Modelling Under Uncertainty: Comparing Three Acid-Rain Models

This paper examines three themes of modelling. Its primary concern is with the problem of representing uncertainty in models, while the issues of interactive computer modelling and the use of models as decision aids also receive some attention. These issues are addressed by way of a comparative analysis of three models of the acid-deposition problem which have been developed in recent years in the UK and USA. The design of these models and the methods employed to represent uncertainty are described. The strengths and weaknesses of these techniques, and the various unresolved issues which these models have highlighted, are discussed.     

An interactive,computer-aided ship scheduling system

This paper is concerned with a fleet scheduling and inventory resupply problem faced by an international chemical operation. The firm uses a fleet of small ocean-going tankers to deliver bulk fluid to warehouses all over the world. The scheduling problem centers around decisions on routes, arrival/departure times, and inventory replenishment quantities. An interactive computer system was developed and implemented at the firm, and was successfully used to address daily scheduling issues as well as longer range planning problems. The purpose of this paper is to first present how the underlying decision problem was analyzed using both a network flow model and a mixed integer programming model, and then to describe the components of the decision support system developed to generate schedules. The use of the system in various decision making applications is also described.     

Non-procedural large-scale modelling: Theoretical and practical significanc

One of the current major developments of computer science is a trend away from procedural programming languages, towards the creation of non-procedural languages. The paper examines the implications of this trend on large-scale mathematical modelling. In a procedural program, the basic rule is the assignment statement. In contrast, a non-procedural program consists of an underdetermined system of equations and nothing else. Consequently a non-procedural program is far more flexible and powerful than its procedural counterpart. While the latter describes only one problem the former may be used to solve every legitimate problem about the object represented by the program. The first major difficulty in designing a non- procedural modelling system is to specify the information to be derived from the non- procedural program. An interactive solution to this problem is presented,based on a purely structural analysis of the program. This solution fully exploits thesparsity of the program, can be efficiently implemented, and enables the user both to identify and to solve every legitimate problem associated with the program.     

Introducing computational thinking through hands-on projects using R with applications to calculus,probability and data analysis

The goal of this paper is to promote computational thinking among mathematics, engineering, science and technology students, through hands-on computer experiments. These activities have the potential to empower students to learn, create and invent with technology, and they engage computational thinking through simulations, visualizations and data analysis. We present nine computer experiments and suggest a few more, with applications to calculus, probability and data analysis, which engage computational thinking through simulations, visualizations and data analysis. We are using the free (open-source) statistical programming language R. Our goal is to give a taste of what R offers rather than to present a comprehensive tutorial on the R language. In our experience, these kinds of interactive computer activities can be easily integrated into a smart classroom. Furthermore, these activities do tend to keep students motivated and actively engaged in the process of learning, problem solving and developing a better intuition for understanding complex mathematical concepts.     

An application of interactive analysis and computer graphics in stochastic modeling

This paper will describe the application of an interactive queueing network analyzer and an interactive graphics system to the analysis of a multiple processor computer system. The application of these tools greatly increased the productivity of the modelers and resulted in insights which would have otherwise been difficult, if not impossible, to obtain. With this experience as background, we discuss how the increasing availability of computing resources, especially high resolution interactive computer graphics and sophisticated modeling packages, is likely to have a profound influence on the applied stochastic modeler.     

Trends in Computer Graphics

The increasing use of powerful interactive microcomputer systems will lead to a much wider use of graphics. This paper presents the basis of interactive computing using graphics terminals, as a contribution to increasing the understanding of this area. In particular, the raster terminal is presented in some detail as a powerful and relatively cheap display.     

An Investigation of Visual Interactive Simulation Methods Using the Job-Shop Scheduling Problem

This paper describes the use of the job-shop scheduling problem in order to investigate the potential of visual interactive simulation methods. Batch simulation methods are compared with visual interactive simulation methods for the job-shop problem. The paper shows that improved solutions can be obtained by having a visual, dynamic representation of a job-shop problem.     

Earth Vision 2000: Examining Students' Representations of Complex Data Sets

Graphic representations are powerful tools used by scientists and other professionals to help them understand multifaceted natural phenomena. They can also serve teachers and students as they attempt to understand complex data sets. This study examines pencil‐and‐paper graphs produced by students at the beginning of a 1‐week summer teacher/student institute, as well as computer‐based graphs produced by the same students at the end of the institute. Initial problems with managing the data set and producing meaningful graphs disappeared quickly as students used a process of “building up” to handle the complexity of web‐based data on water quality. This process is examined, as are findings from the institute related to (a) barriers to accessing web‐based data, (b) students' problem‐solving processes, and (c) the promise of this approach for learning about environmental science issues.     

