A survey on piecewise-linear models of regulatory dynamical systems

Recent developments in understanding the various regulatory systems, especially the developments in biology and genomics, stimulated an interest in modelling such systems. Hybrid systems, originally developed for process control applications, provide advances in modelling such systems. A particular class of hybrid systems which are relatively simpler to analyze mathematically but still capable of demonstrating the essential features of many non-linear dynamical systems is piecewise-linear systems. Implementation of piecewise-linear systems for modelling of regulatory dynamical systems requires different considerations depending on the status of the problem. In this work we considered three different cases. Firstly, we consider the inferential modelling problem based on the empirical observations and study the discrete piecewise-linear system, whose inverse problem is solvable under some assumptions. Secondly, we considered the problem of obtaining some complex regulatory systems by tractable piecewise-linear formulations and study the qualitative dynamic features of the systems and their piecewise-linear models. Finally, we considered Boolean delay equations for building abstract models of regulatory systems, which might be the simplest models demonstrating the essential qualitative features of our interest underlying adaption, learning and memorization.     

Developments in linear and integer programming

In this review we describe recent developments in linear and integer (linear) programming. For over 50 years Operational Research practitioners have made use of linear optimisation models to aid decision making and over this period the size of problems that can be solved has increased dramatically, the time required to solve problems has decreased substantially and the flexibility of modelling and solving systems has increased steadily. Large models are no longer confined to large computers, and the flexibility of optimisation systems embedded in other decision support tools has made on-line decision making using linear programming a reality (and using integer programming a possibility). The review focuses on recent developments in algorithms, software and applications and investigates some connections between linear optimisation and other technologies.     

Artificial Intelligence and Decision Analysis

Much work has been done on the development of modelling techniques to assist in the process of decision-making. The areas of operational research and statistical analysis are well established, and the speed and memory capacity of computers has facilitated the solution of very large problems using such techniques. Recent developments in artificial intelligence, particularly with regard to expert systems, open up the possibility of modelling the decision-maker rather than the decision situation. This would result in a much more sophisticated decision-support system, but as yet it is an approach which has not been investigated to any significant degree. This paper suggests how AI techniques might be combined with traditional problem-based methodologies to provide a comprehensive decision-analysis support-system framework, modelling the activities of a human decision-maker and providing access to a host of traditional and artificial intelligence tools which can be effectively interfaced.     

Tree knapsack approaches for local access network design

In the process of solving many forms of the local access network design problem, the basic model of the tree knapsack problem (TKP) is used as a building block for the search engine of the solution strategy. Various solution strategies can be used to solve this problem. An approach that use standard software coupled with enhanced modelling is presented for the TKP. Enhanced modelling is used to partition the TKP into sub-problems that is easier to solve using standard off the shelve software. The basic approach is described and empirical work is presented. Empirical comparisons are also given relating this approach with some algorithms suggested by other authors.     

Bank-office Process Management in the Financial Services: a Simulation Approach Using a Model Generator

For the last ten years or so, developments in simulation software and methodology have been focused in two areas: (1) automating the model-building process; and (2) interfacing with other techniques and systems. That both academic and commercial research continues to be carried out in these areas is evidence of the continued popularity of the simulation technique. The most popular application areas where simulation modelling is used include manufacturing (engineering and process), warehousing and communications; not surprisingly, research and developments have therefore been concentrated in these areas. This paper describes the development of a simulation model generator for a different application area, that of clerical office processing of paper and documents for financial service companies. It outlines the reasons why there is a need for such a model generator and discusses the initial design requirements. The paper goes on to detail the developments and re-defined criteria required as the model generator brief changes as a result of practical applications.     

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.     

