A mathematical model for dynamic efficiency using data envelopment analysis

In this paper we propose a data envelopment analysis (DEA) based method for assessing the comparative efficiencies of units operating production processes where input-output levels are inter-temporally dependent. One cause of inter-temporal dependence between input and output levels is capital stock which influences output levels over many production periods. Such units cannot be assessed by traditional or 'static' DEA which assumes input-output correspondences are contemporaneous in the sense that the output levels observed in a time period are the product solely of the input levels observed during that same period. The method developed in the paper overcomes the problem of inter-temporal input-output dependence by using input-output 'paths' mapped out by operating units over time as the basis of assessing them. As an application we compare the results of the dynamic and static model for a set of UK universities. The paper is suggested that dynamic model capture the efficiency better than static model. © 2003 Elsevier Inc. All rights reserved.

Statnote 9: The one-way analysis of variance (random effects model)

There is an alternative model of the 1-way ANOVA called the 'random effects' model or ‘nested’ design in which the objective is not to test specific effects but to estimate the degree of variation of a particular measurement and to compare different sources of variation that influence the measurement in space and/or time. The most important statistics from a random effects model are the components of variance which estimate the variance associated with each of the sources of variation influencing a measurement. The nested design is particularly useful in preliminary experiments designed to estimate different sources of variation and in the planning of appropriate sampling strategies.

Data methods in optometry. Part 10: non-linear regression analysis

1. The techniques associated with regression, whether linear or non-linear, are some of the most useful statistical procedures that can be applied in clinical studies in optometry. 2. In some cases, there may be no scientific model of the relationship between X and Y that can be specified in advance and the objective may be to provide a ‘curve of best fit’ for predictive purposes. In such cases, the fitting of a general polynomial type curve may be the best approach. 3. An investigator may have a specific model in mind that relates Y to X and the data may provide a test of this hypothesis. Some of these curves can be reduced to a linear regression by transformation, e.g., the exponential and negative exponential decay curves. 4. In some circumstances, e.g., the asymptotic curve or logistic growth law, a more complex process of curve fitting involving non-linear estimation will be required.

Consumer brand equity : a model for the measurement, analysis and evaluation of consumer perceived value

The topic of my research is consumer brand equity (CBE). My thesis is that the success or otherwise of a brand is better viewed from the consumers’ perspective. I specifically focus on consumers as a unique group of stakeholders whose involvement with brands is crucial to the overall success of branding strategy. To this end, this research examines the constellation of ideas on brand equity that have hitherto been offered by various scholars. Through a systematic integration of the concepts and practices identified but these scholars (concepts and practices such as: competitiveness, consumer searching, consumer behaviour, brand image, brand relevance, consumer perceived value, etc.), this research identifies CBE as a construct that is shaped, directed and made valuable by the beliefs, attitudes and the subjective preferences of consumers. This is done by examining the criteria on the basis of which the consumers evaluate brands and make brand purchase decisions. Understanding the criteria by which consumers evaluate brands is crucial for several reasons. First, as the basis upon which consumers select brands changes with consumption norms and technology, understanding the consumer choice process will help in formulating branding strategy. Secondly, an understanding of these criteria will help in formulating a creative and innovative agenda for ‘new brand’ propositions. Thirdly, it will also influence firms’ ability to simulate and mould the plasticity of demand for existing brands. In examining these three issues, this thesis presents a comprehensive account of CBE. This is because the first issue raised in the preceding paragraph deals with the content of CBE. The second issue addresses the problem of how to develop a reliable and valid measuring instrument for CBE. The third issue examines the structural and statistical relationships between the factors of CBE and the consequences of CBE on consumer perceived value (CPV). Using LISREL-SIMPLIS 8.30, the study finds direct and significant influential links between consumer brand equity and consumer value perception.

A Generic model for the design and analysis of production systems

This dissertation studies the process of operations systems design within the context of the manufacturing organization. Using the DRAMA (Design Routine for Adopting Modular Assembly) model as developed by a team from the IDOM Research Unit at Aston University as a starting point, the research employed empirically based fieldwork and a survey to investigate the process of production systems design and implementation within four UK manufacturing industries: electronics assembly, electrical engineering, mechanical engineering and carpet manufacturing. The intention was to validate the basic DRAMA model as a framework for research enquiry within the electronics industry, where the initial IDOM work was conducted, and then to test its generic applicability, further developing the model where appropriate, within the other industries selected. The thesis contains a review of production systems design theory and practice prior to presenting thirteen industrial case studies of production systems design from the four industry sectors. The results and analysis of the postal survey into production systems design are then presented. The strategic decisions of manufacturing and their relationship to production systems design, and the detailed process of production systems design and operation are then discussed. These analyses are used to develop the generic model of production systems design entitled DRAMA II (Decision Rules for Analysing Manufacturing Activities). The model contains three main constituent parts: the basic DRAMA model, the extended DRAMA II model showing the imperatives and relationships within the design process, and a benchmark generic approach for the design and analysis of each component in the design process. DRAMA II is primarily intended for use by researchers as an analytical framework of enquiry, but is also seen as having application for manufacturing practitioners.

