the qualitative and the quantitative data in the evaluation process through the use of the analytic hierarchy process (AHP). Hence, this paper reports the evaluation of two nurse scheduling methods where the AHP technique is employed to support the selection process of these methods. Five decision criteria are used in the process. The main objective of the scheduling methods (models) is to assign work shifts and off days of the nurses in a particular hospital unit such that, it fulfils certain specified constraints while ensuring continuous high-quality patient care services. The first method is a heuristic procedure that is currently in practice. The other one is a prototype in which a memetic algorithm is adopted in the approach. The application of AHP has been found to provide a better transparency of the capability and efficiency of the scheduling methods. Consequently, the memetic algorithm approach stands out to be the better one based on the evaluation scheme.

The application of analytical hierarchy process (AHP) to the risk analysis of port construction project was investigated. Firstly, the happening probabilities of various risk factors during port construction were calculated. Secondly, the aftereffects of the risks were concluded by consulting the experts. Thirdly, the weight of each risk factor was obtained by AHP. Finally, the total risk of port construction project could be evaluated by fuzzy comprehensive evaluation. This risk analysis method was applied to evaluate the total risk of a real port construction project, and the exemplification verified its feasibility.

There is a need to increase the effectiveness and efficiency with which the operational fund budget is managed at RSUD Brigjend H. Hasan Basry Kandangan. Declining revenue projections and limited resources mean that hospitals must determine budget priorities in an objective and measurable way. This research aims to analyse the application of the Analytical Hierarchy Process (AHP) method to determine operational fund budget priorities, providing recommendations to support more effective decision-making in a hospital environment. A qualitative approach was used, involving data collection through interviews and documentation, and analysis using the AHP method with the assistance of Expert Choice 11 software to compare criteria and service alternatives. The results showed that the main criteria for determining budget priorities are potential income, market demand, operational costs and limited resources. The analysis prioritised home care services due to their high revenue potential and market demand. The application of AHP has also been proven to increase the efficiency, transparency and accountability of budget decision-making processes. This study concludes that the AHP method can be an effective tool for BLUD Hospital's operational budget prioritisation process. It is recommended that the method be integrated into all work units and supported by training for optimal application.

<span id="docs-internal-guid-907206e1-7fff-e645-a854-c45fcc5637ac"><span>The Analytic Hierarchy Process (AHP), is a multi-criteria group decision making (MCGDM) methodology. It generally required aggregating the Individual Judgments (IJ) or Individual Priorities (IP) of a group of experts. Until now, in the scientific community has accepted the Geometric Mean (GM) and the Arithmetic Mean (AM) as aggregation variables. In this paper we offer the statistical Mode as a possible aggregation variable. This could simplify the process of finding the aggregated priorities/weights in the AHP process, particularly in the context of large, homogeneous groups of experts. We argue that the mode offers a viable, efficient, and representative solution under specific distributional constraints. Our analysis includes both empirical validations based on our long-term observations in various applications of AHP and theoretical, mathematical justification. It is complemented by using simulated datasets based on a controlled range around the Mode. Since we have not yet encountered AI that applies Mode as an aggregation variable, our subsequent efforts will be aimed at training an AI model and/or agent that works with Mode as an aggregation variable. The ultimate goal is for the agent to acquire not only the ability to apply AHP with the Mode as an aggregation variable, but also to analyze which is the most appropriate aggregation approach depending on the collected, experts output data.</span></span>

Chapter 4 - Application of analytical hierarchy process (AHP) in landslide susceptibility mapping for Qazvin province, N Iran

