Strongarm arcade games: a case study in mathematical modelling

Two linked cases are described, that have been used many times over many years with MBA students to teach both basic spreadsheet design and mathematical modelling and to act as a framework to stimulate thought about the wider considerations associated with the application of mathematical models. The broad aspects of the mathematical modelling methodology that are taught are first briefly considered. The simpler case together with its more demanding extension are both presented. The students' approaches are then categorised and the common mistakes/weaknesses and the strength of submissions are listed. This paper closes with a consideration of the value of the cases in student teaching. Solutions to both cases, applying the mathematical modelling methodology in detail, are given in Appendices.     

The Validation of Expert Systems — Contrasts with Traditional Methods

Recent research has demonstrated that little validation is carried out during and after the building of operational research models for decision support. In a subject area that has been of great interest for more than a decade, this reflects the fact that validation is not yet firmly embedded into the methodology of mathematical modelling that underpins conventional decision support systems. With the interest now being shown in expert systems, it is important to devise an appropriate methodology of validation for such systems. This paper contributes to this development by describing the types of validation that should be performed with decision support systems, and compares and contrasts the features found in the validation of mathematical models with those required of validation of expert systems.     

A Framework for Teaching OR Techniques

A five-stage approach to mathematical modelling is reviewed. It is shown how this can be used as a framework for introducing the teaching of simple stock control and distribution, financial modelling and planning, linear programming, decision trees, network analysis and discrete-event simulation. The framework puts emphasis on the conceptualization and verbalization stages, which provides a unifying link for the techniques described and is found substantially to improve formulation skills.     

Automated generation of LFT-based parametric uncertainty descriptions from generic aircraft models

A computer assisted modelling methodology is developed for the generation of linearized models with parametric uncertainties described by Linear Fractional Transformations (LFTs). The starting point of the uncertainty modelling is a class of generic nonlinear aircraft models with explicit parametric dependence used for simulation purposes. The proposed methodology integrates specialized software tools for object-oriented modelling, for simulation, and for numerical as well as symbolic computations. The methodology has many generic features being applicable to similar nonlinear model classes.     

Introducing mathematical modelling to undergraduates

Some motivation for, and thoughts behind, the development of a course in mathematical modelling are described. The structure of the course and some of the problems of teaching and assessment are reviewed. The course has the characteristics that it is introductory and discipline‐independent.     

A modelling framework for comparative testing of energy forecasts

A project is described in which a methodology was developed for the comparative testing of medium-term national energy forecasts. The basis of the approach is a computer modelling system which can be used flexibly to investigate the dynamics of alternative assumptions about energy futures. The application of the methodology to the forecasts produced by a particular research group is discussed and the educative value of a modelling approach for the users in this case is explained. The study is intended as a contribution to the U.K. national debate on energy policy.     

Introductory business OR cases: successful use of cases in introductory undergraduate business college operational research courses

A case methodology for developing the modelling skills of students in introductory operational research courses taught in undergraduate business programmes is presented. Motivated by a desire to develop such skills in students when the primary objective of such courses was to expose these students to various solution techniques, the approach takes on greater relevance now that many instructors of such courses have shifted their focus to the development of modelling skills. Example case scenarios that have been used by the author in the classroom are presented, and a comparison of the results achieved by the author after implementation of the case methodology is made with those achieved by the author prior to implementation.     

A positive approach to estimating the weights for quadratic multiple objective programming

This paper integrates positive and normative approaches to modelling. The normative approach uses assumptions associated with multiple objective programming. The positive approach uses past observations to estimate the weights associated with each objective criteria. The technique encompasses both linear and non-linear objectives such as profit, cost and risk as well as quadratic calibration terms. The proposed methodology minimizes the sum of squared errors about the ideal multiple objective function, that is one that would reproduce observed results, rather than to minimize errors between fitted and observed activity levels. The technique removes the need to rely upon the use of abstract restraints normally applied to mathematical programming methods and provides a more objective means of testing the appropriateness of a model than previously. The technique has many applications in the field of mathematical modelling such as forecasting and analysing changes in decision-making and behaviour.     

