Modelling and analysis of multistage stochastic programming problems: A software environment

In many decision problems, time and uncertainty play important roles and stochastic programming models are well suited for capturing both these aspects. In this paper we focus our attention on the difficulties which arise in developing multi-period stochastic models and we outline those challenging aspects where the use of classical modelling techniques for deterministic problems prove to be inadequate. In particular, we discuss the development of a modelling and analysis environment which combines multidimensional databases (MDDB), declarative modelling languages and procedural languages. Our aim is to develop a versatile tool which generates multi-period stochastic models and supports the modeller in browsing of data and solutions across different time stages and among different scenarios.     

Modelling and simulation in business and industry: insights into the processes and practices of expert modellers

The simulation modelling process and individual practices of simulation modellers impact on the outcome of simulation studies. Despite this, the modelling and simulation literature lacks a rich body of evidence on the actual process and practices of modellers in the real world. This qualitative study aims to address this shortcoming by attempting to discover the underlying simulation modelling process of 20 expert modellers working within their typical contexts. Our study makes a valuable addition to simulation research by investigating how the expert modellers develop their simulation models and how their context may affect their simulation practices. The main finding is that most of the participants do not have a clearly defined or a formal process for developing their models. Instead, they follow a set of key steps and their individual practices depend on the context of the study. A number of contextual factors such as the term of model use, the size of the model and the complexity of the model, may affect the way in which a modeller goes about developing a simulation model. For instance, the extent to which a model is documented depends on the model life. This research contributes to enhancing our understanding of the simulation modelling process in varying contexts.     

Psychological aspects of equation-based modelling

Psychological aspects of equation-based modelling languages like Modelica are under-represented in literature. This does not reflect the growth of the corresponding userbase. In this paper we try to close this gap by tackling the problem from three sides: we conduct expert interviews, we conduct an experiment based on self-reported timings to analyse the effects of inheritance on understandability, and we conduct an online experiment to analyse the effects of model representations on the performance at modelling tasks. The expert interviews suggest that experienced modelling experts tend to develop their models from the top-down, while novices do the opposite. Results from the second experiment indicate that the effect of inheritance on the time to understand a model is both significant and large. The results of the last experiment imply that graphical representations outperform block-diagrams for several metrics. These results open a broad research field on the theory of good modelling practice.     

Embedding optimisation algorithms with Mosel

Algebraic modelling languages allow models to be implemented in such a way that they can easily be understood and modified. They are therefore a working environment commonly used by practitioners in Operations Research. Having once developed models, they need to be integrated inside the company information system. This step often involves embedding a model into a programming language environment: many existing algebraic modelling languages make possible to run parameterised models and subsequently retrieve their results, but without any facility for interacting with the model during the model generation or solution process.In this paper we show how to use the Mosel environment to implement complex algorithms directly in the modelling language.The Office cleaning problem is solved by a branch-and-cut algorithm, implemented entirely in the modelling language (including the definition of the callback function for the solver). Secondly, a cutting stock problem is solved by column generation, also implemented in the modelling language.AMS classification: 90Cxx, 65K05, 68N15     

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.     

An Interactive,Graphical Approach to Linear Financial Models

Early attempts to utilize linear algebraic (L.P.) techniques in financial planning met with little success. This was probably due to a misunderstanding of the process by which financial and corporate plans were formulated. The planning process is now better understood and the use of computer-based models is well accepted. However current modelling systems perform only simple arithmetic evaluations. There is a prima facie case for re-examining linear algebraic methods to exploit the considerable amount of information which is available within a plan. This paper describes the work done in the South of Scotland Electricity Board to develop an interactive financial modelling system.     

On dos languages and dos mappings

Roughly speaking,DOS systems formalize the notion of generatively deterministic context free grammars. We explore the containment relationships among the class of languages generated byDOS systems and other subclasses of the class of context free languages. Leaving the axiom of aDOS system unspecified yields aDOS scheme, which defines a mapping from words to languages over a given alphabet. We explore the algebraic properties ofDOS mappings and obtain an algebraic characterization of a fundamental subclass of theDOS mappings generated byDOS schemes which are propagating (non erasing) and have no cycles of derivability among letters of the alphabet. We apply this characterization to show that the mapping equivalence problem for propagatingDOS schemes is decidable.     

