On the nature of discontinuities in system dynamics modelling of disrupted projects

When complex projects result in large-cost over-runs, managers want to understand why this happened. There may be the possibility of making a claim against another party, or managers may simply wish to learn from any mistakes made. When using system dynamics (SD) models to analyse the reasons for project over-runs as a part of a litigation or organizational learning process, there is a strong focus on explaining historical aspects precisely. This leads to a need for the inclusion of discontinuous variables. This paper discusses the nature of discontinuities in SD models of project over-runs. Examples are given to demonstrate that the modelling of such discontinuities needs to be an integral part of the continuous simulation modelling process. Their inclusion helps to improve model validity and also, by forcing validity, uncover the important drivers of project behaviour. The examples given in this paper are significant drivers and suggest important learning about the behaviour of disrupted complex projects.     

Planning logistics operations in the oil industry

In this paper we apply stochastic programming modelling and solution techniques to planning problems for a consortium of oil companies. A multiperiod supply, transformation and distribution scheduling problem—the Depot and Refinery Optimization Problem (DROP)—is formulated for strategic or tactical level planning of the consortium's activities. This deterministic model is used as a basis for implementing a stochastic programming formulation with uncertainty in the product demands and spot supply costs (DROPS), whose solution process utilizes the deterministic equivalent linear programming problem. We employ our STOCHGEN general purpose stochastic problem generator to ‘recreate’ the decision (scenario) tree for the unfolding future as this deterministic equivalent. To project random demands for oil products at different spatial locations into the future and to generate random fluctuations in their future prices/costs a stochastic input data simulator is developed and calibrated to historical industry data. The models are written in the modelling language XPRESS-MP and solved by the XPRESS suite of linear programming solvers. From the viewpoint of implementation of large-scale stochastic programming models this study involves decisions in both space and time and careful revision of the original deterministic formulation. The first part of the paper treats the specification, generation and solution of the deterministic DROP model. The stochastic version of the model (DROPS) and its implementation are studied in detail in the second part and a number of related research questions and implications discussed.     

A Language for Policy-Level Modelling

Despite a history of successful applications to operational-level problems, the vale of OR/MS modelling techniques as aids in policy/strategy formulation has not been widely demonstrated. In this paper, we suggest that the language of traditional OR/MS model structures is too restrictive to deal with issues typically confronted in policy-making. Differences between operational-level decision-making processes and policy/strategy formulation processes are discussed; alternative model structures are described and classified; and a modelling language for addressing issues of policy and strategy is proposed. The language is presented in set-theoretic terms, and the resulting structure implies that certain model classes accommodate policy-level management needs better than others. Furthermore, policy-level models must serve a role distinct from the prediction and optimization role typically served by operational-level models.     

Models for capacitated lot-sizing problem with backlogging,setup carryover and crossover

Setup operations are significant in some production environments. It is mandatory that their production plans consider some features, as setup state conservation across periods through setup carryover and crossover. The modelling of setup crossover allows more flexible decisions and is essential for problems with long setup times. This paper proposes two models for the capacitated lot-sizing problem with backlogging and setup carryover and crossover. The first is in line with other models from the literature, whereas the second considers a disaggregated setup variable, which tracks the starting and completion times of the setup operation. This innovative approach permits a more compact formulation. Computational results show that the proposed models have outperformed other state-of-the-art formulation.     

Assessing science students’ attitudes to mathematics: a case study on a modelling project with mathematical software

This article reports the attitudes of students towards mathematics after they had participated in an applied mathematical modelling project that was part of an Applied Mathematics course. The students were majoring in Earth Science at the National Taiwan Normal University. Twenty-six students took part in the project. It was the first time a mathematical modelling project had been incorporated into the Applied Mathematics course for such students at this University. This was also the first time the students experienced applied mathematical modelling and used the mathematical software. The main aim of this modelling project was to assess whether the students’ attitudes toward mathematics changed after participating in the project. We used two questionnaires and interviews to assess the students. The results were encouraging especially the attitude of enjoyment. Hence the approach of the modelling project seems to be an effective method for Earth Science students.     