Linear,Integer, Separable and Fuzzy Programming Problems: A Unified Approach towards Reformulation

For mathematical programming (MP) to have greater impact as a decision tool, MP software systems must offer suitable support in terms of model communication and modelling techniques. In this paper, modelling techniques that allow logical restrictions to be modelled in integer programming terms are described, and their implications discussed. In addition, it is illustrated that many classes of non-linearities which are not variable separable may be, after suitable algebraic manipulation, put in a variable separable form. The methods of reformulating the fuzzy linear programming problem as a max-min problem is also introduced. It is shown that analysis of bounds plays a key role in the following four important contexts: model reduction, reformulation of logical restrictions as 0-1 mixed integer programmes, reformulation of non-linear programmes as variable separable programmes and reformulation of fuzzy linear programmes. It is observed that, as well as incorporating an interface between the modeller and the optimizer, there is a need to make available to the modeller software facilities which support the model reformulation techniques described here.     

Computer-aided Modelling of Decision-support Systems

Information systems have become increasingly complex over recent years, underscoring the challenge of designing systems which will provide the different functions in an organization with the information necessary for effective decision-making. With rapidly developing computer technology, it is natural that information systems evolve in a manner which is greatly dependent on computing hardware and software. Yet, there has been little development in the techniques of systems analysis and design to handle new and less well-understood functions which are of increasing interest.This paper demonstrates an application of structural modelling concepts to decision-support system synthesis. With the aid of the computer, structural modelling serves as an effective tool for: (1) partitioning a system into a set of subsystems; (2) specifying subsystems sufficiently to permit separate testing before total system tests; (3) eliminating redundant control information flow; and (4) facilitating decision-maker and system-analyst coordination and participation in the design process.     

Macroscopic models for fibroproliferative disorders: A review

In this paper we review some mathematical modelling of organ reparative processes (wound healing) for both the physiological and pathological case. The natural process of healing consists in a series of overlapping phases involving cells, chemicals, extracellular matrix (ECM) and the environment surrounding the wound site. Sometimes the healing process fails and the reparative mechanism produces pathological conditions which are commonly termed fibrosis or fibroproliferative disorders. Biological insight into the pathogenesis, progression and possible regression of fibrosis is lacking and many issues are still open. Mathematical modelling can surely play its part in this field and this paper is aimed at showing what has been done so far and what has still to be done to achieve a unified framework for studying these kinds of problems. Due to the high complexity of this phenomenon, multi-scale modelling is certainly the appropriate approach that should be used for studying these kinds of problems. Unfortunately most of the mathematical literature on this topic consists of macroscopic continuous models which fail to investigate processes occurring at smaller length scales (cellular, sub-cellular). We present a review of some of the mathematical literature, showing the widely used approaches, focusing on the interpretation of results and indicating possible developments in the study of these highly complex systems.     

The Systems Approach in Government? Two Case Studies of Programme Budgeting

Applying the systems approach in practice requires compromises to be made in its ideals. This paper discusses this problem by examining two case studies of programme budgeting which can be seen to be an application of the systems approach; it attempts to expand the dimensions of budgeting away from an annual exercise based on functions to a process of medium-term planning based on programmes. The two case studies are the introduction and suspension of Planning-Programming-Budgeting-System (P.P.B.S.) in U.S. Federal Government and the various developments in the U.K. in the Public Expenditure Survey (P.E.S.C.). These provide illuminating contrasts in their intended scope and successful implementation. This contrasting experience suggests questions about systems theory. Should the essential characteristic of the systems approach be expansionism or adaptability? Can systems writing afford to ignore compromises necessary to achieve implementation, especially those made to satisfy political interests?     

Modelling impacts of cropping systems: Demands and solutions for DEX methodology

Decision modelling of diverse groups of problems makes different requirements to the modelling methodologies and software. We present an actual decision problem and the required characteristics of corresponding decision models. The problem is from agronomy and addresses the ecological and economic impacts of cropping systems, with the focus on the differences between cropping systems with conventional crops and the ones with genetically modified crops. We describe the extensions of an existing DEX qualitative multi-attribute modelling methodology, which were made to cope with the challenges of the problem. The extensions address general hierarchical structures, probabilistic utility functions and numerical values of basic attributes. A new, freely available software tool called proDEX was implemented to support the extended methodology. In this paper we describe the problem of cropping system assessment, propose methodological extensions to DEX, and present the implementation of proDEX.     

