Solving the Least Squares Method problem in the AHP for 3 X 3 and 4 X 4 matrices

The Analytic Hierarchy Process (AHP) is one of the most popular methods used in Multi-Attribute Decision Making. The Eigenvector Method (EM) and some distance minimizing methods such as the Least Squares Method (LSM) are of the possible tools for computing the priorities of the alternatives. A method for generating all the solutions of the LSM problem for 3 × 3 and 4 × 4 matrices is discussed in the paper. Our algorithms are based on the theory of resultants.

Effektiv lagerstyrning med AHP och tvådimensionell artikelklassificering : En fallstudie på Permobil AB, Timrå

Costs related to inventory are usually a significant amount of the company’s total assets. Despite this, companies in general don’t pay a lot of interest in it, even if the benefits from effective inventory are obvious when it comes to less tied up capital, increased customer satisfaction and better working environment. Permobil AB, Timrå is in an intense period when it comes to revenue and growth. The production unit is aiming for an increased output of 30 % in the next two years. To make this possible the company has to improve their way to distribute and handle material,The purpose of the study is to provide useful information and concrete proposals for action, so that the company can build a strategy for an effective and sustainable solution when it comes to inventory management. Alternative methods for making forecasts are suggested, in order to reach a more nuanced perception of different articles, and how they should be managed. Analytic Hierarchy Process (AHP) was used in order to give specially selected persons the chance to decide criteria for how the article should be valued. The criteria they agreed about were annual volume value, lead time, frequency rate and purchase price. The other method that was proposed was a two-dimensional model where annual volume value and frequency was the criteria that specified in which class an article should be placed. Both methods resulted in significant changes in comparison to the current solution. For the spare part inventory different forecast methods were tested and compared with the current solution. It turned out that the current forecast method performed worse than both moving average and exponential smoothing with trend. The small sample of ten random articles is not big enough to reject the current solution, but still the result is a reason enough, for the company to control the quality of the forecasts.

Modified AHP for gene selection and cancer classification using type-2 fuzzy logic

This paper proposes a modification to the analytic hierarchy process (AHP) to select the most informative genes that serve as inputs to an interval type-2 fuzzy logic system (IT2FLS) for cancer classification. Unlike the conventional AHP, the modified AHP allows us to process quantitative factors that are ranking outcomes of individual gene selection methods including t-test, entropy, receiver operating characteristic curve, Wilcoxon test, and signal-to-noise ratio. The IT2FLS is introduced for the classification task due to its great ability for handling nonlinear, noisy, and outlier data, which are common problems in cancer microarray gene expression profiles. An unsupervised learning strategy using the fuzzy c-means clustering is employed to initialize parameters of the IT2FLS. Other classifiers such as multilayer perceptron network, support vector machine, and fuzzy ARTMAP are also implemented for comparisons. Experiments are carried out on three well-known microarray datasets: diffuse large B-cell lymphoma, leukemia cancer, and prostate. Rather than the traditional cross validation, leave-one-out cross-validation strategy is applied for the experiments. Results demonstrate the performance dominance of the IT2FLS against the competing classifiers. More noticeably, the modified AHP improves the classification performance not only of the IT2FLS but of all other classifiers as well. Accordingly, the proposed combination between the modified AHP and IT2FLS is a powerful tool for cancer classification and can be implemented as a real clinical decision support system that is useful for medical practitioners.

Evaluation of deterministic and complex analytical hierarchy process methods for agricultural land suitability analysis in a changing climate