Increasing engineering students' awareness to environment through innovative teaching of mathematical modelling

This article presents the results of two studies on using aninnovative pedagogical strategy in teaching mathematical modellingand applications to engineering students. Both studies are dealingwith introducing non-traditional contexts for engineering studentsin teaching/learning of mathematical modelling and applications:environment and ecology. The aims of using these contexts were:to introduce students to some of the techniques, methodologiesand principles of mathematical modelling for ecological andenvironmental systems; to involve the students in solving real-lifeproblems adjusted to their region emphasizing the aspects ofboth survival (short term) and sustainability (long term); toencourage students to pay attention to environmental issues.On one hand, the contexts are not directly related to engineering.On the other hand, the chances are that many graduates of engineeringwill deal with mathematical modelling of environmental systemsin one way or another in their future work because nearly everyengineering activity has an impact on the environment. The firststudy is a parallel study conducted in New Zealand and Germanysimultaneously with first-year students studying engineeringmathematics. The second study is a case study of the experimentalcourse Mathematical Modelling of Survival and Sustainabilitytaught to a mixture of year 2–5 engineering students inGermany by a visiting lecturer from New Zealand. The modelsused with the students from both studies had several specialfeatures. Analysis of students’ responses to questionnaires,their comments and attitudes towards the innovative approachin teaching are presented in the article.     

Building a local conceptual framework for epistemic actions in a modelling environment with experiments

A local conceptual framework for the construction of mathematical knowledge in learning environments with experiments is developed. For this purpose, the mathematical modelling framework and the epistemic action model for abstraction in context are used simultaneously. In a case study, experiments of pre-service teachers with the motion of a ball on a circular billiard table are analysed within the local conceptual framework. The role of the experiments for epistemic actions of mathematical abstractions is described. In the case study, two different types of students’ approaches to the role of experiments can be distinguished.     

Modelling in Mathematics Classrooms: reflections on past developments and the future

This paper describes the development of mathematical modelling as an element in school mathematics curricula and assessments. After an account of what has been achieved over the last forty years, illustrated by the experiences of two mathematician-modellers who were involved, I discuss the implications for the future—for what remains to be done to enable modelling to make its essential contribution to the «functional mathematics», the mathematical literacy, of future citizens and professionals. What changes in curriculum are likely to be needed? What do we know about achieving these changes, and what more do we need to know? What resources will be needed? How far have they already been developed? How can mathematics teachers be enabled to handle this challenge which, scandalously, is new to most of them? These are the overall questions addressed. The lessons from past experience on the challenges of large-scale of implementation of profound changes, such as teaching modelling in school mathematics, are discussed. Though there are major obstacles still to overcome, the situation is encouraging.     

露天矿卡车运输系统最佳调度的数学模型及其数值解法研究

文章分析了目前卡车调度系统的建模情况,应用最佳控制的理论建立了卡车调度系统的数学模型,并结合一简例,分析了数值解法,给出简例的数值解。通过对数值解的分析,说明数学模型和数值解法都是正确的     

Operational Research and Corporate Planning in Railway Management

The current corporate planning process in Westrail is described and the roles played by operational research and mathematical modelling identified. They do not include forecasting the future. Instead of the "predict and prepare paradigm" a planning approach that tries to design the future has been adopted. The organisation is described in terms of how it has evolved, what it now is, and the key features of its environment. The three stages of planning are described-strategic, tactical and operational. These provide the means for management control of the railway. Environmental assessments linked to goal setting activities are incorporated within the planning process. The significance of operational research in planning, in particular mathematical modelling, is also described. Instead of finding problems to which existing techniques can be applied, O.R. is used to provide effective operational and planning systems as a means of assisting management to design the future for the organisation.     

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.     

