A cyclic production problem: an application of max-algebra

Given are m identical machines, each of which performs the same N operations O_i, 1⩽ i ⩽ N, cyclically and indefinitely, i.e. a production run on a machine looksO₁, O₂,…,O_N, O₁, O₂,…,O_N, O₁…. There are n_i⩽m to to perform operation O_i. The tools are transported between the machines by means of an infinitely fast transport device.Given a particular transport policy we prove the existence of stationary cyclic behaviour, determine the corresponding cycle time, and investigate the long run behaviour of the system starting from a given initial state.     

Determining a subsidy rate for Taiwan's recycling glass industry: an application of bi-level programming

This study attempts to optimize the operations of the Recycling Fund Management Board (RFMB), founded by the Environmental Protection Administration of the R.O.C. Government (on Taiwan), through the decision of a subsidy rate for the domestic glass recycling industry. The hierarchical and interactive nature between the two parties is modelled by bi-level programming, where the RFMB plays the upper-level decision unit while the recycling industry is the lower-level counterpart. In order to solve the problem by optimization software, the bi-level formulation is transformed to a single-level problem via Karush-Kuhn-Tucker optimality conditions and is further transformed to a 0?1 mixed integer programming problem by variable substitution. The problem is solved with real-world data, and the obtained solutions are analysed and compared with the RFMB’s current operations. The results suggest that the proposed approach can improve the operations of the RFMB.     

Bootstrapping to solve the limited data problem in production control: an application in batch process industries

Batch process industries are characterized by complex precedence relationships among operations, which makes the estimation of an acceptable workload very difficult. Previous research indicated that a regression-based model that uses aggregate job set characteristics may be used to support order acceptance decisions. Applications of such models in real-life assume that sufficient historical data on job sets and the corresponding makespans are available. In practice, however, historical data maybe very limited and may not be sufficient to produce accurate regression estimates. This paper shows that such a lack of data significantly impacts the performance of regression-based order acceptance procedures. To resolve this problem, we devised a method that uses the bootstrap principle. A simulation study shows that performance improvements are obtained when using the parameters estimated from the bootstrapped data set, demonstrating that this bootstrapping procedure can indeed solve the limited data problem in production control.     

Pareto set reduction based on an axiomatic approach with application of some metrics

A multicriteria choice problem involving a decision-maker’s binary preference relation is considered. Several two-stage methods are proposed for its solution. First, the Pareto set is reduced by applying an axiomatic approach. Then the problem is scalarized on the resulting set by using the Chebyshev or Euclidean metric. The methods proposed are substantiated with the help of well-known and new techniques for characterizing weakly efficient and proper efficient points. Illustrative examples are given.     

Simple consistent cluster methods based on redescending M-estimators with an application to edge identification in images

We use the local maxima of a redescending M-estimator to identify cluster, a method proposed already by Morgenthaler (in: H.D. Lawrence, S. Arthur (Eds.), Robust Regression, Dekker, New York, 1990, pp. 105–128) for finding regression clusters. We work out the method not only for classical regression but also for orthogonal regression and multivariate location and show that all three approaches are special cases of a general approach which includes also other cluster problems. For the general case we show consistency for an asymptotic objective function which generalizes the density in the multivariate case. The approach of orthogonal regression is applied to the identification of edges in noisy images.     

A group decision making model based on goal programming with fuzzy hierarchy: an application to regional forest planning

In this paper a multi-criteria group decision making model is presented in which there is a heterogeneity among the decision makers due to their different expertise and/or their different level of political control. The relative importance of the decision makers in the group is handled in a soft manner using fuzzy relations. We suppose that each decision maker has his/her preferred solution, obtained by applying any of the techniques of distance-based multi-objective programming [compromise, goal programming (GP), goal programming with fuzzy hierarchy, etc.]. These solutions are used as aspiration levels in a group GP model in which the differences between the unwanted deviations are interpreted in terms of the degree of achievement of the relative importance amongst the group members. In this way, a group GP model with fuzzy hierarchy (Group-GPFH) is constructed. The solution for this model is proposed as a collective decision. To show the applicability of our proposal, a regional forest planning problem is addressed. The objective is to determine tree species composition in order to improve the values achieved by Pan-European indicators for sustainable forest management. This problem involves stakeholders with competing interests and different preference schemes for the aforementioned indicators. The application of our proposal to this problem allows us to be able to comfortably address all these issues. The results obtained are consistent with the preferences of each stakeholder and their hierarchy within the group.     

