Children with mathematical difficulties cope with modelling tasks: what develops?

This study investigates the participation and knowledge growth of children with mathematical difficulties as they work in groups with their classmates on a year-long sequence of modelling tasks. It involves observations of a class of 23 fifth graders, 9 of whom were identified as having difficulties in mathematics. All the students worked for 8 months on a sequence of 12 modelling task in heterogeneous groups. The findings show a gradual growth in modelling competencies and mathematical knowledge of the students with mathematical difficulties together with an increase in their contribution to the group. The growth in modelling competencies involved their ability to analyse situations and the growth of mathematical knowledge was evident in offering mathematical ideas during group work and in a better posttest performance. Student reflections indicated their awareness of these changes and of the appreciation of their ideas by their peers.     

Strategy,performance and operational research

This paper explores the nature of operational research and its interactions with performance measurement and strategy. It is argued that operational research (OR) is well fitted to handle strategic issues as the modelling approach of OR facilitates understanding and learning, and the evaluation of strategies prior to action. The development of problem structuring methods is also a key aid to strategy and policy formulation. OR is also beginning to play a role in performance measurement and there is an opportunity for OR to lead in the improvement of performance measurement systems.     

Facilitated modelling in strategy development: measuring the impact on communication,consensus and commitment

Facilitated modelling is used in supporting the resolution of strategic issues mainly because it is expected to improve communication between decision makers, foster consensus and create commitment. Researchers in both the strategy and facilitated modelling fields call for more systematic research on how strategy development works in practice and how outcomes are created. In this paper, three facilitated modelling cases on strategic issues are studied using both written questionnaires, developed in the strategy and decision support fields, and semi-structured interviews. Results of both measurement approaches are compared to determine (a) to what extent outcomes in participants’ own terms are similar to concepts in the questionnaire and (b) whether changes measured by both methods are similar. Interview results are used to assess (c) which elements of the intervention contribute to outcomes. Findings suggest that questionnaires offer clear benefits as standardized measurement of facilitated modelling outcomes.     

A Case Study in Community Care Using Systems Thinking

This paper uses a recent application of System Dynamics in community care to contribute to a clarification of the role of System Dynamics as a framework for strategic debate. A revised framework for System Dynamics within a philosophy of ‘modelling as learning’ is summarized. This framework is now referred to as Systems Thinking and combines knowledge acquisition and both qualitative and quantitative modelling, supported by microworlds and archetypes to aid dissemination of insights. The emphasis of the paper is on using qualitative models interactively with different groups of participants in the problem domain. The purpose is to assist the development of a shared understanding of how culture, power and politics combine to affect the behaviour of a process, when subjected to externally superimposed changes in responsibility.     

CFD modelling of thickeners at Worsley Alumina Pty Ltd

Computational fluid dynamics (CFD) modelling of process unit operations is a tool that is being used increasingly by mineral processing industries to reduce operating and capital costs and increase throughputs.Worsley Alumina first became involved with CFD modelling through support of the AMIRA Thickener Technology Project 266A in 1994, and subsequent extension projects in which CSIRO has been developing validated CFD models of thickener operation. The CSIRO Division of Minerals has been involved with CFD modelling since 1984 mainly on high temperature furnace applications and has been developing multi-phase thickener models since 1992. The benefits of obtaining a better understanding of flow patterns in thickeners using this modelling method became obvious and projects commenced in the third quarter of 1995 to utilise the CSIRO expertise. Projects have been ongoing almost continuously since that time. The CFD modelling was verified using tracers to measure actual flow patterns in a settler. Once verification had been achieved the CFD model was used to test innovative changes in design aimed at achieving higher throughputs and improved operation. These innovative changes when implemented on the full plant gave results similar to the CFD model predictions and resulted in improved process stabilisation, reduced chemical costs and very large savings in capital requirements for our major expansion that has just been completed. There are a number of assumptions made in the CFD model and these are discussed in detail in the paper together with details of individual CFD modelling projects and cost benefits achieved from completed projects.     