Genetic Algorithm based technique for solving Chance Constrained Problems

Management and measurement of risk is an important issue in almost all areas that require decisions to be made under uncertain information. Chance Constrained Programming (CCP) have been used for modelling and analysis of risks in a number of application domains. However, the resulting mathematical problems are non-trivial to represent using algebraic modelling languages and pose significant computational challenges due to their non-linear, non-convex, and the stochastic nature. We develop and implement C++ classes to represent such CCP problems. We propose a framework consisting of Genetic Algorithm and Monte Carlo Simulation in order to process the problems. The non-linear and non-convex nature of the CCP problems are processed using Genetic Algorithm, whereas the stochastic nature is addressed through Simulation. The computational investigations have shown that the framework can efficiently represent and obtain good solutions for seven test problems.     

Report on the activities of the working group on discrete mathematics

In the past decade there have been significant developments in computer technology and solution techniques for analysing business and industrial decision problems. In recent years good modelling systems have become available to ease the burden of model communication. Currently the single most important barrier to increased use of structured approaches to decision modelling is the acquisition of the necessary skills to initially develop models of complex decision systems. This paper examines the modelling process with reference to linear programming. Two related production planning problems are presented and their associated models developed. The relationship between the two problems is such that student modellers are forced to become involved in the important details of the problems and, by examining the nature of solution spaces in constrained optimisation, students are able to rapidly gain confidence and skills in modelling.     

Affine Mappings in Iterated Function Systems

Today the reproduction of pictures in journals and books is no longer possible without “information compression”. This important process needs “Iterated Function Systems”-in short IFS. Doing so, affine mappings and their properties play a fundamental role. In this paper we distinguish between distance contracting and area contracting mappings and we investigate the connections between. The main goal is to find a criterion which allows to decide if the iteration process of an IFS converges or not.     

Simulating and visualizing neural networks with Mathematica

Artificial neural networks (ANNs) are both mathematical models of the neural basis of higher-order cognitive functions, such as learning, and adaptive variations of the general linear and nonlinear regression. Students of psychology and cognitive science typically encounter ANNs in both contexts of their studies, especially at the graduate level, however, many of these students do not possess the programming skills to write their own simulations to test their application as cognitive and statistical models. In this paper, simulations using the mathematical programming language Mathematica are used to develop appropriate visualizations of one the foundation topics in ANNs (understanding why linear associative networks cannot learn the nonlinearly separable XOR function). It is argued that Mathematica and similar high-level interpreted packages provide a more accessible environment for nonprogramming students to further their understanding of this key area of psychological science and mathematical modelling.     

Statistical modelling and repeatable structures: purpose,process and prediction

Children have limited exposure to statistical concepts and processes, yet researchers have highlighted multiple benefits of experiences in which they design and/or engage informally with statistical modelling. A study was conducted with a classroom in which students developed and utilised data-based models to respond to the inquiry question, Which origami animal jumps the furthest? The students used hat plots and box plots in Tinkerplots to make sense of variability in comparing distributions of their data and to support them to write justified conclusions of their findings. The study relied on classroom video and student artefacts to analyse aspects of the students’ modelling experiences which exposed them to powerful statistical ideas, such as key repeatable structures and dispositions in statistics. Three principles—purpose, process and prediction—are highlighted as ways in which the problem context, statistical structures and inquiry dispositions and cycle extended students’ opportunities to reason in sophisticated ways appropriate for their age. The research question under investigation was, How can an emphasis on purpose, process and prediction be implemented to support children’s statistical modelling? The principles illustrated in the study may provide a simple framework for teachers and researchers to develop statistical modelling practices and norms at the school level.     

A generic model for simulating office process flows

In the field of simulation, the use of application-specific software can bring many benefits to the model-builder in terms of improved productivity and reduced skill requirements. Such software must have at its core a robust generic model for the application area which offers both the generality and sufficient detail to be able to simulate realistically. To develop such a core model, a thorough understanding of the problem area and simulation is needed. This paper describes one design for a generic core model for the simulation of office process flows where work volumes are substantial. It forms a part of a software package called SCOPE which provides a user-interface for data capture, and generates simulation models to be run using the HOCUS simulation software. Also described is the facility for static modelling which has been developed to make further use of the captured data using conventional mathematical modelling.     