Parameter redundancy in neural networks: an application of Chebyshev polynomials

This paper deals with feedforward neural networks containing a single hidden layer and with sigmoid/logistic activation function. Training such a network is equivalent to implementing nonlinear regression using a flexible functional form, but the functional form in question is not easy to deal with. The Chebyshev polynomials are suggested as a way forward, providing an approximation to the network which is superior to Taylor series expansions. Application of these approximations suggests that the network is liable to a ‘naturally occurring’ parameter redundancy, which has implications for the training process as well as certain statistical implications. On the other hand, parameter redundancy does not appear to damage the fundamental property of universal approximation.      

Finite-Layer Method: Determining the Critical Size of an Interlaminar Crack in the Curved Zone of a composite T-Stringer

Mechanics of Composite Materials - Using the finite-layer method, values of the modal components GI and GII and the total value of energy release rate GT for tips of an interlaminar cylindrical...     

The relationship of theory and practice in mathematics teacher professional development: an activity theory perspective

This paper describes certain interactions between the activity of “teaching” and the activity of “researching” in which the teachers participate in a 52-h professional development course aiming to introduce them to research in mathematics education as a tool for inquiry in their teaching. The teachers are involved in different research tasks such as: reading and presenting research papers; analyzing classroom dialogues and tasks; and designing, implementing, and evaluating collaboratively a classroom teaching intervention. From an activity theory (AT) perspective, and in particular Engeström’s (2001) third generation AT, distinguish two activity systems, the activity system of research and the activity system of teaching, to identify links that the participating teachers make. These links indicate the development of an inquiring stance to mathematics teaching and learning as a means of professional learning.     

Broadening the boundaries: an application of critical systems thinking to IS planning in Colombia

Most current information systems (IS) planning methodologies are focused on achieving plans that provide competitive advantage to business and solve the problems of information needs by using the latest technologies available. This paper presents an alternative approach to IS planning based on critical systems thinking—a research perspective that encourages the analysis of stakeholders' understandings of social contexts prior to the selection and/or design of planning methods. The approach is underpinned by a combination of the systems theories of autopoiesis and boundary critique, and it enables participants to reflect on different concerns and values during IS planning. This approach was applied in a project with a Colombian University, and it helped participants to uncover and address important human issues not usually seen as relevant by traditional approaches to IS planning. In addition, it led the authors to undertake further research on ethics after the project had been concluded.     

A distance-based measure of super efficiency in data envelopment analysis: an application to gas companies

Conventional data envelopment analysis (DEA) assists decision makers in distinguishing between efficient and inefficient decision making units (DMUs) in a homogeneous group. Standard DEA models can not provide more information about efficient units. Super-efficiency DEA models can be used in ranking the performance of efficient DMUs and overcome this obstacle. Because of the possible infeasibility, the use of super efficiency models has been restricted. This research proposes a methodology to determine a distance-based measure of super-efficiency. The proposed methodology overcomes the infeasibility problem of the existing ranking methodologies. The applicability of the proposed model is illustrated in the context of the analysis of gas companies?? performance.     

A note on Buczolich's solution of the Weil gradient problem: a construction based on an infinite game

Summary Using an infinite game approach we reprove Buczolich's result that there exists a differentiable function f such that ∇f(0) = 0 and |∇ f |≧1 a.e.     

The planning of marketing strategies in consumer credit: an approach based on graphical chain models for ordinal variables

This paper explores the potential of graphical chain models in defining marketing strategies in the consumer credit field. When ordinal variables are involved, the potential can be increased by exploiting the ordinal scale of variables. In the presented research, the effectiveness of ordinal methods is analysed in three important activities for building a score-card: (1) in coarse classifying of variables, (2) in model selection and (3) in measuring the prediction accuracy of the model.     

Algebraic generation of minimum size orthogonal fractional factorial designs: an approach based on integer linear programming

Generation of orthogonal fractional factorial designs (OFFDs) is an important and extensively studied subject in applied statistics. In this paper we show how searching for an OFFD that satisfies a set of constraints, expressed in terms of orthogonality between simple and interaction effects, is, in many applications, equivalent to solving an integer linear programming problem. We use a recent methodology, based on polynomial counting functions and strata, that represents OFFDs as the positive integer solutions of a system of linear equations. We use this system to set up an optimization problem where the cost function to be minimized is the size of the OFFD and the constraints are represented by the system itself. Finally we search for a solution using standard integer programming techniques. Some applications are also presented in the computational results section. It is worth noting that the methodology does not put any restriction either on the number of levels of each factor or on the orthogonality constraints and so it can be applied to a very wide range of designs, including mixed orthogonal arrays.     