On the optimization of supply chain networking decisions

Companies strive to position themselves to maximize the value they add to the supply chains in which they are embedded. This raises strategic questions such as: Which durable resources should be developed to enhance current core competencies? Which activities should be externalized and to which potential partner should they be given? Which internal activities should be preserved and developed? How should the resources of the enterprise be allocated to activities? The aim of this paper is to propose a mathematical programming model of the extended enterprise which can be used to investigate this type of strategic networking issues. A number of general network modeling constructs are first proposed. A model to optimize the supply chain structure under specific assumptions on the nature of production, cost and value functions in typical production/distribution companies is then derived. A heuristic to obtain solutions from the model is also presented. Finally, an example based on a refrigerator company is used to illustrate the usefulness of the approach.     

Emergence of tables as first-graders cope with modelling tasks

In this action research, first-graders were challenged to cope with a sequence of modelling tasks involving an analysis of given situations and choices of mathematical tools. In the course of the sequence, they underwent a change in the nature of their problem-solving processes and developed modelling competencies. Moreover, during the task sequence, the first-graders spontaneously discovered the power of organizing problem data in a table. They did not merely use their existing mathematical knowledge, but also ‘reinvented’ tables as a new mathematical tool. This paper describes the gradual development of this tool as the children moved along the task sequence. Notably, the first-graders exhibited this progress in spite of having relatively little mathematical knowledge.     

Simulation in manufacturing and business: A review

This paper reports the results of a review of simulation applications published within peer-reviewed literature between 1997 and 2006 to provide an up-to-date picture of the role of simulation techniques within manufacturing and business. The review is characterised by three factors: wide coverage, broad scope of the simulation techniques, and a focus on real-world applications. A structured methodology was followed to narrow down the search from around 20,000 papers to 281. Results include interesting trends and patterns. For instance, although discrete event simulation is the most popular technique, it has lower stakeholder engagement than other techniques, such as system dynamics or gaming. This is highly correlated with modelling lead time and purpose. Considering application areas, modelling is mostly used in scheduling. Finally, this review shows an increasing interest in hybrid modelling as an approach to cope with complex enterprise-wide systems.     

Why are enterprise resource planning systems indispensable to supply chain management?

Supply chain design is becoming a core competency, and the enterprise resource planning (ERP) system is expected to be an integral component of supply chain management (SCM). Installing an ERP system is, however, expensive and risky. IT managers must decide how to use their limited resources and invest in the right product. Can an ERP system directly improve SCM competency? This study proposes a conceptual framework featuring the ERP benefits and SCM competencies, and examines the impacts of the former on the latter. The results confirm the operational, managerial, and strategic benefits of ERP for the SCM competencies, but not the IT infrastructure and organizational benefits as significant predictors of them. Moreover, more than 80% of respondents think it necessary to first adopt an ERP system as the backbone of company operations before deploying other enterprise systems (ES), such as the SCM system.     

Causal maps and the evaluation of decision options—a review

Causal maps are widely employed in problem-structuring interventions. They permit a rich representation of ideas, through the modelling of complex chains of argument as networks. The last stage of a problem-structuring intervention is often to identify and agree to a set of potential strategic options. In some circumstances the preferred direction may emerge naturally from a process of negotiation; in others further, more-or-less formal, analysis to evaluate the options and to understand their impacts on the goals could be helpful. Such analysis may help to bring closure to the process. The main aim of this paper is to review systematically the approaches for evaluating options following from the use of a causal map for problem structuring; some directly using the map structure, others working with concepts extracted from, or an external model derived from, the map. Following a proposed taxonomy, each approach is presented, and its advantages and disadvantages are discussed.     

Supply Chain Optimisation in the Paper Industry

We describe the formulation and development of a supply-chain optimisation model for Fletcher Challenge Paper Australasia (FCPA). This model, known as Paper Industry Value Optimisation Tool (PIVOT), is a large mixed integer program that finds an optimal allocation of supplier to mill, product to paper machine, and paper machine to customer, while at the same time modelling many of the supply chain details and nuances which are peculiar to FCPA. PIVOT has assisted FCPA in solving a number of strategic and tactical decision problems, and provided significant economic benefits for the company.     

Financial Modelling in a Banking Environment

The Bank of Ireland undertakes financial modelling for strategic planning purposes. The work was previously undertaken by a time-sharing bureau but is now performed on microcomputers. The paper briefly describes the modelling process and gives some points on the use of microcomputers.     

