Strategic logistics outsourcing:an integrated QFD and fuzzy AHP approach

This paper develops an integratedapproach, combining quality function deployment (QFD), fuzzy set theory, and analytic hierarchy process (AHP) approach, to evaluate and select the optimal third-party logistics service providers (3PLs). In the approach, multiple evaluating criteria are derived from the requirements of company stakeholders using a series of house of quality (HOQ). The importance of evaluating criteria is prioritized with respect to the degree of achieving the stakeholder requirements using fuzzyAHP. Based on the ranked criteria, alternative 3PLs are evaluated and compared with each other using fuzzyAHP again to make an optimal selection. The effectiveness of proposed approach is demonstrated by applying it to a Hong Kong based enterprise that supplies hard disk components. The proposed integratedapproach outperforms the existing approaches because the outsourcing strategy and 3PLs selection are derived from the corporate/business strategy.

水资源分配的决策模型及应用

水资源规划是一个复杂的系统规划问题,所以,在水资源规划中,含有大量的不精确的统计数据和模糊关系。由于这些特点,水资源规划必须用特殊的方法来解决。 本文将层次分析法(AHP)和模糊规划(Fuzzy Programming)方法相结合,形成了一种多目标规划的求解方法,并应用于大凌河流域水资源规划研究的课题中,通过实际分析可以看到,这种方法具有较好的实用性。

The use of analytical hierarchy process in spatial decision support system for land use management

Geographic information systems give us the possibility to analyze, produce, and edit geographic information. Furthermore, these systems fall short on the analysis and support of complex spatial problems. Therefore, when a spatial problem, like land use management, requires a multi-criteria perspective, multi-criteria decision analysis is placed into spatial decision support systems. The analytic hierarchy process is one of many multi-criteria decision analysis methods that can be used to support these complex problems. Using its capabilities we try to develop a spatial decision support system, to help land use management. Land use management can undertake a broad spectrum of spatial decision problems. The developed decision support system had to accept as input, various formats and types of data, raster or vector format, and the vector could be polygon line or point type. The support system was designed to perform its analysis for the Zambezi river Valley in Mozambique, the study area. The possible solutions for the emerging problems had to cover the entire region. This required the system to process large sets of data, and constantly adjust to new problems’ needs. The developed decision support system, is able to process thousands of alternatives using the analytical hierarchy process, and produce an output suitability map for the problems faced.

Searching for consensus in ahp-group decision making. A bayesian perspective

This paper sets out to identify the initial positions of the different decision makers who intervene in a group decision making process with a reduced number of actors, and to establish possible consensus paths between these actors. As a methodological support, it employs one of the most widely-known multicriteria decision techniques, namely, the Analytic Hierarchy Process (AHP). Assuming that the judgements elicited by the decision makers follow the so-called multiplicative model (Crawford and Williams, 1985; Altuzarra et al., 1997; Laininen and Hämäläinen, 2003) with log-normal errors and unknown variance, a Bayesian approach is used in the estimation of the relative priorities of the alternatives being compared. These priorities, estimated by way of the median of the posterior distribution and normalised in a distributive manner (priorities add up to one), are a clear example of compositional data that will be used in the search for consensus between the actors involved in the resolution of the problem through the use of Multidimensional Scaling tools

Modelagem da decisão por pacotes de viagem: um estudo usando processo de hierarquia analítica AHP

The objective of this dissertation is to propose a Multi Criteria Decision Aid Model to be used by the costumers of the travel agencies and help them to choose the best package travel. The main objective is to contribute for the simplification of the travel package decision choice from the identification of the models of values and preference of the customers and applying them to the existing package. It is used the Analytic Hierarchy Process (AHP) method to structuralize a decision hierarchic model composed by six criteria (package cost, hotel category, security of the city, travel time, direct flight and position in ranking of the 10 most visited destination) and five real alternatives of packages for a holiday of three days created from travel agency data. The decision analysis was realized for the choice of a travel package by a group composed by two couples that regularly travels together, to which was asked to do a pairwise judgment of the criteria and the alternatives. The mains results show that, although been a group that travels together, there are different models of values in the weights of the criteria and a certain convergence in the scales of preferences of the alternatives in the criteria. It was not pointed a dominant alternative for all the members of the group separately, but an analysis of a total utility of the group shows a classification and an order of the travel packages and an alternative clearly in front of the others. The sensitivity analysis revels that there are changes in the ranking, but the two alternatives best classified in the normal analysis are the same ones in the sensitivity analysis, although with the positions changed. The analysis also led to a simplification of the process with the exclusion of alternatives dominated for the others ones. As main conclusion, it is evaluated that the model and method suggested allow a simplification of the decision process in the choice of travel packages