A Computational Algorithm Associated with Patient Progress Modelling

Patient progress modelling, which was first introduced to provide an alternative to traditional randomised control trials, has now been used in numerous contexts including evaluation of screening programmes and assessment of the public health impact of large scale developments such as waste disposal incinerators. The method uses stochastic compartmental models whose solutions may depend on solving large sets of matrix differential equations. Although specialist software packages are available for this purpose, we propose an alternative method for deriving the solution to such equations that is simple to implement.     

Linear programming on a micro computer: An application in refinery modelling

Given the complexity of refinery modelling, linear programming for this application has until now been developed essentially on mainframes. New developments in microcomputer LP software now allow us to handle real life problems. This paper will describe the process of a general refinery, and how a micro based model has been designed to study its economics.     

Recent developments in Dual Resource Constrained (DRC) system research

Real world manufacturing systems are usually constrained by both machine and human resources. Human operators are often the constraining resource and transfer between workstations to process jobs when required. This kind of system is known as a Dual Resource Constrained (DRC) system and presents additional technical challenges which must be considered during planning and scheduling. These technical challenges can be categorised into the five main dimensions of job release mechanisms, job dispatching, worker flexibility, worker assignment and transfer costs. This paper aims to provide an overview of recent developments in DRC research concerned with each of these areas and also discusses some possible approaches to solving the resource scheduling problem in a DRC system. The focus is on materials published after 1995 and up to 2009. Previous reviews on DRC systems are commented on and followed by a review of recent works associated with each of the five dimensions of DRC system research. Advancements made and new methodologies proposed are discussed and future research directions are identified.     

Enriched workflow modelling and Stochastic Branch-and-Bound

Workflow systems provide means and techniques for modelling, designing, performing and controlling repetitive (business) processes. The quality of commercial workflow systems is usually determined to a large extent by their versatility and multi-purpose application. One of the current trends in improving workflow systems lies in enriching modelling methods and techniques in order to enlarge design alternatives.The need for such advanced methods is particularly apparent in those fields in which the process duration can be determined only vaguely, but whose completion schedules are at the same time strictly enforced by a highly competitive market by means of fines and penalties. The risk of an overrun has to be weighed against the expected costs and benefits of certain measures reducing turn-around time and their combinations. Because they can help to avoid such penalties—or, at least, keep any potential losses low by identifying critical subprocesses and evaluate appropriate measures—modelling and evaluation techniques are becoming essential features of workflow systems.Methodologically, we use Stochastic Branch-and-Bound as a technique for finding “optimal” bundles of measures. A numerical study shows the benefits of this meta-approach by means of five stepwise-developed decision scenarios requiring rich modelling. Petri nets as a modelling tool and Stochastic Branch-and-Bound as an optimization technique determine for multi-mode resource constrained workflows of varying complexity an optimal workforce strategy with respect to the number of workers and their qualification.     

Applications of the urban traffic control strategy TUC

Despite the long-lasting research and developments in the field of urban traffic control systems, the continuously increasing mobility requirements urge for solutions that will release urban areas from the serious congestion problems and their consequences. From the control point of view, this may be translated into the employment of traffic-responsive systems that respond automatically to the prevailing traffic conditions. This is the aim of the signal control strategy TUC, whose basic philosophy, design methodology, characteristics and application results under both simulated and field conditions are presented in this paper. Based on a store-and-forward type of mathematical modelling and using well-known methodological tools from Automatic Control Theory, the TUC strategy addresses in a simple but efficient way, as demonstrated from the applications so far, the problem of co-ordinated, traffic-responsive signal control in large-scale urban networks.     

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.     

Why Expert Systems Fail

Although many papers have been published on the subject of expert systems, relatively few of them have been concerned with systems which failed.In this paper some of the major reasons why expert systems fail are described, along with some techniques for alleviating these problems.Expert system developments fail for the same reasons as conventional software systems. However, they may also fail because the problem they are dealing with is not or cannot be understood, because they require common sense or knowledge of the limitations of their knowledge, because they cannot be tested, or because they cannot or will not be trusted.