Decision development in facilitated modelling workshops

While the facilitated modelling literature recognises the importance of the group process within facilitated modelling workshops, published empirical research rarely examines their dynamic nature. In this paper, we address this gap in the literature in two ways. First, we propose to locate facilitated modelling workshops as the main focus of investigation, and adopt decision development as the analytical lens. Second, we provide guidance regarding how to implement a research strategy that is informed by such a focus. We start by mapping the different conceptualisations of decision development that seem embedded within the facilitated modelling tradition, and contrast them with theoretical models from the group communication field. Our analysis identifies a number of potentially useful areas for the study of facilitated modelling workshops from a decision development perspective, and articulates a number tentative research questions and testable propositions amenable to empirical research. Central to our proposal are research methods for the study of dynamic group processes. We thus discuss the steps required to extract group process data from facilitated modelling workshops that are usable and open to analysis. This includes a review of issues regarding research design, coding scheme development, data coding and choice of analytical techniques. Finally, we offer conclusions and briefly discuss some feasibility issues related to the implementation of our proposal.     

The Deployment of Personnel in a Branch Network—a Case Study in OR Methodology

This paper describes a successful study which was concerned with identifying appropriate levels of supernumerary staff in a branch network of a national service company. The case study is used to illustrate a number of OR methodology issues relating to problem identification, model design, implementation and choice of modelling approach:     

<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.     

Investigating Why Teachers Reported Continued Use and Sharing of an Educational Innovation After the Research Has Ended

We investigated prospects for reported sustainable adoption and sharing of an educational innovation through survey research including online questionnaires and telephone interviews. This investigation is part of the Scaling-Up SimCalc experimental program, which combines dynamic representational algebra software (SimCalc MathWorlds) with integrated curriculum and small professional development workshops focused on how to use the software and how to integrate this intervention into the larger year-long curriculum. Teachers who (1) perceived the usefulness of the SimCalc professional development as being consistent with personal aims and (2) perceived specific affordances of the software/curriculum to be valuable were more likely to report continued use of the innovation after the research had ended and that they had shared it with colleagues over time.     

On the modelling of nested risk-neutral stochastic processes with applications in insurance

We propose a modelling framework for risk-neutral stochastic processes nested in a real-world stochastic process. The framework is important for insurers that deal with the valuation of embedded options and in particular at future points in time. We make use of the class of State Space Hidden Markov models for modelling the joint behaviour of the parameters of a risk-neutral model and the dynamics of option market instruments. This modelling concept enables us to perform non-linear estimation, forecasting and robust calibration. The proposed method is applied to the Heston model for which we find highly satisfactory results. We use the estimated Heston model to compute the required capital of an insurance company under Solvency II and we find large differences compared to a basic calibration method.     

Beliefs and Perspectives of First‐Year,Alternative Preparation,Elementary Teachers in Urban Classrooms

Results from an earlier study ( Hart, 2002 ) suggested that a group of 14 teachers participating in an alternative preparation program for elementary teachers had developed beliefs that were consistent with current thinking in mathematics education. The current study follows 8 of those teachers into their first year of teaching in an urban classroom. Qualitative data were collected from three sources: reflection logs, mathematics case discussions, and field notes made during classroom observations. This provided a triangulation of perspectives: the teachers' views of themselves, the teachers' views of others, and the university faculty member's view of them. Also, teachers completed the Standards Belief Instrument (Zollman & Mason, 1996) at the end of Phase I and at the end of Phase II. Results from the instrument and the qualitative analysis suggest that the teachers maintained a strong reform perspective in their beliefs, but they were unable to consistently implement pedagogy that was consistent with those beliefs.     

Judgement and supply chain dynamics

Forecasting demand at the individual stock-keeping-unit (SKU) level often necessitates the use of statistical methods, such as exponential smoothing. In some organizations, however, statistical forecasts will be subject to judgemental adjustments by managers. Although a number of empirical and ‘laboratory’ studies have been performed in this area, no formal OR modelling has been conducted to offer insights into the impact such adjustments may have on supply chain performance and the potential development of mitigation mechanisms. This is because of the associated dynamic complexity and the situation-specific nature of the problem at hand. In conjunction with appropriate stock control rules, demand forecasts help decide how much to order. It is a common practice that replenishment orders may also be subject to judgemental intervention, adding further to the dynamic system complexity and interdependence. The system dynamics (SD) modelling method can help advance knowledge in this area, where mathematical modelling cannot accommodate the associated complexity. This study, which constitutes part of a UK government funded (EPSRC) project, uses SD models to evaluate the effects of forecasting and ordering adjustments for a wide set of scenarios involving: three different inventory policies; seven different (combinations of) points of intervention; and four different (combinations of) types of judgmental intervention (optimistic and pessimistic). The results enable insights to be gained into the performance of the entire supply chain. An agenda for further research concludes the paper.     