Aplicação do Processo Analítico Hierarquico (AHP) Para Priorização de Obras de Intervenção em Áreas e Setores de Risco Geológico nos Municípios de Itapecerica da Serra e Suzano (SP)

Municipal Plans of Risk Reducing (PMRR's) were produced in settlements in the municipalities of Itapecerica da Serra (SP) and Suzano (SP), covering areas at risk of landslides and washouts of banks of streams. The development of PMRR's provided the delimitation of areas of risk, the indication of intervention works in order to eliminate and / or reduce risks, and consequently an indication of the areas and priority sectors for implementation of intervention works. The prioritization of areas and sectors that should receive the works of reducing or eliminating risk was performed by an expert involved in risk mapping. Despite the specialist's judgment exercise caution, the decision regarding the priority sites for implementation of alternative interventions is subjective. Since there is no way to eliminate this subjectivity, the use of decision-making techniques is important to evaluate whether the expert's reasoning is consistent. One of the first techniques developed for multiple criteria is the AHP (Analytic Hierarchy Process). This paper describes the results of a research carried out in order to assess whether the use of Analytic Hierarchy Process contributes to the results of the indication of the areas and priority sectors for implementation of interventions can be considered more consistent than in situations where the priority occurs without the use of decision making techniques. Results were compared between the prioritization of interventions for implementation contained in PMRR's of Itapecerica da Serra and Suzano and those obtained from the use of Analytic Hierarchy Process (AHP). It was concluded that such techniques permits an evaluation of the expert's judgment is logically coherent, thus contributing to produce results more technically based.

Método AHP como instrumento de apoio à decisão para a manutenção da qualidade da água do reservatório de Ilha Solteira

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Multi-criteria analysis in the strategic environmental assessment of the sugar and alcohol sector

The Strategic Environmental Assessment (SEA) of the sugar and alcohol sector guides a territorial and sectoral planning that benefits most of the local society and supports this economic activity in all its stages. In this way, the present work aims to determine an index of aggregation of the indicators generated in the baseline of the SEA process, called Index of Sustainability of Expansion of the Sugar and Alcohol Sector (IScana). For this, it was used the normalization of the indicators of each city by the fuzzy logic and attribution of weights by the Analytic Hierarchy Process (AHP). Then, the IScana values had been spatialized in the region of 'Grande Dourados'-Mato Grosso do Sul State. The northern portion concentrated the highest values of IScana, 0.48 and 0.55, referring to the cities of Nova Alvorada do Sul and Rio Brilhante, while, in the central portion, the city of Dourados presented the lowest value, 0.10. The selection of the set of indicators forming the IScana, and their relative importance, was satisfactory for the application of fuzzy logic and AHP techniques. The IScana index supplies objective information regarding the diagnosis of the region for the application of SEA.

Modelo para la integración del trazado de infraestructuras lineales en el paisaje y el medio ambiente basado en SIG