Land suitability analysis is employed to evaluate the appropriateness of land for a particular purpose whilst integrating both qualitative and quantitative inputs, which can be continuous in nature. However, in agricultural modelling there is often a disregard of this contiguous aspect. Therefore, some parametric procedures for suitability analysis compartmentalise units into defined membership classes. This imposition of crisp boundaries neglects the continuous formations found throughout nature and overlooks differences and inherent uncertainties found in the modelling. This research will compare two approaches to suitability analysis over three differing methods. The primary approach will use an Analytical Hierarchy Process (AHP), while the other approach will use a Fuzzy AHP over two methods; Fitted Fuzzy AHP and Nested Fuzzy AHP. Secondary to this, each method will be assessed into how it behaves in a climate change scenario to understand and highlight the role of uncertainties in model conceptualisation and structure. Outputs and comparisons between each method, in relation to area, proportion of membership classes and spatial representation, showed that fuzzy modelling techniques detailed a more robust and continuous output. In particular the Nested Fuzzy AHP was concluded to be more pertinent, as it incorporated complex modelling techniques, as well as the initial AHP framework. Through this comparison and assessment of model behaviour, an evaluation of each methods predictive capacity and relevance for decision-making purposes in agricultural applications is gained.

A framework for analyzing system intelligence of the building control system : a study of the integrated building management system

The lack of satisfactory consensus for characterizing the system intelligence and structured analytical decision models has inhibited the developers and practitioners to understand and configure optimum intelligent building systems in a fully informed manner. So far, little research has been conducted in this aspect. This research is designed to identify the key intelligent indicators, and develop analytical models for computing the system intelligence score of smart building system in the intelligent building. The integrated building management system (IBMS) was used as an illustrative example to present a framework. The models presented in this study applied the system intelligence theory, and the conceptual analytical framework. A total of 16 key intelligent indicators were first identified from a general survey. Then, two multi-criteria decision making (MCDM) approaches, the analytic hierarchy process (AHP) and analytic network process (ANP), were employed to develop the system intelligence analytical models. Top intelligence indicators of IBMS include: self-diagnostic of operation deviations; adaptive limiting control algorithm; and, year-round time schedule performance. The developed conceptual framework was then transformed to the practical model. The effectiveness of the practical model was evaluated by means of expert validation. The main contribution of this research is to promote understanding of the intelligent indicators, and to set the foundation for a systemic framework that provide developers and building stakeholders a consolidated inclusive tool for the system intelligence evaluation of the proposed components design configurations.

A framework for analysing system intelligence of the building control system: a study of the integrated building management system

The lack of satisfactory consensus for characterizing the system intelligence and structured analytical decision models has inhibited the developers and practitioners to understand and configure optimum intelligent building systems in a fully informed manner. So far, little research has been conducted in this aspect. This research is designed to identify the key intelligent indicators, and develop analytical models for computing the system intelligence score of smart building system in the intelligent building. The integrated building management system (IBMS) was used as an illustrative example to present a framework. The models presented in this study applied the system intelligence theory, and the conceptual analytical framework. A total of 16 key intelligent indicators were first identified from a general survey. Then, two multi-criteria decision making (MCDM) approaches, the analytic hierarchy process (AHP) and analytic network process (ANP), were employed to develop the system intelligence analytical models. Top intelligence indicators of IBMS include: self-diagnostic of operation deviations; adaptive limiting control algorithm; and, year-round time schedule performance. The developed conceptual framework was then transformed to the practical model. The effectiveness of the practical model was evaluated by means of expert validation. The main contribution of this research is to promote understanding of the intelligent indicators, and to set the foundation for a systemic framework that provide developers and building stakeholders a consolidated inclusive tool for the system intelligence evaluation of the proposed components design configurations.

An entry mode decision-making model for the international expansion of construction enterprises

Purpose – The purpose of this paper is to provide a new type of entry mode decision-making model for construction enterprises involved in international business. Design/methodology/approach – A hybrid method combining analytic hierarchy process (AHP) with preference ranking organization method for enrichment evaluations (PROMETHEE) is used to aid entry mode decisions. The AHP is used to decompose the entry mode problem into several dimensions and determine the weight of each criterion. In addition, PROMETHEE method is used to rank candidate entry modes and carry out sensitivity analyses. Findings – The proposed decision-making method is demonstrated to be a suitable approach to resolve the entry mode selection decision problem. Practical implications – The research provides practitioners with a more systematic decision framework and a more precise decision method. Originality/value – The paper sheds light on the further development of entry strategies for international construction markets. It not only introduces a new decision-making model for entry mode decision making, but also provides a conceptual framework with five determinants for a construction company entry mode selection based on the unique properties of the construction industry.