The Analytic Hierarchy Process (AHP) of Saaty (1980) is a widely used method for MCDA, presumably because it elicitates preference information from the decision makers in a manner which they find easy to understand. The basic step is the pairwise comparison of two so-called stimuli, two alternatives under a given criterion, for instance, or two criteria. The decision maker is requested to state whether he/she is indifferent between the two stimuli or whether he/she has a weak, strict, strong, or very strong preference for one of them. The original AHP has been criticized in the literature because the algorithmic steps do not properly take into account that the method is based upon ratio information. The shortcomings can easily be avoided in the Additive and the Multiplicative AHP to be discussed in the present chapter. The Additive AHP is the SMART procedure with pairwise comparisons on the basis of difference information. The Multiplicative AHP with pairwise comparisons on the basis of ratio information is a variant of the original AHP. There is a logarithmic relationship between the Additive AHP (SMART) and the Multiplicative AHP. Both versions can easily be fuzzified. The reasons why we deviate from the original AHP will be explained at the end of this chapter.KeywordsFuzzy LogicAnalytic Hierarchy ProcessCriterion WeightFinal GradeIndifference CurveThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

With the increase of the world’s nuclear facilities decommissioning activities, people all over the world pay more and more attention to decommissioning strategy. In order to strengthen the exchange of experience related to decommissioning activities in the world, both in 2002 Germany Berlin and in 2006 Greece Athens, IAEA held the international conference on lessons learned from the decommissioning twice. Decommissioning was one of the most important conference topics each time. The meeting also reached a consensus that it is necessary to consider decommissioning as soon as possible. This paper analyzes and discusses nine kinds of factors influencing decommissioning strategy, including source survey, waste management, government policy, decommissioning step, decommissioning cost, decommissioning technology, public acceptance, soil acceptable level and optimization of radiation protection. These nine factors are chosen for a variety of factors on the comprehensive consideration of affecting degree. In other word, they are more important factors to represent the problem as thoroughly as possible. Analytic hierarchy process (AHP) is a systematic and hierarchical multi-objective decision analysis method. It is a basic approach to decision making which is proposed by T L. Saaty in 1970s, who is a professor of Pittsburgh University and the primary theoretician of AHP. In this paper, the goal is how to choose the appropriate decommissioning strategy using the method of AHP. The preferred decommissioning strategy should consider various factors, such as policy, economy, radiation protection, public acceptance, waste management and so on. Some factors are quantitative while others are qualitative. At present, there are three kinds of nuclear power plant (NPP) decommissioning strategy including immediate dismantling, deferred dismantling and entombment. The three kinds of decommissioning strategies all have their respective pros and cros. Analytic hierarchy model includes goal layer, criterion layer and program layer. In this paper, selection of decommissioning strategy is the goal layer. Nine chosen factors make up the criterion layer and three different decommissioning strategies constitute the program layer. The next step is comparative judgment which means the elements on the criterion layer are arranged into a matrix and the goal makes judgment about the relative importance of the elements with respect to the overall goal. The matrixes of pairwise comparisons of facts in criterion layer to program layer are also given in the paper. The fundamental scale of values to represent the intensities of judgments is the 1∼9 scale. For each pairwise comparison matrix, the maximum eigenvalue and corresponding eigenvector are calculated. Consistency index (CI), random Consistency Index (RI) and consistency ratio (CR) are used to check consistency. In case inspection result meets the conformance requirement, normalized feature vector is the weight vector. On the contrary, it is needed to reconstruct the pairwise comparison matrix. Only by all matrixes go through consistency checking can results meet the satisfied conformance requirements. Meanwhile, the weights of nine factors in pairwise comparison matrixes are also discussed in the paper. In summary, based on the principle of AHP, an analytic hierarchy model of NPP decommissioning strategy choice has been established. Paired comparison judgments in the AHP are applied to pairs of these factors. The AHP method uses pairwise comparison of factors and contrasts them using a relative scale in order to minimize the difference in the nature of the different factors to compare with each other and also improve accuracy. The calculation results show that deferred dismantling (Weight: 0.4663) is superior to immediate dismantling (Weight: 0.3768), and immediate dismantling is better than entombment (Weight: 0.1569). These factors are ranked according to the weight of calculation results. The top three factors are government policies (Weight: 0.3512), decommissioning cost (Weight: 0.2038) and waste management (Weight: 0.1611).