An Efficient Geometric Integrator for Thermostatted Anti-/Ferromagnetic Models

(Anti)-/ferromagnetic Heisenberg spin models arise from discretization of Landau–Lifshitz models in micromagnetic modelling. In many applications it is essential to study the behavior of the system at a fixed temperature. A formulation for thermostatted spin dynamics was given by Bulgac and Kusnetsov, which incorporates a complicated nonlinear dissipation/driving term while preserving spin length. It is essential to properly model this term in simulation, and simplified schemes give poor numerical performance, e.g., requiring an excessively small timestep for stable integration. In this paper we present an efficient, structure-preserving method for thermostatted spin dynamics.     

Aspects of mathematical modelling related to optimization

Many practical optimization problems involved mathematical models of complex real-world phenomena. This paper discusses some aspects of modelling that influence the performance of optimization methods. Information and advice are given concerning the construction of smooth models, the transformation of an optimization problem from one category to another, scaling, formulation of constraints, and techniques for special types of models.     

On the modelling of heat exchangers and heat exchanger network dynamics using bond graphs

ABSTRACT

Heat exchanger networks are important systems in most thermal engineering systems and are found in applications ranging from power plants and the process industry to domestic heating. Achieving cost-effective design of heat exchanger networks relies heavily on mathematical modelling and simulation-based design. Today, stationary design calculations are carried out for all new designs, but for some special applications, the transient response of complete networks has been researched. However, simulating large heat exchanger networks poses challenges due to computational speed and stiff initial value problems when flow equations are cast in differential algebraic form. In this article, a systems approach to heat exchanger and heat exchanger network modelling is suggested. The modelling approach aims at reducing the cost of system model development by producing modular and interchangeable models. The approach also aims at improving the capability for large and complex network simulation by suggesting an explicit formulation of the network flow problem.     

Numerical Methods and Volatility Models for Valuing Cliquet Options

Several numerical issues for valuing cliquet options using PDE methods are investigated. The use of a running sum of returns formulation is compared to an average return formulation. Methods for grid construction, interpolation of jump conditions, and application of boundary conditions are compared. The effect of various volatility modelling assumptions on the value of cliquet options is also studied. Numerical results are reported for jump diffusion models, calibrated volatility surface models, and uncertain volatility models.     

What is important in the simulation of spray dryer performance and how do current CFD models perform?

Spray dryers are of considerable importance in many industrial drying operations, yet their modelling has been relatively neglected. Here we present a summary of many years work performed at Sydney University investigating the fundamental flow behaviour in dryers and their modelling using a commercial CFD code. The key point to emerge is the need to perform three-dimensional, transient calculations and to include hindered drying and wall interaction models if important issues of flow stability and wall deposition are to be studied. This issue of the need to have proper resolution of the flow at an affordable cost is addressed.     

Behavioural modelling of career progression in the European Commission

Though manpower planning models have been part of OR for many years, and simulation has always been acknowledged as a potential approach, there are few reported applications of its use. In this case-based study we report on a micro-simulation model that exploits the structure of the European Commission’s appraisal and promotion rules, and includes regression-based sampling schemes which allow for non-Normal error terms to represent behavioural factors that led to the need for a new system. With a suitably parsimonious formulation the 20,000 person model runs very effectively, and the transparency associated with simulation proves an important factor in the successful use of the model as the basis for designing a promotion box system that was implemented across the Commission in 2009. The simulation modelling incorporates many Markov-type elements, and we reflect on important lessons learned from this combined use of micro-simulation and Markov-based approaches to manpower modelling.     

Energy-economy models: A survey

In the turbulent environment that is now surrounding us, it has become obvious that the energy system cannot be treated in isolation, but within the context of a broader system which is the economy. Energy-economy models have thus attracted the attention of energy policy analysts, particularly in the last five years. This paper presents a critical review of some of the more recent models, and draws some conclusions on the actual and potential contribution of energy modelling in energy policy formulation. The first part of the paper presents a conceptual framework for energy-economy interactions. The process is described and key parameters are identified. The second part, after describing the general structure of energy-economy models and highlighting the basic structural components, reviews some representative models. The third part analyses the deficiencies of the models as forecasting devices and stresses their merits as tools for analysis in the energy policy formulation process.     