An algorithm for least squares analysis of spectroscopic data

This paper describes a variant of the Gauss-Newton-Hartley algorithm for nonlinear least squares, in which aQR implementation is used to solve the linear least squares problem. We follow Grey's idea of updating variables at intermediate stages of the orthogonalization. This technique, applied in partitions identified with known or suspected spectral lines, appears to be especially suited to the analysis of spectroscopic data. We suggest that this algorithm is an attractive candidate for the optimization role in Ekenberg's interactive computer graphics curve fitting program.     

Searching for knowledge in a world flooded with facts

The wide availability of computer technology and large electronic storage media has led to an enormous proliferation of databases in almost every area of human endeavour. This naturally creates an intense demand for powerful methods and tools for data analysis. Current methods and tools are primarily oriented toward extracting numerical and statistical data characteristics. While such characteristics are very important and useful, they are often insufficient. A decision maker typically needs an interpretation of these findings, and this has to be done by a data analyst. With the growth in the amount and complexity of the data, making such interpretations is an increasingly difficult problem. As a potential solution, this paper advocates the development of methods for conceptual data analysis. Such methods aim at semi-automating the processes of determining high-level data interpretations, and discovering qualitative patterns in data. It is argued that these methods could be built on the basis of algorithms developed in the area of machine learning. An exemplary system utilizing such algorithms, INLEN, is discussed. The system integrates machine learning and statistical analysis techniques with database and expert system technologies. Selected capabilities of the system are illustrated by examples from implemented modules.     

Optimisation of maintenance scheduling strategies on the grid

The emerging paradigm of Grid Computing provides a powerful platform for the optimisation of complex computer models, such as those used to simulate real-world logistics and supply chain operations. This paper introduces a Grid-based optimisation framework that provides a powerful tool for the optimisation of such computationally intensive objective functions. This framework is then used in the optimisation of maintenance scheduling strategies for fleets of aero-engines, a computationally intensive problem with a high-degree of stochastic noise, achieving substantial improvements in the execution time of the algorithm.     

Locating an undesirable facility with a minimax criterion

The problem considered in this paper involves the location of an undesirable facility such that the maximum weighted inverse square distance from the facility to n given points is minimized. The region in which the facility is to be located is bounded and contains the n points with which the facility to be located will interact. Applications can include siting an undesirable facility that produces some form of pollutant such as radiation, noise and some gases. Any problem that involves the location of a facility that emits pollutants whose concentrations follow the inverse square law is a candidate for the use of this work. A mathematical programming algorithm is developed for the situation in which the location problem involves a convex polygonal region. An interactive computer graphics approach is described for the case when the location problem involves a general region.     

Seller—buyer System Co-operation in a Monopolistic Market

This paper deals with a situation in which the buyer is in a monopolistic position with respect to the seller, and examines the issues and advantages of co-operation in a seller–buyer inventory control system. Game theory concepts form the foundation for the analysis of these issues. Initially, the relationship between the seller and the buyer is modelled as a non-cooperative two-stage game, and it is noted that the traditional EOQ formula is one of the results. Then, interactive game theory is utilized to address the problem of system co-operation as well as to determine optimal system order quantity-pricing strategies. Mutual incentives and motivations for system co-operation are also discussed. Among several alternative methods, the combination of an equal profit sharing role implemented via quantity discounting is demonstrated as the best mechanism for achieving system co-operation. Finally, the similarities and differences between the proposed model and those in the literature are discussed.     

An interactive visual simulation system for industrial management

This paper describes a discrete event interactive simulation system which allows a user to watch the progress of a simulation model on a visual display terminal. The user may interact with the model in a flexible manner, in order to explore the consequence of alternative decisions or strategies. Output from the simulation may be directed, in an animated form, to a refresh display computer graphics screen, a black and white visual display unit or an intelligent colour visual display divice. The interactive system has been specifically designed to assist in decision making processes associated with industrial management problem situations.     