El análisis de las diferentes alternativas en la planificación y diseño de corredores y trazados de carreteras debe basarse en la correcta definición de variables territoriales que sirvan como criterios para la toma de decisión y esto requiere un análisis ambiental preliminar de esas variables de calidad. En España, los estudios de viabilidad de nuevas carreteras y autovías están asociados a una fase del proceso de decisión que se corresponde con el denominado Estudio Informativo, el cual establece condicionantes físicos, ambientales, de uso del suelo y culturales que deben ser considerados en las primeras fases de la definición del trazado de un corredor de carretera. Así, la metodología más frecuente es establecer diferentes niveles de capacidad de acogida del territorio en el área de estudio con el fin de resumir las variables territoriales en mapas temáticos y facilitar el proceso de trazado de las alternativas de corredores de carretera. El paisaje es un factor limitante a tener en cuenta en la planificación y diseño de carreteras y, por tanto, deben buscarse trazados más sostenibles en relación con criterios estéticos y ecológicos del mismo. Pero este factor no es frecuentemente analizado en los Estudios Informativos e incluso, si es considerado, los estudios específicos de la calidad del paisaje (estético y ecológico) y de las formas del terreno no incorporan las recomendaciones de las guías de trazado para evitar o reducir los impactos en el paisaje. Además, los mapas de paisaje que se generan en este tipo de estudios no se corresponden con la escala de desarrollo del Estudio Informativo (1:5.000). Otro déficit común en planificación de corredores y trazados de carreteras es que no se tiene en cuenta la conectividad del paisaje durante el proceso de diseño de la carretera para prevenir la afección a los corredores de fauna existentes en el paisaje. Este déficit puede originar un posterior efecto barrera en los movimientos dispersivos de la fauna y la fragmentación de sus hábitats debido a la ocupación parcial o total de las teselas de hábitats con importancia biológica para la fauna (o hábitats focales) y a la interrupción de los corredores de fauna que concentran esos movimientos dispersivos de la fauna entre teselas. El objetivo principal de esta tesis es mejorar el estudio del paisaje para prevenir su afección durante el proceso de trazado de carreteras, facilitar la conservación de los corredores de fauna (o pasillos verdes) y la localización de medidas preventivas y correctoras en términos de selección y cuantificación de factores de idoneidad a fin de reducir los impactos visuales y ecológicos en el paisaje a escala local. Concretamente, la incorporación de valores cuantitativos y bien justificados en el proceso de decisión permite incrementar la transparencia en el proceso de diseño de corredores y trazados de carreteras. Con este fin, se han planteado cuatro preguntas específicas en esta investigación (1) ¿Cómo se seleccionan y evalúan los factores territoriales limitantes para localizar una nueva carretera por los profesionales españoles de planificación del territorio en relación con el paisaje? (2) ¿Cómo pueden ser definidos los corredores de fauna a partir de factores del paisaje que influyen en los movimientos dispersivos de la fauna? (3) ¿Cómo pueden delimitarse y evaluarse los corredores de fauna incluyendo el comportamiento parcialmente errático en los movimientos dispersivos de la fauna y el efecto barrera de los elementos antrópicos a una escala local? (4) ¿Qué y cómo las recomendaciones de diseño de carreteras relacionadas con el paisaje y las formas del terreno pueden ser incluidas en un modelo de Sistemas de Información Geográfica (SIG) para ayudar a los ingenieros civiles durante el proceso de diseño de un trazado de carreteras bajo el punto de vista de la sostenibilidad?. Esta tesis doctoral propone nuevas metodologías que mejoran el análisis visual y ecológico del paisaje utilizando indicadores y modelos SIG para obtener alternativas de trazado que produzcan un menor impacto en el paisaje. Estas metodologías fueron probadas en un paisaje heterogéneo con una alta tasa de densidad de corzo (Capreolus capreolus L.), uno de los grandes mamíferos más atropellados en la red de carreteras españolas, y donde está planificada la construcción de una nueva autovía que atravesará la mitad del área de distribución del corzo. Inicialmente, se han analizado las variables utilizadas en 22 estudios de proyectos de planificación de corredores de carreteras promovidos por el Ministerio de Fomento entre 2006 y 2008. Estas variables se agruparon según condicionantes físicos, ambientales, de usos del suelo y culturales con el fin de comparar los valores asignados de capacidad de acogida del territorio a cada variable en los diferentes estudios revisados. Posteriormente, y como etapa previa de un análisis de conectividad, se construyó un mapa de resistencia de los movimientos dispersivos del corzo en base a la literatura y al juicio de expertos. Usando esta investigación como base, se le asignó un valor de resistencia a cada factor seleccionado para construir la matriz de resistencia, ponderándolo y combinándolo con el resto de factores usando el proceso analítico jerárquico y los operadores de lógica difusa como métodos de análisis multicriterio. Posteriormente, se diseñó una metodología SIG para delimitar claramente la extensión física de los corredores de fauna de acuerdo a un valor umbral de ancho geométrico mínimo, así como la existencia de múltiples potenciales conexiones entre cada par de teselas de hábitats presentes en el paisaje estudiado. Finalmente, se realizó un procesado de datos Light Detection and Ranging (LiDAR) y un modelo SIG para calcular la calidad del paisaje (estético y ecológico), las formas del terreno que presentan características similares para trazar una carretera y la acumulación de vistas de potenciales conductores y observadores de los alrededores de la nueva vía. Las principales contribuciones de esta investigación al conocimiento científico existente en el campo de la evaluación del impacto ambiental en relación al diseño de corredores y trazados de carreteras son cuatro. Primero, el análisis realizado de 22 Estudios Informativos de planificación de carreteras reveló que los métodos aplicados por los profesionales para la evaluación de la capacidad de acogida del territorio no fue suficientemente estandarizada, ya que había una falta de uniformidad en el uso de fuentes cartográficas y en las metodologías de evaluación de la capacidad de acogida del territorio, especialmente en el análisis de la calidad del paisaje estético y ecológico. Segundo, el análisis realizado en esta tesis destaca la importancia de los métodos multicriterio para estructurar, combinar y validar factores que limitan los movimientos dispersivos de la fauna en el análisis de conectividad. Tercero, los modelos SIG desarrollados Generador de alternativas de corredores o Generator of Alternative Corridors (GAC) y Eliminador de Corredores Estrechos o Narrow Corridor Eraser (NCE) pueden ser aplicados sistemáticamente y sobre una base científica en análisis de conectividad como una mejora de las herramientas existentes para la comprensión el paisaje como una red compuesta por nodos y enlaces interconectados. Así, ejecutando los modelos GAC y NCE de forma iterativa, pueden obtenerse corredores alternativos con similar probabilidad de ser utilizados por la fauna y sin que éstos presenten cuellos de botella. Cuarto, el caso de estudio llevado a cabo de prediseño de corredores y trazado de una nueva autovía ha sido