Developing a Visual Interactive Model for Corporate Cash Management

The operational research/management science journals contain an extensive literature that addresses the corporate cash management problem; yet few, if any, companies make use of any of this published work in their daily cash-management decision making. A review of the literature suggests that the reason for this lack of applications may well be poor problem formulation—the problems that are solved in the literature as ‘cash management’ problems evolve from a ‘hard systems’ view of real-world cash management. However, the problem as perceived by cash managers involves both dynamic and loosely structured components which are difficult to model using classical (i.e. ‘hard systems’) approaches.We therefore decided to approach the cash management problem as an experiment in the use of a novel visual interactive problem solving (VIPS) methodology. The aim of the experiment was to develop an implementable, visual interactive model to support daily cash management decision making. Working closely with a corporate cash manager, we first developed a visual model of his daily decision problem and then agreed on the feasible options and the interactive requirements. At this stage, the problem was sufficiently well defined for a mathematical model to be built and the visual model made ‘smart’.This paper discusses the results of this experiment and suggests that VIPS may have distinct advantages as a problem-solving technique in loosely structured, ‘messy’ problem situations.     

Towards a System of Systems Methodologies

This paper sets out to consider O.R. as a problem-solving methodology in relation to other systems-based problem-solving methodologies. A ‘system of systems methodologies’ is developed as the interrelationship between different methodologies is examined along with their relative efficacy in solving problems in various real-world problem contexts. In a final section the conclusions and benefits which stem from the analysis are presented. The analysis points to the need for a co-ordinated research programme designed to deepen understanding of different problem contexts and the type of problem-solving methodology appropriate to each.     

Evolution of ‘N’ polar curves by extension of focal points (by more than two) of an Ellipse

The author introducedA third focal point (during 1965) in between the two focii of an Ellipse in order that a curve similar to thelongitudinal cut section of an egg results. Such a curve was required to prove the author’s assumption that theabnormal load sustaining capacity of an egg is due to its CURVATURE and ultimately to exploit this property in possible Engineering designs. In this paper, the properties of a new curve withThree collinear focii (to be defined as anegglipse) are presented. Further, the general polar curve with ‘N’collinear poles called ‘N’polar curve is introduced.     

Beyond a System of Systems Methodologies

This paper describes a research programme which used the idea that there is a ‘system of systems methodologies’ to analyse the relationship between OR and other systems-based, problem-solving approaches, and to relate different systems methodologies to appropriate problem-contexts. The results are promising for those who wish to broaden the theoretical basis of OR in order to extend its domain of effective application. Further progress, however, depends upon reconstituting the research programme on surer theoretical foundations. Unless this is done, both the potential of the original work and its initial intent risk being lost. It is now necessary to go beyond ‘a system of systems methodologies’ and to embed that work in an explicit proposal for a critical management science.     

Problem-Solving Methodology Design on the Run

This paper discusses a risk analysis study which considered the best way to cross a river with a large diameter gas pipeline, one possibility being a bridge carrying a large diameter oil line. About 30 ‘riskateers’ were involved, over a 3-month period, most of whom were engineers or economists with no risk analysis, O.R. or systems experience. A large number of interested parties were involved, with different perspectives. The paper stresses methodology design as an organizational vehicle, and the implications of designing problem-solving methodology in the midst of a problem-solving process.     

Designing Effective Simulation-based Decision Support Systems: An Empirical Assessment of Three Types of Decision Support Systems

This paper addresses the design of effective simulation-based decision support systems (DSS). An experiment was conducted using three different DSS tools developed around three types of simulation model—traditional, conventional visual interactive simulation (VIS), and ‘paired-systems’ VIS. Subjects were asked to perform a decision making task and their performance was evaluated. Subjects who used the DSS based on a ‘paired systems’ VIS model were found to be both the most effective and the most efficient at the problem-solving task. Subjects provided with the DSS based upon a conventional VIS model were found to be more effective at the task than the group provided with the traditional simulation-based DSS.     

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.     