Interaction of intelligent and autonomous systems – part I: qualitative structuring of interaction

In this part I of the study, the development and the background of a meta-modelling technique to structure complex environments of systems is illustrated. A special situation-operator-model (SOM) developed to model the human-machine-interaction (HMI) is understood as a structuring approach modelling the interaction of intelligent systems in general. Part I of this study is structured as follows: Section 1 reflects on the term modelling with respect to the task: how to model interaction of unknown interaction partners, Section 2 briefly reviews the basics of the previously published foundations of the work and the SOM. The developed situation-operator-metamodelling approach is used to illustrate the connections between control loops and algorithms in Section 3, including a systematic view of systems' interaction mechanisms. In part II (part II available in this issue, pp. 319–339) of the contribution, the practical applications of the introduced approach are shown.     

An integer programming approach to short-term production scheduling in a tobacco plant

In this paper, a mathematical model is developed that facilitates daily production scheduling in a tobacco processing plant. The implied objectives are to meet specific horizon production targets (obtained from a master production schedule), to maintain safety stock requirements and to ensure that the demand for labour lies within given limits. The express objective is to minimise the number of machines used in the production process. Additionally, the model incorporates work-in-progress, aspects of the demand for product transportation within the plant and machine capacity (utilisation) reduction effects associated with production sequencing. These aspects are relevant when dealing with time intervals as small as a day but can be averaged out when dealing with monthly time intervals. The developments in this paper represents stage II of the modelling of the tobacco plant, where stage I (already completed) was centred on obtaining a monthly master production schedule for a year ahead and assisting in macro planning activities. This paper also sees the development of a simple user-friendly heuristic which facilitates production sequencing on a daily basis given the master production schedule obtained from Stage I.     

Facilitated modelling in operational research

The traditional way of employing operational research in organisational interventions has been the expert mode. In this mode, the problem situation faced by the client is given to the operational research consultant, who then builds a model of the situation, solves the model to arrive at an optimal (or quasi-optimal) solution, and then provides a recommendation to the client based on the obtained solution. An alternative mode of engagement is to conduct the whole intervention together with the client: from structuring and defining the nature of the problem situation of interest, to supporting the evaluation of priorities and development of plans for subsequent implementation. In this latter mode, the operational researcher works throughout the intervention not only as an analyst, but also as a facilitator to the client. This paper discusses this latter mode of engagement with clients, with particular emphasis on the use of facilitated modelling as the intervention tool. Drawing on research scattered across a range of publications and domains, the review presented here provides a formal definition of facilitated modelling, together with a general framework that allows the conceptualisation of a wide variety of facilitated modelling approaches to organisational intervention. Design issues in facilitated modelling and their practical implication are discussed, and directions for future research identified.     

Constructing Good Solutions for the Spanish School Timetabling Problem

In the school timetabling problem a set of lessons (combinations of classes, teachers, subjects and rooms) has to be scheduled within the school week. Considering classes, teachers and rooms as resources for the lessons, the problem may be viewed as the scheduling of a project subject to resource constraints. We have developed an algorithm with three phases. In Phase I an initial solution is built by using the scheme of parallel heuristic algorithm with priority rules, but imbedding at each period the construction of a maximum cardinality independent set on a resource graph. In Phase II a tabu search procedure starts from the solution of Phase I and obtains a feasible solution to the problem. The solution obtained is improved in Phase III. Several procedures based on the calculation of negative cost cycles and shortest paths in a solution graph are used to get more compact timetables.The algorithms have been imbedded in a package designed to solve the problem for Spanish secondary schools. The computational results show its performance on a set of real problems. Nevertheless, it can be applied to more general problems and results on a set of large random problems are also provided.     

A Distribution-Free Phase II EWMA Control Chart for Joint Monitoring of Location and Scale

A single distribution-free (nonparametric) Phase II exponentially weighted moving average (EWMA) chart based on the Cucconi statistic, referred to as the EWMA-Cucconi (EC) chart, is considered here for simultaneously monitoring shifts in the unknown location and scale parameters of a univariate continuous process. A comparison with some other existing nonparametric EWMA charts is presented in terms of the average, the standard deviation and some percentiles of the run length distribution. Numerical results based on Monte Carlo analysis show that the EC chart provides quite a satisfactory performance. The effect of the Phase I (reference) sample size on the IC performance of the EC chart is studied in detail. The application of the EC chart is illustrated by two real data examples.     