novedoso incluyendo una clasificación semisupervisada de las formas del terreno, filtrando una nube de puntos LiDAR e incluyendo la nueva geometría 3D de la carretera en el Modelo Digital de Superficie (MDS). El uso combinado del procesamiento de datos LiDAR y de índices y clasificaciones geomorfológicas puede ayudar a los responsables encargados en la toma de decisiones a evaluar qué alternativas de trazado causan el menor impacto en el paisaje, proporciona una visión global de los juicios de valor más aplicados y, en conclusión, define qué medidas de integración paisajística correctoras deben aplicarse y dónde. ABSTRACT The assessment of different alternatives in road-corridor planning and layout design must be based on a number of well-defined territorial variables that serve as decision-making criteria, and this requires a high-quality preliminary environmental analysis of those quality variables. In Spain, feasibility studies for new roads and motorways are associated to a phase of the decision procedure which corresponds with the one known as the Informative Study, which establishes the physical, environmental, land-use and cultural constraints to be considered in the early stages of defining road corridor layouts. The most common methodology is to establish different levels of Territorial Carrying Capacity (TCC) in the study area in order to summarize the territorial variables on thematic maps and facilitate the tracing process of road-corridor layout alternatives. Landscape is a constraint factor that must be considered in road planning and design, and the most sustainable layouts should be sought based on aesthetic and ecological criteria. However this factor is not often analyzed in Informative Studies and even if it is, baseline studies on landscape quality (aesthetic and ecological) and landforms do not usually include the recommendations of road tracing guides designed to avoid or reduce impacts on the landscape. The resolution of the landscape maps produced in this type of studies does not comply with the recommended road design scale (1:5,000) in the regulations for the Informative Study procedure. Another common shortcoming in road planning is that landscape ecological connectivity is not considered during road design in order to avoid affecting wildlife corridors in the landscape. In the prior road planning stage, this issue could lead to a major barrier effect for fauna dispersal movements and to the fragmentation of their habitat due to the partial or total occupation of habitat patches of biological importance for the fauna (or focal habitats), and the interruption of wildlife corridors that concentrate fauna dispersal movements between patches. The main goal of this dissertation is to improve the study of the landscape and prevent negative effects during the road tracing process, and facilitate the preservation of wildlife corridors (or green ways) and the location of preventive and corrective measures by selecting and quantifying suitability factors to reduce visual and ecological landscape impacts at a local scale. Specifically the incorporation of quantitative and well-supported values in the decision-making process provides increased transparency in the road corridors and layouts design process. Four specific questions were raised in this research: (1) How are territorial constraints selected and evaluated in terms of landscape by Spanish land-planning practitioners before locating a new road? (2) How can wildlife corridors be defined based on the landscape factors influencing the dispersal movements of fauna? (3) How can wildlife corridors be delimited and assessed to include the partially erratic movements of fauna and the barrier effect of the anthropic elements at a local scale? (4) How recommendations of road design related to landscape and landforms can be included in a Geographic Information System (GIS) model to aid civil engineers during the road layout design process and support sustainable development? This doctoral thesis proposes new methodologies that improve the assessment of the visual and ecological landscape character using indicators and GIS models to obtain road layout alternatives with a lower impact on the landscape. These methodologies were tested on a case study of a heterogeneous landscape with a high density of roe deer (Capreolus capreolus L.) –one of the large mammals most commonly hit by vehicles on the Spanish road network– and where a new motorway is planned to pass through the middle of their distribution area. We explored the variables used in 22 road-corridor planning projects sponsored by the Ministry of Public Works between 2006 and 2008. These variables were grouped into physical, environmental, land-use and cultural constraints for the purpose of comparing the TCC values assigned to each variable in the various studies reviewed. As a prior stage in a connectivity analysis, a map of resistance to roe deer dispersal movements was created based on the literature and experts judgment. Using this research as a base, each factor selected to build the matrix was assigned a resistance value and weighted and combined with the rest of the factors using the analytic hierarchy process (AHP) and fuzzy logic operators as multicriteria assessment (MCA) methods. A GIS methodology was designed to clearly delimit the physical area of wildlife corridors according to a geometric threshold width value, and the multiple potential connections between each pair of habitat patches in the landscape. A Digital Surface Model Light Detection and Ranging (LiDAR) dataset processing and a GIS model was performed to determine landscape quality (aesthetic and ecological) and landforms with similar characteristics for the road layout, and the cumulative viewshed of potential drivers and observers in the area surrounding the new motorway. The main contributions of this research to current scientific knowledge in the field of environmental impact assessment for road corridors and layouts design are four. First, the analysis of 22 Informative Studies on road planning revealed that the methods applied by practitioners for assessing the TCC were not sufficiently standardized due to the lack of uniformity in the cartographic information sources and the TCC valuation methodologies, especially in the analysis of the aesthetic and ecological quality of the landscape. Second, the analysis in this dissertation highlights the importance of multicriteria methods to structure, combine and validate factors that constrain wildlife dispersal movements in the connectivity analysis. Third, the “Generator of Alternative Corridors (GAC)” and “Narrow Corridor Eraser (NCE)” GIS models developed can be applied systematically and on a scientific basis in connectivity analyses to improve existing tools and understand landscape as a network composed of interconnected nodes and links. Thus, alternative corridors with similar probability of use by fauna and without bottlenecks can be obtained by iteratively running GAC and NCE models. Fourth, our case study of new motorway corridors and layouts design innovatively included semi-supervised classification of landforms, filtering of LiDAR point clouds and new 3D road geometry on the Digital Surface Model (DSM). The combined used of LiDAR data processing and geomorphological indices and classifications can help decision-makers assess which road layouts produce lower impacts on the landscape, provide an overall insight into the most commonly applied value judgments, and in conclusion, define which corrective measures should be applied in terms of landscaping, and where.

