Forms of conversation and problem structuring methods: a conceptual development

Problem structuring methods (PSMs) are a family of participatory and interactive methods whose purpose is to assist groups of diverse composition tackle a complex problematic situation of common interest. This is achieved through modelling and facilitation, with a view to generating consensus on problem structure, and agreement on initial commitments. Despite the apparent success of PSMs reported in the literature, little progress has been made towards the development of theoretical models that integrate these experiences and guide PSM practitioners and academics in developing and implementing effective PSM interventions. In particular, no theoretical models have been presented concerning how conversational processes within a group are affected by PSMs. This paper develops a theoretical model of conversation intended to provide a means to identify a specific role for the analytical assistance provided through PSMs, and for evaluating their effectiveness. The hypothesis articulated from this model is that PSMs have the potential to improve the quality of the conversation in which actors participate. PSMs generate this effect through facilitating the structuring and sense-making activities embedded within a conversation. Improvement in the quality of conversation should tend to help actors engage in dialogue as a particular form of conversation, achieve shared understanding, and increase the actors’ ownership of the commitments achieved during the conversation. The paper concludes with a discussion of the implications of the model for research and practice.     

Quantitative problem structuring methods for multi-actor problems: an analysis of reported applications

Problem structuring methods (PSMs) are proposed as vital tools for coping with complex and unstructured problems that help decision-makers make decisions or come to a shared understanding of a problem situation. Despite their popularity, choosing a PSM for an unstructured problem situation is problematic as good categorization and evaluation of PSMs is lacking. As a first step we postulate a categorization of quantitative PSMs applied to multi-actor situations. We list the different application areas, the types of design that were used, and the type of outcomes the methods provide. To understand why and how certain PSMs are applied, we categorize applications of metagames/conflict analysis, hypergames, drama theory, Q-methodology, and transactional analysis. We find that method choice and validation of the applications are yet underdeveloped for this specific sub-field, and suggest further work on this as it will help to understand the added value of PSMs.     

Assessing the impact of problem structuring methods in multi-organizational settings: an empirical investigation

Problem structuring methods (PSMs) have most commonly been employed with groups operating within single-organizational contexts. This paper argues that PSMs are by their nature also appropriate for supporting the work of multi-organizational groups (MOGs) operating within a partnership context. An experience of the use of a PSM in this context is reported and evaluated. The research findings suggest that there is indeed scope for the use of PSMs with MOGs, and that these methods do appear to have a positive role in achieving some of the products claimed for PSM interventions. In particular, the experience as a whole tends to demonstrate that mutual accommodations between the organizations represented in the MOG can be the result of the use of PSMs. The paper concludes with a discussion of the significance of the experience, and proposes some directions for further research.     

On becoming expert in the use of problem structuring methods

While much has been written about the theory and practice of using problem structuring methods (PSMs) there is little formal discussion of how individuals may effectively learn about their use. In this paper it is argued that a foundation for designing and providing a suitable learning environment lies in understanding the nature of being an expert user of PSMs and the knowledge that such experts hold and deploy. An analysis of how knowledge and expertise are grounded in the work involved in using PSMs is offered. This leads to some proposals for what is required if processes to support the acquisition of expertise in the use of PSMs are to be implemented.     

Exploring new directions for research in problem structuring methods: on the role of cognitive style

Prior research has argued that cognitive style can have a significant impact on group decision making. In addition, several scholars have proposed that cognitive style can play a key role in the design and use of group decision support systems. However, cognitive style has not received a great deal of attention in the problem structuring methods (PSMs) community. This is surprising, given that PSMs are specifically developed to support a group in their decision making. The purpose of this paper is thus to examine the significance of cognitive style within PSMs. The paper identifies and explores the role of four different cognitive style functions in problem structuring interventions. This analysis is carried out by focusing on the different tasks embedded within a group process supported by PSMs. Implications for the research and practice of PSMs are then discussed.     

Evaluating problem-structuring methods: developing an approach to show the value and effectiveness of PSMs

This paper discusses the challenges associated with the evaluation of problem-structuring methods (PSMs). PSMs are seen as complex interventions that seek wide-level change and action at many levels including individual and system. There is now a widespread acceptance that the traditional evaluation approaches are inappropriate for the evaluation of PSMs. The difficulty is compounded when PSMs are used in multi-agency settings. The paper proposes that evaluation, while pragmatic and situated, must be a theory-based exercise. Part of the challenge is to provide a narrative of the intervention as well as an agreed assessment.     

