The non-codified use of problem structuring methods and the need for a generic constitutive definition

When we use a PSM what is it we are actually doing? An answer to this question would enable the PSM community to considerably enlarge the available source of case studies by the inclusion of examples of non-codified PSM use. We start from Checkland’s own proposal for a “constitutive definition” of SSM, which originated from trying to answer the question of knowing when a claim of SSM use was legitimate. By extending this idea to a generic constitutive definition for all PSMs leads us to propose a self-consistent labelling schema for observed phenomena arising from PSMs in action. This consists of a set of testable propositions, which, through observation of putative PSM use, can be used to assess validity of claims of PSM use. Such evidential support for the propositions as may be found in putative PSM use can then make it back into a broader axiomatic formulation of PSMs through the use of a set-theoretic approach, which enables our method to scale to large data sets. The theoretical underpinning to our work is in causal realism and middle range theory. We illustrate our approach through the analysis of three case studies drawn from engineering organisations, a rich source of possible non-codified PSM use. The combination of a method for judging cases of non-codified PSM use, sound theoretical underpinning, and scalability to large data sets, we believe leads to a demystification of PSMs and should encourage their wider use.     

Understanding problem structuring methods interventions

This article presents a conceptual framework and methodological guide for researching and understanding OR interventions particularly problem structuring methods (PSM). The article argues that OR/PSM interventions are complex events which can not be understood by traditional approaches alone. In this paper an alternative methodology is developed, where the units of analysis are the narratives and networks produced during PSM interventions. The paper outlines the main theoretical and methodological concerns that need to be appreciated in studying PSM interventions. The paper then explores actor-network theory and narrative analysis as approaches to study them. A case study describing the use of these approaches is provided.     

SSM and technology management: Developing multimethodology through practice

Growing competition and economic recession is driving the need for more rapid redesign of operations enabled by innovative technologies. The acquisition, development and implementation of systems to manage customer complaints and control the quality assurance process is a critical area for engineering and manufacturing companies. Multimethodologies, and especially those that can bridge ‘soft’ and ‘hard’ OR practices, have been seen as a possible means to facilitate rapid problem structuring, the analysis of alternative process design and then the specification through to implementation of systems solutions. Despite the many ‘hard’ and ‘soft’ OR problem structuring and management methods available, there are relatively few detailed empirical research studies of how they can be combined and conducted in practice. This study examines how a multimethodology was developed, and used successfully, in an engineering company to address customer complaints/concerns, both strategically and operationally. The action research study examined and utilised emerging ‘soft’ OR theory to iteratively develop a new framework that encompasses problem structuring through to technology selection and adoption. This was based on combining Soft Systems Methodology (SSM) for problem exploration and structuring, learning theories and methods for problem diagnosis, and technology management for selecting between alternatives and implementing the solution. The results show that, through the use of action research and the development of a contextualised multimethodology, stakeholders within organisations can participate in the design of new systems and more rapidly adopt technology to address the operational problems of customer complaints in more systemic, innovative and informed ways.     

Problem structuring methods ‘in the Dock’: Arguing the case for Soft OR

Problem structuring methods (‘soft’ OR) have been around for approximately 40 years and yet these methods are still very much overlooked in the OR world. Whilst there is almost certainly a number of explanations for this, two key stumbling blocks are: (1) the subjective nature of the modelling yielding insights rather than testable results, and (2) the demand on users to both manage content (through modelling) and processes (work with rather than ‘on behalf’ of groups). However, as evidenced from practice there are also a number of significant benefits. This paper therefore aims to examine the case of Soft OR through examining the case for and against problem structuring methods.     

Issues Mapping: A problem structuring method for addressing science and technology conflicts

There are new opportunities for the application of problem structuring methods to address science and technology risk conflicts through stakeholder dialogue. Most previous approaches to addressing risk conflicts have been developed from a traditional risk communication perspective, which tends to construct engagement between stakeholders based on the assumption that scientists evaluate technologies using facts, and lay participants do so based on their values. ‘Understanding the facts’ is generally privileged, so the value framings of experts often remain unexposed, and the perspectives of lay participants are marginalized. When this happens, risk communication methodologies fail to achieve authentic dialogue and can exacerbate conflict. This paper introduces ‘Issues Mapping’, a problem structuring method that enables dialogue by using visual modelling techniques to clarify issues and develop mutual understanding between stakeholders. A case study of the first application of Issues Mapping is presented, which engaged science and community protagonists in the genetic engineering debate in New Zealand. Participant and researcher evaluations suggest that Issues Mapping helped to break down stereotypes of both scientists and environmental activists; increased mutual understanding; reduced conflict; identified common ground; started building trust; and supported the emergence of policy options that all stakeholders in the room could live with. The paper ends with some reflections and priorities for further research.     