Market-based pricing in grids: On strategic manipulation and computational cost

Grid technologies and the related concepts of utility computing and cloud computing enable the dynamic sourcing of computer resources and services, thus allowing enterprises to cut down on hardware and software expenses and to focus on key competencies and processes. Resources are shared across administrative boundaries, e.g. between enterprises and/or business units. In this dynamic and inter-organizational setting, scheduling and pricing become key challenges. Market mechanisms show promise for enhancing resource allocation and pricing in grids. Current mechanisms, however, are not adequately able to handle large-scale settings with strategic users and providers who try to benefit from manipulating the mechanism. In this paper, a market-based heuristic for clearing large-scale grid settings is developed. The proposed heuristic and pricing schemes find an interesting match between scalability and strategic behavior.     

Energy models for decision making

Since the 1973 oil crisis there has been an explosion in energy modelling activities throughout the world. A bewildering array of models have been or are being developed. The models differ in their geographical scope (local, national, regional or global), their technical scope (a process, an industry, an energy source or all energy industries), their timescale (one to one hundred years) and their systems boundaries (energy, economy, society). In addition there are crucial differences in the level of detail modelled, in the way time is structured and in the way in which decisions are included or perhaps excluded from the model.The natural questions to ask are what sort of models are now available; which models are suitable for which purposes; what has been learnt so far; which are the promising directions for future developments? This paper draws on modelling experience both within the National Coal Board and elsewhere to discuss these questions. The paper contains the following sections: energy models and decision making processes; choosing model boundaries; logic and facts, the basis of the model; choice of energy model; links to the economy; future directions. The subject will be of interest to specialist energy modellers and those interested more generally in strategic modelling for government and industry.     

Qualitative chain graphs and their application

For many problem domains, such as medicine, chain graphs are more attractive than Bayesian networks as they support representing interactions between variables that have no natural direction. In particular, interactions between variables that result from certain feedback mechanisms can be represented by chain graphs. Using qualitative abstractions of probabilistic interactions is also of interest, as these allow focusing on patterns in the interactions rather than on the numerical detail. Such patterns are often known by experts and sufficient for making decisions. So far, qualitative abstractions of probabilistic interactions have only been developed for Bayesian networks in the form of qualitative probabilistic networks. In this paper, such qualitative abstractions are developed for chain graphs with the practical aim of using qualitative knowledge as constraints on the hyperspace of probability distributions. The usefulness of qualitative chain graphs is explored for modelling and reasoning about the interactions between diseases.     

Measuring and investigating strategic knowledge about drawing to solve geometry modelling problems

We report on the construction, validation, and implementation of an instrument for measuring students’ strategic knowledge about drawing for geometry modelling problems, namely, the strategic knowledge about drawing scale. We conducted a qualitative study and a quantitative study to validate the proposed construction and interpretation of the scale and to obtain initial findings on students’ strategic knowledge about drawing. Results showed that ninth-grade students in the intermediate achievement track had less elaborated strategic knowledge about drawing than their peers in the high achievement track. Further, strategic knowledge about drawing was found to be related to drawing accuracy and modelling performance even when cognitive abilities and interest were controlled for. The current study suggests that promoting strategic knowledge about drawing might be a means to increase drawing and modelling performance—especially among non-high-achieving students.     

Using spatial games to model dynamic evolutionary systems

Modelling the dynamics of evolutionary competing species on a physical grid is a challenging modelling problem. This paper presents a novel modelling approach for synthesizing evolutionary dynamics of competing species using a spatial game perspective. This modelling approach describes the movement of players (‘species’ in our context) across a lattice. The model is based on a payoff function which controls the move likelihood and direction of the players (‘predators’ and ‘preys’). Using simulated results, the paper provides a comparison between the spatial game model and an existing predator-prey dynamic model. Finally, a case study is performed to illustrate the application of this formalism and validate the model.     

O.R. Applications in Industry and Problems of Industrialisation of a Developing Economy with Special Reference to India

The paper has two distinct parts. The first part reviews industrial applications of O.R. in developing countries in general and India in particular. Based on the analysis, the paper suggests concrete steps for further use of operational research in industry.The second part of the paper deals critically with the problems of industrialisation leading to a specific industrial structure in the economy of a developing country. Analysing various relevant criteria for industrialisation of developing economies the paper outlines a methodology suitable for modelling the problem. It then attempts to identify the prerequisites for successful use of O.R. in the multicriteria problem of industrialisation. The paper also discusses the role that national and international agencies can play in bringing about more meaningful applications of O.R. in developing economies.