On the information about individual utilities used in social choice

This paper investigates the consequences of the requirement tha a social choice method should convey as much information as possible about the individuals' values. It is first shown that if interpersonal comparisons of utilities are excluded, then the only information about individual values that can be used in the context of social choice is ordinal information. It is then argued that Arrow's independence condition demands that only a part of the information about the individual preferences be used in the social choice. Finally, it is shown that the requirement of maximal information gives strong support to Smith's (1973) ‘separability’ condition. In combination with Smith's result this shows that the choice methods that convey the most information about individual preferences are the ‘generalized point systems’ (also called ‘scoring functions’ or ‘ranking systems’).     

Frameworks of Inquiry: OR Practice Across the Hard—Soft Divide

The growing interest in understanding the practice of OR has, not unnaturally, tended to concentrate upon experience with those ‘soft’ methodologies which address both process and content management issues. This paper uses a detailed account of one practitioner's work in a ‘traditional’ area of OR (linear programming) to demonstrate how process-related issues are handled there, and argues that more extensive reporting of such conventional practice is essential for the health of the discipline. In particular, it suggests that an emphasis on discussing the development of working relationships between OR practitioners and their clients might usefully supplant the contemporary emphasis on the ‘project’.     

Variations on a theme: introducing new representations of fraction into two classrooms

Abstract

The interplay between generalisations and particular instances—examples—is an essential feature of mathematics teaching and learning. In this paper, we bring together our experiences of personal and classroom mathematics activity, and demonstrate that examples do not always fulfil their intended purpose (to point to generalisations). A distinction is drawn between ‘empirical’ and ‘structural’ generalisation, and the role of generic examples is discussed as a means of supporting the second of these qualities of generalisation.     

On Existence of Solution, Oscillatory and Non-Oscillatory Properties of Delay Impulsive Differential Equations Containing ‘Maximum’

In this paper, we determined the criteria for the existence of solutions for delay impulsive differential equations containing ‘maximum’ (DIDEM) using the Morales’ fixed point theorem. An impulsive analogue of the Gronwall-Bellman’s inequality with deviating argument is also considered. Some results on the oscillation and non-oscillation of solutions of the (DIDEM) are also obtained. Applications of the oscillatory results obtained are made to four non-linear examples one of which is a military model and upper bounds found for the solutions of the impulsive Fitzhugh-Naguno model and an impulsive nonlinear control system.     

Fixed point theorems for fuzzy numbers

In this paper we study the problem of the existence of fixed points for fuzzy maps. We first define uniform structures on sets of fuzzy subsets and describe the ‘closed convergence’ and ‘myope convergence’ structures which have properties close to the corresponding traditional ones. We then give two ways in order to obtain fixed point results. We finally give applications of these results, particularly to fuzzy Markov processes.     

Beyond methodology choice: critical systems thinking as critically systemic discourse

Professional competence in applied disciplines such as OR/MS requires both technical expertise and critically reflective skills. Yet, a widespread misconception has taken hold of the OR/MS community: ‘critical’ and ‘emancipatory’ systems methodologies are opposed to ‘hard’ and ‘soft’ ones as if they were sensible alternatives. Accordingly, adequate ‘methodology choice’ is now widely considered a key condition of reflective professional practice; critical systems thinking (CST) is understood to deal mainly with this issue. The present paper argues that this conception of CST is neither theoretically sound nor conducive to reflective practice. An examination of the two major current strands of CST suggests some basic requirements of an alternative conception: (1) Reflective practice depends more on a framework of critical argumentation and discourse than on a framework of methodology choice. (2) A well-conceived discursive systems approach will give a proper place to the public sphere. (3) The much-discussed emancipatory orientation of CST inheres in the methodological requirements of discourse rather than in an arbitrary ‘commitment’ on the part of the systems practitioner. (4) Systemic boundary critique—the methodological core concept of critical systems heuristics (CSH)—allows us to translate these requirements into practical methodology. (5) Contrary to present conceptions of methodological pluralism or ‘complementarism’, boundary critique must not be subordinated to methodology choice, for it is constitutive of all critical inquiry and practice. These considerations lead to a reconstitution of CST, and to a new view of reflective professional practice in general, as critically systemic discourse.     