Messing about in transformations: Structured systemic planning for systemic solutions to systemic problems

The literature on multimethodology indicates that cognitive mapping is relevant to enriching the preliminary, information-gathering phase of Soft Systems Methodology (SSM), and especially the rich picture. By noting the structural complementarity evidenced between SSM’s transformations and the bipolar constructs used in the cognitive mapping methodology known as Strategic Options Development and Analysis (SODA), this paper shows how SODA can be applied beyond SSM’s initial stage, and much more analytically within the heart of SSM, to guide the manner in which a systemic resolution to a problematic situation may be approached. It is proposed, and illustrated through examples, that a SODA map of large numbers of transformations, resulting from an exercise in SSM, offers a methodological means for structuring what might otherwise be perceived as a mess. The paper discusses how in such cases ‘strategic options development and analysis’ of transformations, or SODA-T maps, serve, among other things, to identify relations between transformations, their hierarchies and priorities, problem epicenters and starting points for intervention. In addition, the arsenal of graph theory can be used to cut through what would otherwise appear as interlinked chaos requiring structured operationalization. In this respect, the SODA-T map offers a high-level connective orientation which can guide the interconnections between the respective human activity systems of the transformations, resulting in the final systemic plan. Ultimately, SODA-T mapping is shown to facilitate a structured approach toward systemic planning.     

Mixing OR methods in practice: Past, present and future directions

Although mixing of OR methods is an area of increasing interest to the OR community, there has been little discussion regarding generic lessons that can be learnt from mixing methods in practice. The aim of this paper is to carry out such an analysis through considering generic lessons that may be associated with mixing methods, regardless of the methods chosen. To identify these lessons, published case studies on how OR methods have been mixed are analysed giving rise to a number of themes revealing the lessons. These themes include; the implications from the use of different facilitators/modellers, how methods have been mixed together, the nature of the modelling interventions, the client value and the rationale given for mixing methods. The paper discusses the lessons learnt in each of these themes and presents opportunities for future work.     

A problem structuring method for ecosystem-based management: The DPSIR modelling process

The purpose of this paper is to learn from Complex Adaptive Systems (CAS) theory to inform the development of Problem Structuring Methods (PSMs) both in general and in the specific context of marine management. The focus on marine management is important because it is concerned with a CAS (formed through the interconnection between natural systems, designed systems and social systems) which exemplifies their particularly ‘wicked’ nature. Recognition of this compels us to take seriously the need to develop tools for knowledge elicitation and structuring which meet the demands of CAS. In marine management, chief among those tools is the DPSIR (Drivers – Pressures – State Changes – Impacts – Responses) model and, although widely applied, the extent to which it is appropriate for dealing with the demands of a CAS is questionable. Such questioning is particularly pertinent in the context of the marine environment where there is a need to not only recognise a broad range of stakeholders (a question of boundary critique) but also to manage competing knowledge (economic, local and scientific) and value claims. Hence this paper emphasises how a CAS perspective might add impetus to the development of a critical perspective on DPSIR and PSM theory and practice to promote a more systemic view of decision-making and policy development.     

An MCDA approach for the selection of bike projects based on structuring and appraising activities

This paper presents an MCDA approach for the structuring and appraising activities of a large and complex decision problem. More specifically, the paper makes use of the three-step structuring process for decision analysis proposed by von Winterfeldt and Edwards: (1) identifying the problem; (2) selecting an appropriate analytic approach; and (3) developing a detailed analytic structure. For illustration of the approach a case study dealing with the assessment task of prioritising and selecting initiatives and projects from a public pool with limited funds is examined throughout the paper. The process is embedded in a Decision Support System (DSS) making use of the REMBRANDT technique for pair wise comparisons to determine project rankings. A procedure for limiting the number of pair wise comparisons to be made in the process is in this connection presented. Finally, strengths and weaknesses in the approach are discussed and conclusions are made.     

Making decisions in the absence of clear facts

Bennis and O’Toole [Bennis, W.G., O’Toole, J., 2005. How business schools lost their way. Harvard Business Review 83, 96–104] have recently argued that decision makers need guidance in ‘making decisions in the absence of clear facts’. As such, decision makers must be able to resourcefully use whatever limited information is available and advantageously portray its implications. Based on recently published theory which directly addresses this requirement, this paper demonstrates, through a practical example, how decision makers can make systemic decisions in situations characterized by extremely limited information and, furthermore, what form such decisions can take. Evidence is provided, therefore, that operational research can effectively address what appears to be a gap in management training.     