A new method for quantifying the contribution of different critical agents on railway bridge deterioration

Railway Bridges deteriorate over time due to different critical factors including, flood, wind, earthquake, collision, and environment factors, such as corrosion, wear, termite attack, etc. In current practice, the contributions of the critical factors, towards the deterioration of railway bridges, which show their criticalities, are not appropriately taken into account. In this paper, a new method for quantifying the criticality of these factors will be introduced. The available knowledge as well as risk analyses conducted in different Australian standards and developed for bridge-design will be adopted. The analytic hierarchy process (AHP) is utilized for prioritising the factors. The method is used for synthetic rating of railway bridges developed by the authors of this paper. Enhancing the reliability of predicting the vulnerability of railway bridges to the critical factors, will be the significant achievement of this research.

Impact of child labor on academic performance : evidence from the program "Edúcame Primero Colombia"

In this study, the effects of different variables of child labor on academic performance are investigated. To this end, 3302 children participating in the child labor eradication program “Edúcame Primero Colombia” were interviewed. The interview format used for the children's enrollment into the program was a template from which socioeconomic conditions, academic performance, and child labor variables were evaluated. The academic performance factor was determined using the Analytic Hierarchy Process (AHP). The data were analyzed through a logistic regression model that took into account children who engaged in a type of labor (n = 921). The results showed that labor conditions, the number of weekly hours dedicated to work, and the presence of work scheduled in the morning negatively affected the academic performance of child laborers. These results show that the relationship between child labor and academic performance is based on the conflict between these two activities. These results do not indicate a linear and simple relationship associated with the recognition of the presence or absence of child labor. This study has implications for the formulation of policies, programs, and interventions for preventing, eradicating, and attenuating the negative effects of child labor on the social and educational development of children.

A multi-criteria analysis approach for ranking and selection of microorganisms for the production of oils for biodiesel production

Oleaginous microorganisms have potential to be used to produce oils as alternative feedstock for biodiesel production. Microalgae (Chlorella protothecoides and Chlorella zofingiensis), yeasts (Cryptococcus albidus and Rhodotorula mucilaginosa), and fungi (Aspergillus oryzae and Mucor plumbeus) were investigated for their ability to produce oil from glucose, xylose and glycerol. Multi-criteria analysis (MCA) using analytic hierarchy process (AHP) and preference ranking organization method for the enrichment of evaluations (PROMETHEE) with graphical analysis for interactive aid (GAIA), was used to rank and select the preferred microorganisms for oil production for biodiesel application. This was based on a number of criteria viz., oil concentration, content, production rate and yield, substrate consumption rate, fatty acids composition, biomass harvesting and nutrient costs. PROMETHEE selected A. oryzae, M. plumbeus and R. mucilaginosa as the most prospective species for oil production. However, further analysis by GAIA Webs identified A. oryzae and M. plumbeus as the best performing microorganisms.

Information preferences for the evaluation of coastal development impacts on ecosystem services: A multi-criteria assessment in the Australian context

Ecosystem based management requires the integration of various types of assessment indicators. Understanding stakeholders' information preferences is important, in selecting those indicators that best support management and policy. Both the preferences of decision-makers and the general public may matter, in democratic participatory management institutions. This paper presents a multi-criteria analysis aimed at quantifying the relative importance to these groups of economic, ecological and socio-economic indicators usually considered when managing ecosystem services in a coastal development context. The Analytic Hierarchy Process (AHP) is applied within two nationwide surveys in Australia, and preferences of both the general public and decision-makers for these indicators are elicited and compared. Results show that, on average across both groups, the priority in assessing a generic coastal development project is for the ecological assessment of its impacts on marine biodiversity. Ecological assessment indicators are globally preferred to both economic and socio-economic indicators regardless of the nature of the impacts studied. These results are observed for a significantly larger proportion of decision-maker than general public respondents, questioning the extent to which the general public's preferences are well reflected in decision-making processes.

Are organisations prepared for e-health implementation to respond to pandemic influenza?