Virtual manufacturing:a study of some important issues relating to the transformation of traditional manufacturing organisations

This thesis starts with a literature review, outlining the major issues identified in the literature concerning virtual manufacturing enterprise (VME) transformation. Then it details the research methodology used – a systematic approach for empirical research. next, based on the conceptual framework proposed, this thesis builds three modules to form a reference model, with the purpose of clarifying the important issues relevant to transforming a traditional manufacturing company into a VME. The first module proposes a mechanism of VME transformation – operating along the VME metabolism. The second module builds a management function within a VME to ensure a proper operation of the mechanism. This function helps identify six areas as closely related to VME transformation: lean manufacturing; competency protection; internal operation performance measurement; alliance performance measurement; knowledge management; alliance decision making. The third module continues and proposes an alliance performance measurement system which includes 14 categories of performance indicators. An analysis template for alliance decision making is also proposed and integrated into the first module. To validate these three modules, 7 manufacturing organisations (5 in China and 2 in the UK) were investigated, and these field case studies are analysed in this thesis. The evidence found in these organisations, together with the evidence collected from the literature, including both researcher views and literature case studies, provide support for triangulation evidence. In addition, this thesis identifies the strength and weakness patterns of the manufacturing companies within the theoretical niche of this research, and clarifies the relationships among some major research areas from the perspective of virtual manufacturing. Finally, the research findings are summarised, as well as their theoretical and practical implications. Research limitations and recommendations for future work conclude this thesis.

A new fuzzy additive model for determining the common set of weights in Data Envelopment Analysis

The main advantage of Data Envelopment Analysis (DEA) is that it does not require any priori weights for inputs and outputs and allows individual DMUs to evaluate their efficiencies with the input and output weights that are only most favorable weights for calculating their efficiency. It can be argued that if DMUs are experiencing similar circumstances, then the pricing of inputs and outputs should apply uniformly across all DMUs. That is using of different weights for DMUs makes their efficiencies unable to be compared and not possible to rank them on the same basis. This is a significant drawback of DEA; however literature observed many solutions including the use of common set of weights (CSW). Besides, the conventional DEA methods require accurate measurement of both the inputs and outputs; however, crisp input and output data may not relevant be available in real world applications. This paper develops a new model for the calculation of CSW in fuzzy environments using fuzzy DEA. Further, a numerical example is used to show the validity and efficacy of the proposed model and to compare the results with previous models available in the literature.

The development and stability analysis of a nonlinear growth model for microorganisms

A nonlinear dynamic model of microbial growth is established based on the theories of the diffusion response of thermodynamics and the chemotactic response of biology. Except for the two traditional variables, i.e. the density of bacteria and the concentration of attractant, the pH value, a crucial influencing factor to the microbial growth, is also considered in this model. The pH effect on the microbial growth is taken as a Gaussian function G0e-(f- fc)2/G1, where G0, G1 and fc are constants, f represents the pH value and fc represents the critical pH value that best fits for microbial growth. To study the effects of the reproduction rate of the bacteria and the pH value on the stability of the system, three parameters a, G0 and G1 are studied in detail, where a denotes the reproduction rate of the bacteria, G0 denotes the impacting intensity of the pH value to microbial growth and G1 denotes the bacterial adaptability to the pH value. When the effect of the pH value of the solution which microorganisms live in is ignored in the governing equations of the model, the microbial system is more stable with larger a. When the effect of the bacterial chemotaxis is ignored, the microbial system is more stable with the larger G1 and more unstable with the larger G0 for f0 > fc. However, the stability of the microbial system is almost unaffected by the variation G0 and G1 and it is always stable for f0 < fc under the assumed conditions in this paper. In the whole system model, it is more unstable with larger G1 and more stable with larger G0 for f0 < fc. The system is more stable with larger G1 and more unstable with larger G0 for f0 > fc. However, the system is more unstable with larger a for f0 < fc and the stability of the system is almost unaffected by a for f0 > fc. The results obtained in this study provide a biophysical insight into the understanding of the growth and stability behavior of microorganisms.