A crystal plasticity framework based on the Continuum Dislocation Dynamics theory: relaxation of an idealized micropillar

The motion and interaction of dislocation lines are the physical basis of the plastic deformation of metals. Although ‘discrete dislocation dynamic’ (DDD) simulations are able to predict the kinematics of dislocation microstructure (i.e. the motion of dislocations in a given velocity field) and therefore the plastic behavior of crystals in small length scales, the computational cost makes DDD less feasible for systems larger than a few micro meters. To overcome this problem, the Continuum Dislocation Dynamics (CDD) theory was developed. CDD describes the kinematics of dislocation microstructure based on statistical averages of internal properties of dislocation systems. In this paper we present a crystal plasticity framework based on the CDD theory. It consists of two separate parts: a classical 3D elastic boundary value problem and the evolution of dislocation microstructure within slip planes according to the CDD constitutional equations. We demonstrate the evolution of dislocation density in a micropillar with a single slip plane. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysing communication in a complex service process: an application of social network analysis in the Scottish Prison Service

This article utilizes social network analysis (SNA) and associated statistical techniques to examine a complex process known as Sentence Management in a Scottish Prison Service facility. Findings indicate that communication did not always follow the formal hierarchical process defined by that organization, significant fragmentation existed between certain key roles, and four central actors controlled much of the process. This research demonstrates the applicability of the SNA as an operations management tool to analyse structural communication patterns. This case study further suggests that SNA may be particularly applicable to the public service sector, to better understand informal communication networks within operations that are largely dependent on human performance.     

Four (algorithms) in one (bag): an integrative framework of knowledge for teaching the standard algorithms of the basic arithmetic operations

In this article we present an integrative framework of knowledge for teaching the standard algorithms of the four basic arithmetic operations. The framework is based on a mathematical analysis of the algorithms, a connectionist perspective on teaching mathematics and an analogy with previous frameworks of knowledge for teaching arithmetic operations with rational numbers. In order to evaluate the potential applicability of the framework to task design, it was used for the design of mathematical learning tasks for teachers. The article includes examples of the tasks, their theoretical analysis, and empirical evidence of the sensitivity of the tasks to variations in teachers’ knowledge of the subject. This evidence is based on a study of 46 primary school teachers. The article concludes with remarks on the applicability of the framework to research and practice, highlighting its potential to encourage teaching the four algorithms with an emphasis on conceptual understanding.     

Efficiency of the strategic style of pension funds: an application of the variants of the slacks-based measure in DEA

A 2010 paper by Kaoru Tone proposes four variants of the slacks-based measure of efficiency (SBM) to overcome the limitations of this well-known Data Envelopment Analysis (DEA) approach when the reference points of the efficient frontier may not be adequate. In this study, we apply these variants for the first time to a real-world problem to evaluate the efficiency of one of the most relevant decisions in pension fund management: The strategic asset allocation. The results highlight the relevance of SBM Variation III, which considers clusters of portfolios with similar characteristics, to appropriately identify the reference set of each portfolio. Therefore, this variant allows for the identification of locally efficient but globally inefficient portfolios. Our results also reject the notion of a positive relation between management resources and efficiency of the strategic investment style.     

机制转换条件下股市收益率跳跃行为研究:基于RS-ARJI模型的以中国股市为例的实证分析

为检验股市收益率机制转换特性,考察机制转换条件下股市收益率的跳跃特征,以及在不同机制下跳跃行为对股市收益率的冲击效应,将Markov机制转换思想引入自回归跳跃(ARJI)模型,构建一个机制转换自回归跳跃(RS-ARM)模型.基于该模型对中国股市进行实证研究,结果表明:股市存在高、低波动两种机制,高波动时期的跳跃幅度和强度及其对股市收益率的冲击均大于低波动时期.同时,波动率估计和预测评价指标显示,RS-ARJI模型优于目前被广泛使用的GARCH模型和ARJI模型.     

Practice makes perfect on the blackboard: A cultural analysis of mathematics instructional patterns in Taiwan

Studies show a sharp difference in math achievement between students in the U.S. and students in several East Asian countries, amongst them Taiwan. It is suggested that the patterns of math instruction applied by teachers may have contributed to these differences. This study intends to investigate the patterns of math instruction applied by the Taiwanese teachers and to delve into the cultural roots of these patterns. Data source includes videotaping of instruction by three middle school math teachers and a questionnaire survey of 297 eighth-graders. It was found that the Taiwanese math instruction pattern may be summarized as a cultural activity of “practice makes perfect, on the blackboard”. The underlying cultural beliefs are further explored, including the incremental view of human intelligence, self-improvement through diligent effort, and the teacher's role as an authority figure.