E-health can facilitate communication and interactions among stakeholders involved in pandemic responses. Its implementation, nevertheless, represents a disruptive change in the healthcare workplace. Organisational preparedness assessment is an essential requirement prior to e-health implementation; including this step in the planning process can increase the chances of programme success. The objective of this study is to develop an e-health preparedness assessment model for pandemic influenza (EHPM4P). Following the Analytic Hierarchy Process (AHP), 20 contextual interviews were conducted with domain experts from May to September 2010. We examined the importance of all preparedness components within a fivedimensional hierarchical framework that was recently published. We also calculated the relative weight for each component at all levels of the hierarchy. This paper presents the hierarchical model (EHPM4P) that can be used to precisely assess healthcare organisational and providers' preparedness for e-health implementation and potentially maximise e-health benefits in the context of an influenza pandemic. Copyright © 2013 Inderscience Enterprises Ltd.

Non-industrial private forest landowners’ choices of timber management strategies and potential allowable cut.

In the study, the potential allowable cut in the district of Pohjois-Savo - based on the non-industrial private forest landowners' (NIPF) choices of timber management strategies - was clarified. Alternative timber management strategies were generated, and the choices and factors affecting the choices of timber management strategies by NIPF landowners were studied. The choices of timber management strategies were solved by maximizing the utility functions of the NIPF landowners. The parameters of the utility functions were estimated using the Analytic Hierarchy Process (AHP). The level of the potential allowable cut was compared to the cutting budgets based on the 7th and 8th National Forest Inventories (NFI7 and NFI8), to the combining of private forestry plans, and to the realized drain from non-industrial private forests. The potential allowable cut was calculated using the same MELA system as has been used in the calculation of the national cutting budget. The data consisted of the NIPF holdings (from the TASO planning system) that had been inventoried compartmentwise and had forestry plans made during the years 1984-1992. The NIPF landowners' choices of timber management strategies were clarified by a two-phase mail inquiry. The most preferred strategy obtained was "sustainability" (chosen by 62 % of landowners). The second in order of preference was "finance" (17 %) and the third was "saving" (11 %). "No cuttings", and "maximum cuttings" were the least preferred (9 % and 1 %, resp.). The factors promoting the choices of strategies with intensive cuttings were a) "farmer as forest owner" and "owning fields", b) "increase in the size of the forest holding", c) agriculture and forestry orientation in production, d) "decreasing short term stumpage earning expectations", e) "increasing intensity of future cuttings", and f) "choice of forest taxation system based on site productivity". The potential allowable cut defined in the study was 20 % higher than the average of the realized drain during the years 1988-1993, which in turn, was at the same level as the cutting budget based on the combining of forestry plans in eastern Finland. Respectively, the potential allowable cut defined in the study was 12 % lower than the NFI8-based greatest sustained allowable cut for the 1990s. Using the method presented in this study, timber management strategies can be clarified for non-industrial private forest landowners in different parts of Finland. Based on the choices of timber managemet strategies, regular cutting budgets can be calculated more realistically than before.