Computing the Pareto frontier of a bi-objective bi-level linear problem using a multiobjective mixed-integer programming algorithm

In this article, we study the bi-level linear programming problem with multiple objective functions on the upper level (with particular focus on the bi-objective case) and a single objective function on the lower level. We have restricted our attention to this type of problem because the consideration of several objectives at the lower level raises additional issues for the bi-level decision process resulting from the difficulty of anticipating a decision from the lower level decision maker. We examine some properties of the problem and propose a methodological approach based on the reformulation of the problem as a multiobjective mixed 0–1 linear programming problem. The basic idea consists in applying a reference point algorithm that has been originally developed as an interactive procedure for multiobjective mixed-integer programming. This approach further enables characterization of the whole Pareto frontier in the bi-objective case. Two illustrative numerical examples are included to show the viability of the proposed methodology.     

Exact algorithms for dominating set

The measure and conquer approach has proven to be a powerful tool to analyse exact algorithms for combinatorial problems like Dominating Set and Independent Set. This approach is used in this paper to obtain a faster exact algorithm for Dominating Set. We obtain this algorithm by considering a series of branch and reduce algorithms. This series is the result of an iterative process in which a mathematical analysis of an algorithm in the series with measure and conquer results in a convex or quasiconvex programming problem. The solution, by means of a computer, to this problem not only gives a bound on the running time of the algorithm, but can also give an indication on where to look for a new reduction rule, often giving a new, possibly faster algorithm. As a result, we obtain an O(1.4969ⁿ) time and polynomial space algorithm.     

IDES: influence diagram based expert system

Influence diagrams have been used effectively in applied decision analysis to model complex systems, identify probabilistic dependence and characterize the flow of information. Their graphical representation and intuitive framework are particularly effective in representing knowledge from experts with diverse backgrounds and varying degrees of technical proficiency. They allow both a symbolic representation of the system interrelationships and a quantitative measure that can be of discrete or continuous functional form. By exploiting this abstraction hierarchy, successive degrees of specification can be made by several individuals, each encoding his or her expert knowledge of the problem and bounds on critical parameters. It is proposed that an interactive computer program that automates this influence diagram technology would provide an excellent tool for building expert systems. This paper describes such a modeling tool: the IDES (Influence Diagram Based Expert System) developed at the University of California at Berkeley as a modeling tool for building expert systems requiring reasoning with uncertain or incomplete information. The Diagnostician's Problem is presented as a tutorial for describing the IDES solution procedure.     

iPlots eXtreme: next-generation interactive graphics design and implementation of modern interactive graphics

Interactive graphics provide a very important tool that facilitates the process of exploratory data and model analysis which is a crucial step in real-world applied statistics. Only a very limited set of software exists that provides truly interactive graphics for data analysis, partially because it is not easy to implement. Very often specialized software is created to offer graphics for a particular problem, but many fundamental plots are omitted since it is not considered new research. In this paper we discuss a general framework that allows to create interactive graphics software on a sound foundation that offers consistent user interface, fast prototyping of new plots and extensibility to support interactive models. In addition, we also discuss one implementation of the general framework: iPlots eXtreme—next-generation interactive graphics for analysis of large data in R. It provides most fundamental plot types and allows new interactive plots to be created. The implementation raises interactive graphics performance to an entirely new level. We will discuss briefly several methods that allowed us to achieve this goal and illustrate the use of advanced programmability features in conjunction with R.     

Approximate and exact algorithms for the fixed-charge knapsack problem

The subject of this paper is the formulation and solution of a variation of the classical binary knapsack problem. The variation that is addressed is termed the “fixed-charge knapsack problem”, in which sub-sets of variables (activities) are associated with fixed costs. These costs may represent certain set-ups and/or preparations required for the associated sub-set of activities to be scheduled. Several potential real-world applications as well as problem extensions/generalizations are discussed. The efficient solution of the problem is facilitated by a standard branch-and-bound algorithm based on (1) a non-iterative, polynomial algorithm to solve the LP relaxation, (2) various heuristic procedures to obtain good candidate solutions by adjusting the LP solution, and (3) powerful rules to peg the variables. Computational experience shows that the suggested branch-and-bound algorithm shows excellent potential in the solution of a wide variety of large fixed-charge knapsack problems.     

Fuzzy multiple level programming

The use of fuzzy set concept to overcome the computational difficulties of multi-level optimization for large systems appears to be a powerful approach and can solve practical large problems in a very simplified manner. Furthermore, unlike the duo-ploy or multi-ploy approaches, the proposed interactive concept provides flexibility, which is essential due to the different styles of management in different organizations. The approach is formulated based on exploring the fuzziness or indefiniteness, which is almost always present in a decentralized large hierarchy organization. The advantage of this approach is that, not only the problem is much more simplified for solution purposes, the original problem is also much more realistically represented.