WASAN: The development of a facilitated methodology for structuring a waste minimisation problem

This paper contributes a new methodology called Waste And Source-matter ANalyses (WASAN) which supports a group in building agreeable actions for safely minimising avoidable waste. WASAN integrates influences from the Operational Research (OR) methodologies/philosophies of Problem Structuring Methods, Systems Thinking, simulation modelling and sensitivity analysis as well as industry approaches of Waste Management Hierarchy, Hazard Operability (HAZOP) Studies and As Low As Reasonably Practicable (ALARP). The paper shows how these influences are compiled into facilitative structures that support managers in developing recommendations on how to reduce avoidable waste production. WASAN is being designed as Health and Safety Executive Guidance on what constitutes good decision making practice for the companies that manage nuclear sites. In this paper we report and reflect on its use in two soft OR/problem structuring workshops conducted on radioactive waste in the nuclear industry.     

Noising methods for a clique partitioning problem

This paper deals with the application of noising methods to a clique partitioning problem for a weighted graph. The aim is to study different ways to add noise to the data, and to show that the choice of the noise-adding-scheme may have some impact on the performance of these methods. Among the noise-adding-schemes described here, two of them are totally new, leading to the “forgotten vertices” and to the “forgotten edges” methods. We also experimentally study a generic noising method that automatically tunes its parameters. For each noise-adding-scheme, we compare a variant which inserts descents and a variant which does not.     

Branch-and-bound methods for solving systems of Lipschitzian equations and inequalities

In this note, we show how branch-and-bound methods previously proposed for solving broad classes of multiextremal global optimization problems can be applied for solving systems of Lipschitzian equations and inequalities over feasible sets defined by various types of constraints. Some computational results are given.This research was accomplished while the second author was a fellow of the Alexander von Humboldt Foundation at the University of Trier, Trier, West Germany.     

Towards a framework for developing students' fraction proficiency

The importance of the knowledge of fractions in mathematical learning, coupled with the difficulties students have with them, has prompted researchers to focus on this particular area of mathematics. The term ‘fraction proficiency' used in this article refers to a person's conceptual comprehension, procedural skills and the ability to approach daily situations involving fractions. In the area of fractions, there has been a call for more research to study how, and where, efforts should be focused in order to integrate the various aspects of fraction knowledge for students, and even for teachers, to help them develop proficiency in fractions. Thus, the article presents a theoretical synthesis of the specialized literature in the learning and teaching of fractions, with the aim of proposing a framework for developing students' fraction proficiency. The frameworks presented in the article may shed light upon the implications for the design of fraction instruction, which should focus on developing a multi-faceted knowledge of fractions, rather than simply isolating one facet from the others.     

An exploratory framework for handling the complexity of mathematical problem posing in small groups

The paper introduces an exploratory framework for handling the complexity of students’ mathematical problem posing in small groups. The framework integrates four facets known from past research: task organization, students’ knowledge base, problem-posing heuristics and schemes, and group dynamics and interactions. In addition, it contains a new facet, individual considerations of aptness, which accounts for the posers’ comprehensions of implicit requirements of a problem-posing task and reflects their assumptions about the relative importance of these requirements. The framework is first argued theoretically. The framework at work is illustrated by its application to a situation, in which two groups of high-school students with similar background were given the same problem-posing task, but acted very differently. The novelty and usefulness of the framework is attributed to its three main features: it supports fine-grained analysis of directly observed problem-posing processes, it has a confluence nature, it attempts to account for hidden mechanisms involved in students’ decision making while posing problems.     

Some filter regularization methods for a backward heat conduction problem

In this paper, a one-dimensional backward heat conduction problem is investigated. It is well known that such problem is ill-posed. Some filter regularization methods are used to solve it. Convergence estimates under two a-priori bound assumptions for the exact solution are given based on the conditional stabilities. Finally, numerical examples are given to show that our used numerical methods are effective and stable.     

Necessary and sufficient conditions for the convergence of iterative methods for the linear complementarity problem

Necessary and sufficient conditions are established for the convergence of various iterative methods for solving the linear complementarity problem. The fundamental tool used is the classical notion of matrix splitting in numerical analysis. The results derived are similar to some well-known theorems on the convergence of iterative methods for square systems of linear equations. An application of the results to a strictly convex quadratic program is also given.This research was based on work supported by the National Science Foundation under Grant No. ECS-81-14571.The author gratefully acknowledges several comments by K. Truemper on the topics of this paper.     

Analysis and computation of least‐squares methods for a compressible Stokes problem

We develop and analyze a negative norm least‐squares method for the compressible Stokes equations with an inflow boundary condition. Least‐squares principles are derived for a first‐order form of the equations obtained by using ω = ?×u and φ = ? · u as new dependent variables. The resulting problem is incompletely elliptic, i.e., it combines features of elliptic and hyperbolic equations. As a result, well‐posedness of least‐squares functionals cannot be established using the ADN elliptic theory and so we use direct approaches to prove their norm‐equivalence. The article concludes with numerical examples that illustrate the theoretical convergence rates. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006