Dynamic programming in cricket: optimizing batting order for a sticky wicket

In cricket, a rain-affected pitch can make batting more difficult than normal. Several other conditions such as poor light or an initially lively pitch, may also result in difficulties for the batsmen. In this note, we refer to all of them as ‘sticky wickets’. On sticky wickets, lower order batsmen are often sent into ‘hold the fort’ until conditions improve. In this paper, a stochastic dynamic programming model is used to examine the appropriateness of this policy. The model suggests that the tactic is often optimal when the sticky wicket persists until the end of the day's play, but not often when the sticky wicket is transitory. In some circumstances, it is worthwhile, on a normal wicket near the end of the day, to send in a lower order batsman to hold the fort (a night watchman): when the wicket is sticky, this tactic is even more worthwhile.     

Transportation policies for single and multi-objective transportation problem using fuzzy logic

In this paper, single and multi-objective transportation models are formulated with fuzzy relations under the fuzzy logic. In the single-objective model, objective is to minimize the transportation cost. In this case, the amount of quantities transported from an origin to a destination depends on the corresponding transportation cost and this relation is verbally expressed in an imprecise sense i.e., by the words ‘low’, ‘medium’, ‘high’. For the multi-objective model, objectives are minimization of (i) total transportation cost and (ii) total time for transportation required for the system. Here, also the transported quantity from a source to a destination is determined on the basis of minimum total transportation cost as well as minimum transportation time. These relations are imprecise and stated by verbal words such as ‘very high’, ‘high’, ‘medium’, ‘low’ and ‘very low’. Both single objective and multi-objective problems using Real coded Genetic Algorithms (GA and MOGA) are developed and used to solve the single level and bi-level logical relations respectively. The models are illustrated with numerical data and optimum results are presented.     

High school prospective teachers’ problem-solving reasoning that involves the coordinated use of digital technologies

The aim of this study was to characterize and discuss ways of reasoning that prospective high school mathematics teachers develop and exhibit in a problem-solving scenario that involves the coordinated use of digital technologies. A conceptual framework that includes Virtual Learning Spaces (VLS) and Resources, Activities, Support and Evaluation (RASE) essentials is used to introduce and support a problem-solving approach to structure learners’ problem-solving activities that encouraged them to share ideas, discuss and extend mathematical discussions beyond formal settings. Main results indicated that prospective high school teachers relied on a set of tool affordances (dragging objects, looking and exploring object’s loci, using sliders, quantifying and visualizing mathematical relations, etc.) to formulate, explore and identify properties or relations to share, discuss and support mathematical conjectures. In this context, the participants recognized and valued the importance of using several tools to both dynamically represent and explore mathematical tasks and to share and constantly refine their mathematical ideas and problem-solving approaches.     

Rethinking tradeoffs and OR/MS methodology

The purpose of this paper is to explore the role of a process known as the ‘evaporating cloud’ (EC) as a way of enhancing OR/MS modelling. While other authors have described the use of the EC process to explore the tradeoffs in a traditional Economic Order Quantity model, this paper demonstrates the use of the EC with a facilities location problem, which was originally solved via mixed integer programming. We relate our findings to OR/MS modelling in general, and argue that the EC could contribute effectively to different phases of the problem-solving process, for example, aiding the problem-structuring phase and helping to find better solutions in many OR/MS modelling situations. We demonstrate that the EC is a valuable tool to use in modelling practice as a problem-structuring tool, as a way of dealing specifically with tradeoffs, and that it can therefore be a useful complement to OR/MS methodology, and contribute to OR/MS practice and teaching.     

The fuzzy decision problem: An approach to the point estimation problem with fuzzy information

This paper is devoted to the extension of the Bayesian method for the point estimation, when the available information is ‘vague’.In the nonfuzzy case, the parametric estimation can be approached as a particularization in the statistical decision problem. This motivates us to accomplish the mentioned extension by looking at the parametric estimation in the fuzzy case as a special situation in the fuzzy decision problem (defined by Tanaka, Okuda and Asia).In this way, concepts in the fuzzy decision problem are first ‘expressed’ in the estimation terminology. Then, on the basis of these concepts, we shall introduce some notions and state some interesting results. Finally, several illustrative examples will be exposed.     

On focal locus of submanifolds of naturally reductive compact Riemannian homogeneous spaces

The purpose of this paper is to discuss focal points of submanifolds of naturally reductive compact Riemannian homogeneous spaces. Focal points have been studied by other workers [1, 4, 7]. In this paper we have estimated location of focal points along geodesic and obtained a condition under which a point is a focal point along geodesic.