A new tool for measurement of process-based performance of multispecialty tertiary care hospitals

There is an increasing need of a model for the process-based performance measurement of multispecialty tertiary care hospitals for quality improvement. Analytic hierarchy process (AHP) is utilized in this study to evolve such a model. Each step in the model was derived by group-discussions and brainstorming sessions among experienced clinicians and managers. This tool was applied to two tertiary care teaching hospitals in Barbados and India. The model enabled identification of specific areas where neither hospital performed very well, and helped to suggest recommendations to improve those areas. AHP is recommended as a valuable tool to measure the process-based performance of multispecialty tertiary care hospitals. © Emerald Group Publishing Limited.

Which is the best solar thermal collection technology for electricity generation in north-west India? Evaluation of options using the analytical hierarchy process

This study of concentrating solar thermal power generation sets out to evaluate the main existing collection technologies using the framework of the Analytical Hierarchy Process (AHP). It encompasses parabolic troughs, heliostat fields, linear Fresnel reflectors, parabolic dishes, compound parabolic concentrators and linear Fresnel lenses. These technologies are compared based on technical, economic and environmental criteria. Within these three categories, numerous sub-criteria are identified; similarly sub-alternatives are considered for each technology. A literature review, thermodynamic calculations and an expert workshop have been used to arrive at quantitative and qualitative assessments. The methodology is applied principally to a case study in Gujarat in north-west India, though case studies based on the Sahara Desert, Southern Spain and California are included for comparison. A sensitivity analysis is carried out for Gujarat. The study concludes that the linear Fresnel lens with a secondary compound parabolic collector, or the parabolic dish reflector, is the preferred technology for north-west India.