<Emphasis Type="Italic">Quid pro quo</Emphasis>: Reflections on the value of problem structuring group workshops

Attracting clients who are willing to invest in using a problem structuring method (PSM) can be particularly difficult for the emerging generation of modellers. There are many reasons for this, not least that the benefits of a problem structuring intervention are vague and evidence of benefits are often anecdotal for example, claims of constructing a deeper understanding of the problem or building the commitment of a group to implementing an outcome. This paper contributes to the evaluation of problem structuring methods by reflecting on the quid pro quo that a client and problem structuring modeller can enjoy from collaboration. The paper reflects on 21 cases, where Journey Making (a problem structuring method) was used with 16 organizations to help managers agree a suite of actions to tackle a complex strategic issue. The reflections are clustered around those benefits that pertain to: PSMs in general; PSMs that use computer-supported workshops; the Journey Making methodology.     

Problem structuring in project management: an application of soft systems methodology (SSM)

Recent research suggests a major role for problem structuring methods (PSMs) in the field of project management, particularly at the front-end of projects, where objectives are often unclear and where different constituencies have conflicting aims. This paper presents a case example of soft systems methodology (SSM) at the front-end of a major project within Tesco Stores Ltd. A detailed account of the intervention is given, including the results achieved and a discussion of how the methodology was used for multiple purposes within the same intervention. Within the literature, there remains a lack of detailed examples from which people can learn more about the use of PSMs in project management. By providing a detailed example of SSM in action, this paper seeks to highlight the importance of problem structuring at the front-end of projects and the potential role an approach such as SSM can play at this crucial stage.     

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.     

Problem structuring without workshops? Experiences with distributed interaction within a PSM process

Problem structuring methods (PSMs) have been widely and successfully used in many organizations, but the reliance on face-to-face meetings and workshops makes a typical PSM project difficult and time-consuming to organize, and means that the process may only involve a narrow cross-section of the organization. Yet much interaction in organizations is neither face-to-face nor even synchronous. This research seeks to (1) explore how the issues that arise in moderating such distributed interaction differ from the issues involved in facilitating a workshop and (2) identify the circumstances under which it makes sense to consider using the distributed mode of interaction within a PSM process. Three pairs of action research case studies using a distributed variant on the strategic options development and analysis (SODA) process are described, together with our answers to the above questions.     

PANEL DISCUSSIONS

Representations of mathematical concepts play an important role in understanding: both in helping learners understand the to-be-learned material and in facilitating teachers’ understanding of pedagogical processes which, in turn, are involved in developing learners’ understanding. In this paper, we report on work with a cohort of pre-service primary teachers, with the aim of developing their understanding of mathematics, their confidence in their subject knowledge and their confidence in teaching mathematics. This was attempted through the introduction and use of a ‘representational approach’ to the teaching of the mathematical concepts required of teachers training to teach in primary schools in the UK. We present the results of attitude measures and a follow-up qualitative questionnaire in identifying whether and how the use of this representational approach supported pre-service teachers’ understanding and their confidence in teaching mathematics. The results suggest that the representational approach used had a positively significant impact on the attitudes towards studying and teaching mathematics.     

A multi-criteria large neighbourhood search for the transportation of disabled people

This paper addresses the problem of optimizing the transportation of disabled persons from home to specialized centres or schools. It is modelled as a Dial-a-ride problem (DARP), where several people share the same destination. Particular emphasis is placed on the objective function in order to consider several potentially conflicting interests. We propose a multi-criteria model from Multi-attribute Utility Theory based on the Choquet integral. The resulting multi-criteria DARP is then solved with a large neighbourhood search algorithm. This method includes classical destroy and repair heuristics as well as new operators exploiting the shared destination feature and criterion-specific operators. The algorithm is evaluated on a set of 14 real-world instances in the field of health care logistics, with up to 200 requests and 51 destination points.     

Satisfying moments during the transition-to-proof: Characteristics of moments of significant positive emotion

There is an increasing acknowledgment of the importance of student affect on mathematics learning. Our understanding of emotions is underexamined in comparison to affect of longer duration, e.g. attitudes and beliefs. Yet, it is short-term, in-the-moment affect such as emotion, occurring in real-time, that is malleable by instruction. Across a series of four semi-structured interviews, undergraduate students enrolled in a transition-to-proof course shared their satisfying moments, experiences characterized by significant positive emotion. An expansive range of characteristics of satisfying moments emerged across the overarching categories of accomplishments, sense-making, properties of mathematics, and interactions with people. Satisfying moments tended to exhibit multiple characteristics, but a small set of characteristics were present across many moments: understanding, overcoming challenges, and accomplishments without struggle. Through understanding what elicits satisfaction in mathematics, we can more precisely build learning opportunities that provide positive mathematical experiences to students.     