Mathematical Programming Modelling Using MGG

MGG is a software package for the application of mathematicalprogramming (MP). It complements the Sciconic MP code by providinga facility for developing MP models quickly and efficiently,and it enables changes to be made easily to established models.It is available on a wide range of minis and mainframes anda version of it is available as part of the Micro LP systemon IBM PCs and compatibles. MGG is based on an approach to modellingMP problems which stresses the primacy of the mathematical formulation.The process of MP modelling is divided into two stages: modelpreparation and running of the model. The user writes a mathematicalformulation, which MGG converts to matrix generator and reportwriter programs. This is done once to produce the programs whichcan then be run many times on different data. This paper describesMGG and draws comparisons with other matrix generator and mathematicalprogramming languages. It starts by considering how an MP problemcan be described, and then sets out a methodology for formulation.The MGG language is based upon this approach. A simple exampleis presented which is shown both as an algebraic formulationand in the MGG language. The process of building and runningmodels with MGG is then described. Finally, some comments areoffered on experience of using the software.     

Modeling covariance matrices via partial autocorrelations

We study the role of partial autocorrelations in the reparameterization and parsimonious modeling of a covariance matrix. The work is motivated by and tries to mimic the phenomenal success of the partial autocorrelations function (PACF) in model formulation, removing the positive-definiteness constraint on the autocorrelation function of a stationary time series and in reparameterizing the stationarity-invertibility domain of ARMA models. It turns out that once an order is fixed among the variables of a general random vector, then the above properties continue to hold and follow from establishing a one-to-one correspondence between a correlation matrix and its associated matrix of partial autocorrelations. Connections between the latter and the parameters of the modified Cholesky decomposition of a covariance matrix are discussed. Graphical tools similar to partial correlograms for model formulation and various priors based on the partial autocorrelations are proposed. We develop frequentist/Bayesian procedures for modelling correlation matrices, illustrate them using a real dataset, and explore their properties via simulations.     

Modelling and solving environments for mathematical programming (MP): a status review and new directions

Languages and computing environments that support Mathematical Programming (MP) modelling continue to develop and evolve. In this paper: (i) We address declarative and procedural features of modelling languages. (ii) We assess developments which couple the modelling and the solving processes, typically column generation, the branch-and-price approach to Integer Programming (IP), and the sampling of scenarios within Stochastic Programming (SP). (iii) We consider how data modelling and symbolic modelling naturally come together and are used within the information value chain. (iv) Finally, we investigate the features of new tools, which support prototyping of optimisation based Decision Support (DS) applications.     

Assuring consistency in mixed models

Information systems security defines three properties of information: confidentiality, integrity, and availability. These characteristics remain major concerns throughout the commercial and military industry. Ordinary users have taken these features as basis for their businesses. Furthermore, users may find it necessary to combine policies in order to protect their information in a suitable way. However, inconsistencies may arise as a result of implementing multiple secrecy and privacy models; and therefore, render these services unsecure. In this paper, we propose an approach to detect and report inconsistencies when choosing mixed models for integrity and security. It is based on specifying the policies in first order logic and applying formal analysis. We demonstrate the feasibility of our proposition by applying it to the Clark Wilson and role based access control models. We use the Alloy language and analyzer to formalize the mixed model and check for any inconsistencies.     

Forecasting model with asymmetric market response and its application to pricing of consumer package goods

This paper presents a dynamic forecasting model that accommodates asymmetric market responses to marketing mix variable—price promotion—by threshold models. As a threshold variable to generate a mechanism for different market responses, we use the counterpart to the concept of a price threshold applied to a representative consumer in a store. A Bayesian approach is taken for statistical modelling because of advantages that it offers over estimation and forecasting. The proposed model incorporates the lagged effects of a price variable. Thereby, myriad pricing strategies can be implemented in the time horizon. Their effectiveness can be evaluated using the predictive density. We intend to improve the forecasting performance over conventional linear time series models. Furthermore, we discuss efficient dynamic pricing in a store using strategic simulations under some scenarios suggested by an estimated structure of the models. Empirical studies illustrate the superior forecasting performance of our model against conventional linear models in terms of the root mean square error of the forecasts. Useful information for dynamic pricing is derived from its structural parameter estimates. This paper develops a dynamic forecasting model that accommodates asymmetric market responses to marketing mix variable—price promotion—by the threshold models. Copyright © 2005 John Wiley & Sons, Ltd.