Strategic sourcing:a combined QFD and AHP approach in manufacturing

Purpose – This paper aims to develop an integrated analytical approach, combining quality function deployment (QFD) and analytic hierarchy process (AHP) approach, to enhance the effectiveness of sourcing decisions. Design/methodology/approach – In the approach, QFD is used to translate the company stakeholder requirements into multiple evaluating factors for supplier selection, which are used to benchmark the suppliers. AHP is used to determine the importance of evaluating factors and preference of each supplier with respect to each selection criterion. Findings – The effectiveness of the proposed approach is demonstrated by applying it to a UK-based automobile manufacturing company. With QFD, the evaluating factors are related to the strategic intent of the company through the involvement of concerned stakeholders. This ensures successful strategic sourcing. The application of AHP ensures consistent supplier performance measurement using benchmarking approach. Research limitations/implications – The proposed integrated approach can be principally adopted in other decision-making scenarios for effective management of the supply chain. Practical implications – The proposed integrated approach can be used as a group-based decision support system for supplier selection, in which all relevant stakeholders are involved to identify various quantitative and qualitative evaluating criteria, and their importance. Originality/value – Various approaches that can deal with multiple and conflicting criteria have been adopted for the supplier selection. However, they fail to consider the impact of business objectives and the requirements of company stakeholders in the identification of evaluating criteria for strategic supplier selection. The proposed integrated approach outranks the conventional approaches to supplier selection and supplier performance measurement because the sourcing strategy and supplier selection are derived from the corporate/business strategy.

Strategic logistics outsourcing: an integrated QFD and AHP approach

Third-party logistics service providers (3PLs) play a vital role in contemporary supply chain management. Evaluation and selection of the right 3PLs depends on a wide range of quantitative and qualitative criteria rather than cost-based factors. Although various multi-criteria decision making approaches have been proposed, they have not considered the impact of business objectives and requirements of company stakeholders on the evaluating criteria. To enable the "voice" of company stakeholders is considered, this paper develops an integrated approach for selecting 3PL strategically. In the approach, multiple evaluating criteria are derived from the requirements of company stakeholders using a series of house of quality (HOQ). The importance of evaluating criteria is prioritized with respect to the degree of achieving the stakeholder requirements using analytic hierarchy process (AHP). Based on the ranked criteria, alternative 3PLs are evaluated and compared with each other using AHP again to make an optimal selection.

An Approach for a more Objective Evaluation of Practical Projects, Used in the Training Process

Well–prepared, adaptive and sustainably developing specialists are an important competitive advantage, but also one of the main challenges for businesses. One option of the education system for creation and development of staff adequate to the needs is the development of pro jects with topics from real economy ("Practical Projects"). The objective assessment is an essential driver and motivator, and is based on a system of well-chosen, well-defined and specific criteria and indicators. An approach to a more objective evaluation of practical projects is finding more objective weights of the criteria. A natural and reasonable approach is the accumulation of opinions of proven experts and subsequent bringing out the weights from the accumulated data. The preparation and conduction of a survey among recognized experts in the field of project-based learning in mathematics, informatics and information technologies is described. The processing of the data accumulated by applying AHP, allowed us to objectively determine weights of evaluation criteria and hence to achieve the desired objectiveness. ACM Computing Classification System (1998): K.3.2.

A method for solving LSM problems of small size in the AHP

The Analytic Hierarchy Process (AHP) is one of the most popular methods used in Multi-Attribute Decision Making. It provides with ratio-scale measurements of the prioirities of elements on the various leveles of a hierarchy. These priorities are obtained through the pairwise comparisons of elements on one level with reference to each element on the immediate higher level. The Eigenvector Method (EM) and some distance minimizing methods such as the Least Squares Method (LSM), Logarithmic Least Squares Method (LLSM), Weighted Least Squares Method (WLSM) and Chi Squares Method (X2M) are of the tools for computing the priorities of the alternatives. This paper studies a method for generating all the solutions of the LSM problems for 3 × 3 matrices. We observe non-uniqueness and rank reversals by presenting numerical results.