System dynamics applications to European health care issues

Taking a European perspective, a review is made of some system dynamics models which address health care issues. Suggestions are made for the types of role which these models should take, bearing in mind the strategic orientation of system dynamics modelling. Examples are described of qualitative models where influence diagrams are the main analytical tool. Quantitative system dynamics models have a contribution to make in epidemiological studies and have been used to analyse the AIDS epidemic. A detailed example of one aspect of model formulation is given. This concerns the AIDS incubation time distribution and shows how real-world complications arising from virological staging and treatment effects are handled in a model of AIDS spread.     

An Interactive Aid to Financial Planning

The problem of producing financial plans for the subsidiary of a multinational corporation is one which is critical, especially in uncertain times. In addition there is always a pressing time constraint. This paper describes a suite of models which are in use by Caltex Oil South Africa to assist in this area. The approach adopted was to provide simple models which work interactively. The financial planning analysts were able to be very involved in the project because a high level modelling language was used which they could easily comprehend. The tremendous benefits of this type of approach in terms of user acceptance and in other areas are examined.     

Modelling and information systems for senior management in local government: problems and prospects

The paper considers the role of modelling systems at senior levels in democratically accountable multi-service public sector organisations such as local government.The main basis for the arguments proposed is three years of project work terminating in mid-1977. During this period the writer acted as a consultant to the IBM (UK) Scientific Centre and was responsible for the day-to-day co-ordination of a major project undertaken in the first tier Welsh local authority, Clwyd County Council.The project, which involved substantial resource inputs from both IBM and the local authority, led to definitive conclusions as to the nature and potential value of the modelling system developed.The main purpose of this paper is to consider the extent to which multi-service modelling systems in general are of relevance to local government. The system developed in the Welsh local authority may be described as affording means oriented resource planning facilities. Further it was designed to generate short and medium term (up to five years) information.It is concluded that although at first sight the implementation of an extensive modelling system may seem to involve intervention on a narrow front the reality is that it impinges upon all the main organisational variables. Because of this the prospect for realising the potential of the system will vary considerably from organisation to organisation. It is important that this should be appreciated by senior management before they approve the commitment of resources to developments of this nature.     

Lagrangian and Eulerian models for simulating turbulent dispersion and coalescence of droplets within a spray

Lagrangian and Eulerian modelling approaches are compared for simulating turbulent dispersion and coalescence of droplets within a spray. Both models predict similar droplet dispersion rates and shifts in droplet size distribution due to coalescence within the spray, over a wide range of droplet and gas flows, and for sprays with different droplet-size distributions at the nozzle exit. The computer time required for simulating coalescence within a steady axisymmetric spray is of a similar order of magnitude regardless of which formulation, Eulerian or Lagrangian, is adopted. However, the Lagrangian formulation is more practical in terms of the range of applicability and ease of implementation.     

Modelling and evaluation of time aspects in business processes

There is a need for modelling and performance evaluation techniques and tools for a fast and reliable design of workflow systems. This paper introduces a modelling methodology based on coloured stochastic Petri nets. It allows the integration of control flow, organizational, information related and timing aspects in one modelling framework. The processing delays include stochastic distributions in addition to deterministic times. Several workflows and the effects of constrained shared resources needed for different tasks can easily be described and analysed together. Control flow and organizational aspects are modelled separately in resource and workflow models. These models are automatically compiled into one model, which can then be used for qualitative analysis or performance evaluation. The proposed modelling and evaluation method is supported by the software tool TimeNET. An application example shows its use.     

Teaching mathematical modelling in microeconomics

Three modelling excercises from microeconomics are presented, both as examples of a methodology for teaching economics to mathematically inclined students, and as a vehicle for teaching modelling as a general skill. The first exercise, a price adjustment model for perfect competition, is given in detail within a formulation/solution/generalization/validation scheme with suggestions for an interactive teaching strategy. The results of giving the exercise to a second‐year BSc class in Mathematics and Computing are reported. Outlines of two further exercises relating to oligopoly and related models are given, and an Appendix provides a series of graduated problems for the first of these exercises.