Flip or flop? Students’ perspectives of a flipped lecture in mathematics

This paper describes students’ perspectives of a one-off flipped lecture in a large undergraduate mathematics service course. The focus was on calculating matrix determinants and was designed specifically to introduce debate and argumentation into a mathematics lecture. The intention was to promote a deeper learning and understanding through engagement with the added hope of instilling some passion for the subject. During the lecture, students were asked to vote with their feet, literally moving around the lecture theatre to form groups according to their shared favourite technique for calculating matrix determinants. Group discussions were then followed by a whole class debate facilitated by the lecturers, before they wrapped up the lecture by resolving the professional disagreements that had come to light during the debate. Following the lecture, data on student perspectives was gathered using both surveys and focus groups. Within this paper, we share the data and reveal the interesting results that emerged from our analysis. Despite remaining unconvinced as to whether flipped lectures are better for learning, students reported greater engagement and increased understanding of the material covered.     

The Homology of Partial Monoid Actions and Petri Nets

The aim of this paper is to study the homology theory of partial monoid actions and apply it to computing the homology groups of mathematical models for concurrency. We study the Baues–Wirsching homology groups of a small category associated with a partial monoid action on a set. We prove that these groups can be reduced to the Leech homology groups of the monoid. For a trace monoid with a partial action on a set, we build a complex of free Abelian groups for computing the homology groups of this small category. It allows us to solve the problem posed by the author on the construction of an algorithm to computing the homology groups of elementary Petri nets. We describe the algorithm and give examples of computing the homology groups.     

Past,present and future of problem structuring methods

To be able to exploit the future opportunities for Operational Research (OR), we need to prepare for them now. To conceptualize alternative futures for OR, we need to understand the potentialities of the present. To understand the present, we need to have a grasp of the past history that gave us the OR that we have, rather than some other analytic practice. OR was thrown up by a situation where traditional management methods were proving inadequate to handle the growing complexity of organizational arrangements. Problem structuring methods (PSMs) in turn were generated out of a sense that the trajectory of OR had led it away from important areas of social decision-making. PSMs have made great strides but are still encountering barriers to acceptance. This paper will explore the factors that presently constrain PSMs, and what developments could take them into new fields.     

Allocating the gains from resource pooling with the Shapley Value

To make their cost structure more efficient, firms often pool their critical resources: small divisions of a large firm may negotiate a joint contract to benefit from volume discounts; or firms may outsource their call centres to an independent provider who is able to increase utilization by reducing variability since demand is now pooled. Since pooling demand reduces total joint costs, an immediate question is how the realized savings should be shared. We model the problem as a cooperative game and use the resulting allocation schemes to distribute the savings. One popular scheme is the Shapley Value, which always exists and, we show, represents each player's incremental value to the pool. When the pooled savings depend on the sum of each player's demand, we label the game coalition symmetric and propose, for those games, an algorithm that makes pseudo-polynomial the computation of the Shapley Value.     

Singular solutions for the constant Q-curvature problem

This paper is devoted to the construction of weak solutions to the singular constant Q-curvature problem. We build on several tools developed in the last years. This is the first construction of singular metrics on closed manifolds of sufficiently large dimension with constant (positive) Q-curvature.     

考虑多仓库的共享单车重新配置问题研究

共享单车是我国大力提倡的低碳交通出行模式,加快共享单车发展是解决最后一公里、城市拥堵和环境污染等问题的重要途径。由于人们停放共享单车的无规律性,使得共享单车系统中各车桩的单车库存量存在不平衡。如何合理的对车桩中的单车进行重新调配,来满足用户的需求,是相关企业亟待解决的问题。共享单车的调配路线优化是优化车桩库存量的重要手段之一。本文研究多仓库条件下的货车调配路线优化问题,建立了一个混合整数非线性规划模型。不同于传统的路径优化问题的研究大多是以成本或时间为目标,本文采用基于车桩库存量的非线性惩罚函数来表示用户需求,从而使得所研究的问题是一个凸函数优化问题。为了简化本文的问题,将目标函数分段线性化。基于车桩网络的特点,设计了变邻域搜索算法,以及构建初始解的贪婪算法。最后,以某共享单车公司为例,进行算例分析,来说明模型和算法的合理性和有效性。     

Beyond problem structuring methods: reinventing the future of OR/MS

Some of the most influential pioneers of OR felt disappointed by the way it developed in the 1960s and 1970s. In their view, the original intention to create a holistic, interdisciplinary science addressed to strategic problems was betrayed. Problem structuring methods (PSMs) have made a significant contribution to taking OR/MS forward again in the direction charted by those pioneers. From a theoretical perspective, however, it is clear that the opportunities provided by PSMs tend to be limited to those drawn from the interpretive paradigm. That is only one way of adding to the positivist/quantitative approach of classical OR/MS. This paper suggests that OR has an obligation to explore a wider range of theoretical options and to convert the possibilities offered by all of these into a form that managers and management scientists can use. Only in this way can OR be reinvented to live up to the ambitions of its founders.