Modelling and Simulation of Heat and Mass Transfer,via Symbolic Computation

This basically tutorial/case study paper illustrates the application of symbolic computation for two classical cases of chemical engineering, namely the modelling and simulation of a heat transfer process intensified by fin-covered surface, and a convective mass transport with first order irreversible chemical reaction. It has been shown that computer algebra provides a comfortable and elegant way to solve such technical problems in fully analytical form, with standard mathematical knowledge.     

Modelling variations in hospital service delivery based on real time locating information

Variations in service delivery have been identified as a major challenge to the success of process improvement studies in service departments of hospital such as radiology. Largely, these variations are due to inherent system level factors, i.e., system variations such as unavailability of resources (nurse, bed, doctors, and equipment). These system variations are largely unnecessary/unwarranted and mostly lead to longer waiting times, delays, and lowered productivity of the service units. There is limited research on identifying system variations and modelling them for service improvements within hospital. Therefore, this paper proposes a modelling methodology to model system variations in radiology based on real time locating system (RTLS) tracking data. The methodology employs concepts from graph theory to identify and represent system variations. In particular, edge coloured directed multi-graphs (ECDMs) are used to model system variations which are reflected in paths adopted by staff, i.e., sequence of rooms/areas traversed while delivering services. The main steps of the methodology are: (i) identifying the most standard path followed by staff for service delivery; (ii) filtering the redundant events in RTLS tracking database for analysis; (iii) identifying rooms/areas of hospital site involved in the service delivery; (iv) determining patterns of paths adopted by staff from filtered tracking database; and, (v) representation of patterns in graph based model called as edge coloured directed multigraphs (ECDMs) of a role. A case study of MR scanning process is utilized to illustrate the implementation of the proposed methodology for modelling system variations reflected in the paths adopted by staff.     

Diverse Imprecise Goal Programming Model Formulations

The goal programming (GP) model is probably the best known in mathematical programming with multiple objectives. Available in various versions, GP is one of the most powerful multiple objective methods which has been applied in much varied fields. It has also been the target of many criticisms among which are those related to the difficulty of determining precisely the goal values as well as those concerning the decision-maker's near absence in this modelling process. In this paper, we will use the concept of indifference thresholds for modelling the imprecision related to the goal values. Many classical imprecise and fuzzy GP model formulations can be considered as a particular case of the proposed formulation.     

Time series analysis

Current univariate and multivariate time series modelling procedures are reviewed. Areas of disagreement are discussed, such as the choice of a forecasting method, whether to use time series analysis or econometrics for economic data, the merits of prior seasonal adjustment, and the advisability of prewhitening in multivariate modelling. Some recent developments in model identification, estimation and model criticism are described. It is argued that too little attention has been paid to allowing for departures from the model; this leads to a discussion of exploratory and robust techniques. Finally, it is pointed out that little has been done on modelling positive and discrete-valued time series of importance in OR such as lifetimes and counts; some recent proposals are described.     

An overview of heuristic solution methods

Besides those analysts who are already familiar with a number of heuristic methods, this paper should also be of interest to those analysts and managers who, although not yet aware of specific heuristic approaches, are quite comfortable with the use of mathematical modelling as an aid to decision making. It is concerned with obtaining usable solutions to well-defined mathematical representations of real-world problem situations. Heuristic procedures are defined and reasons for their importance are listed. A wide variety of heuristic methods, including several metaheuristics, are described. In each case, references for further details, including applications, are provided. There is also considerable discussion related to performance evaluation.     

A Problem-driven Approach to Expert System Development

Expert system technology can fairly be described as high profile at present. Yet its track record as a useful method for tackling problems is subject to widely differing views. This paper considers the domain of production planning and control, which has been described as a good application area for expert systems a domain where OR has had little success. The authors argue that mainstream expert system methodology is exploratory rather than problem-driven and thus is not suited to the domain. A problem-driven approach to expert system development is presented, an approach which makes use of soft systems methodology. The reasons for such an approach within production planning and control are discussed, and the use of soft systems methodology within the approach is reflected on.