Seismic Microzonation: Principles,Practices and Experiments

This paper presents an overview of the seismic microzonation and the grade/level based study along with methods used for estimating hazard. The principles of seismic microzonation along with some current practices are discussed. Summary of seismic microzonation experiments carried out in India is presented. A detailed work of seismic microzonation of Bangalore has been presented as a case study. In this case study, a seismotectonic map for microzonation area has been developed covering 350 km radius around Bangalore, India using seismicity and seismotectonic parameters of the region. For seismic microzonation Bangalore Mahanagar Palike (BMP) area of 220 km2 has been selected as the study area. Seismic hazard analysis has been carried out using deterministic as well as probabilistic approaches. Synthetic ground motion at 653 locations, recurrence relation and peak ground acceleration maps at rock level have been generated. A detailed site characterization has been carried out using borehole with standard penetration test (SPT) ―N‖ values and geophysical data. The base map and 3-dimensional sub surface borehole model has been generated for study area using geographical information system (GIS). Multichannel analysis of surface wave (MASW)method has been used to generate one-dimensional shear wave velocity profile at 58 locations and two- dimensional profile at 20 locations. These shear wave velocities are used to estimate equivalent shear wave velocity in the study area at every 5m intervals up to a depth of 30m. Because of wider variation in the rock depth, equivalent shear for the soil overburden thickness alone has been estimated and mapped using ArcGIS 9.2. Based on equivalent shear wave velocity of soil overburden thickness, the study area is classified as ―site class D‖. Site response study has been carried out using geotechnical properties and synthetic ground motions with program SHAKE2000.The soil in the study area is classified as soil with moderate amplification potential. Site response results obtained using standard penetration test (SPT) ―N‖ values and shear wave velocity are compared, it is found that the results based on shear wave velocity is lower than the results based on SPT ―N‖ values. Further, predominant frequency of soil column has been estimated based on ambient noise survey measurements using instruments of L4-3D short period sensors equipped with Reftek 24 bit digital acquisition systems. Predominant frequency obtained from site response study is compared with ambient noise survey. In general, predominant frequencies in the study area vary from 3Hz to 12Hz. Due to flat terrain in the study area, the induced effect of land slide possibility is considered to be remote. However, induced effect of liquefaction hazard has been estimated and mapped. Finally, by integrating the above hazard parameters two hazard index maps have been developed using Analytic Hierarchy Process (AHP) on GIS platform. One map is based on deterministic hazard analysis and other map is based on probabilistic hazard analysis. Finally, a general guideline is proposed by bringing out the advantages and disadvantages of different approaches.

Seismic Microzonation of Bangalore - Preliminary Maps

This paper presents an overview of the seismic microzonation and the grade/level based study along with methods used for estimating hazard. The principles of seismic microzonation along with some current practices are discussed. Summary of seismic microzonation experiments carried out in India is presented. A detailed work of seismic microzonation of Bangalore has been presented as a case study. In this case study, a seismotectonic map for microzonation area has been developed covering 350 km radius around Bangalore, India using seismicity and seismotectonic parameters of the region. For seismic microzonation Bangalore Mahanagar Palike (BMP) area of 220 km2 has been selected as the study area. Seismic hazard analysis has been carried out using deterministic as well as probabilistic approaches. Synthetic ground motion at 653 locations, recurrence relation and peak ground acceleration maps at rock level have been generated. A detailed site characterization has been carried out using borehole with standard penetration test (SPT) ―N‖ values and geophysical data. The base map and 3-dimensional sub surface borehole model has been generated for study area using geographical information system (GIS). Multichannel analysis of surface wave (MASW)method has been used to generate one-dimensional shear wave velocity profile at 58 locations and two- dimensional profile at 20 locations. These shear wave velocities are used to estimate equivalent shear wave velocity in the study area at every 5m intervals up to a depth of 30m. Because of wider variation in the rock depth, equivalent shear for the soil overburden thickness alone has been estimated and mapped using ArcGIS 9.2. Based on equivalent shear wave velocity of soil overburden thickness, the study area is classified as ―site class D‖. Site response study has been carried out using geotechnical properties and synthetic ground motions with program SHAKE2000.The soil in the study area is classified as soil with moderate amplification potential. Site response results obtained using standard penetration test (SPT) ―N‖ values and shear wave velocity are compared, it is found that the results based on shear wave velocity is lower than the results based on SPT ―N‖ values. Further, predominant frequency of soil column has been estimated based on ambient noise survey measurements using instruments of L4-3D short period sensors equipped with Reftek 24 bit digital acquisition systems. Predominant frequency obtained from site response study is compared with ambient noise survey. In general, predominant frequencies in the study area vary from 3Hz to 12Hz. Due to flat terrain in the study area, the induced effect of land slide possibility is considered to be remote. However, induced effect of liquefaction hazard has been estimated and mapped. Finally, by integrating the above hazard parameters two hazard index maps have been developed using Analytic Hierarchy Process (AHP) on GIS platform. One map is based on deterministic hazard analysis and other map is based on probabilistic hazard analysis. Finally, a general guideline is proposed by bringing out the advantages and disadvantages of different approaches.