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??A single distribution-free (nonparametric) Phase II exponentially weighted moving average (EWMA) chart based on the Cucconi statistic, referred to as the EWMA-Cucconi (EC) chart, is considered here for simultaneously monitoring shifts in the unknown location and scale parameters of a univariate continuous process. A comparison with some other existing nonparametric EWMA charts is presented in terms of the average, the standard deviation and some percentiles of the run length distribution. Numerical results based on Monte Carlo analysis show that the EC chart provides quite a satisfactory performance. The effect of the Phase I (reference) sample size on the IC performance of the EC chart is studied in detail. The application of the EC chart is illustrated by two real data examples.     

Highly efficient parallel algorithm for finite difference solution to Navier–Stoke''s equation on a hypercube

It has been shown in [Nuclear Science and Engineering 93 (1986) 6799] that the finite difference discretization of Navier–Stoke's equation leads to the solution of N×N system written in the matrix form as My=B, where M is a quasi-tridiagonal having non-zero elements at the top right and bottom left corners. We present an efficient parallel algorithm on a p-processor hypercube implemented in two phases. In phase I a generalization of an algorithm due to Kowalik [High Speed Computation, Springer, New York] is developed which decomposes the above matrix system into smaller quasi-tridiagonal (p+1)×(p+1) subsystem, which is then solved in Phase II using an odd–even reduction method.     

A restriction and feasible direction algorithm for a capacity expansion problem

This paper examines the problem of optimally expanding existing capacity in order to meet an expected load in the context of an electric utility. A pre-optimization (Phase I) analysis is presented in order to easily determine (a) the capacities of existing equipments which will be used at an optimal solution; (b) the optimal (nonnegative) capacities of a subset of the new equipments to be purchased, and (c) a good quality starting solution. Having thus restricted a part of the solution to its optimal value, the problem is transformed into one of minimizing a convex, differentiable function, subject to a single generalized upper bounding constraint along with nonnegativity restrictions. An efficient specialization of a feasible directions algorithm (Phase II) is presented to solve this problem. The algorithm is versatile in that it provides a preview of whether or not all existing equipment capacity will be used in the light of available equipments, and which new equipments may be used in the optimal expansion plan. The algorithm can also solve the problem which enforces the use of all existing equipment capacity. Furhtermore, Phase I, which is the principal part of this algorithm, provides the user with insightful information. A numerical problem is analyzed to illustrate the effectiveness of the procedure.     

Secondary-school teachers’ noticing of aspects of mathematics teaching talk in the context of one-day workshops

In a research project with one-day teacher education workshops for secondary-school mathematics teachers, our study explores the potential of tool-supported discussions in helping them to notice important and critical aspects of mathematics teaching talk. Mathematical practices of naming and explaining in teaching talk, students’ content learning challenges, and noticing processes of identifying, interpreting and deciding are the components of our framework and the tools that guided the design and implementation of three workshops on linear equations, fractions and plane isometries. The data was collected during the discussions with the seven teachers and the teacher educator throughout these workshops. The coding of the discussions allowed us to see discourse moves that reveal the teachers’ noticing of: (i) challenges in the identification of mathematical naming, (ii) mathematical explaining that voices the students’ learning, (iii) classroom practice in relation to mathematical naming and explaining.     

Assigning students to course sections using tabu search

In this paper we describe a new student registration system which has been developed at the University of Valencia, Spain. The system has two steps. First, the students make a computer-aided course selection from the courses available at the University. Thereafter, an assignment procedure allocates students to sections in order to respect two criteria: to provide the students with satisfactory schedules and to get balanced section enrollments. The assignment process has two phases. In Phase I, we obtain a set of the best solutions for each student. The algorithm is based on the construction of maximum cardinality independent sets. In Phase II, these solution sets are put together and a tabu search algorithm looks for a satisfactory balance between course sections without causing the solution obtained for each student to worsen significantly. The system was used at the beginning of the academic year 1996/97 in the Faculty of Mathematics and could be extended in the near future to the rest of the University. This revised version was published online in June 2006 with corrections to the Cover Date.     

Optimal design and control of queues

We have divided this review into two parts. The first part is concerned with the optimal design of queueing systems and the second part deals with the optimal control of queueing systems. The second part, which has the lion’s share of the review since it has received the most attention, focuses mainly on the modelling aspects of the problem and describes the different kinds of threshold (control) policy models available in the literature. To limit the scope of this survey, we decided to limit ourselves to research on papers dealing with the three policies (N, T, and D), where a cost function is designed specifically and optimal thresholds that yield minimum cost are sought.     

Bayesian statistical process control for Phase I count type data

Count data, most often modeled by a Poisson distribution, are common in statistical process control. They are traditionally monitored by frequentist c or u charts, by cumulative sum and by exponentially weighted moving average charts. These charts all assume that the in‐control true mean is known, a common fiction that is addressed by gathering a large Phase I sample and using it to estimate the mean. “Self‐starting” proposals that ameliorate the need for a large Phase I sample have also appeared. All these methods are frequentist, ie, they allow only retrospective inference during Phase I, and they have no coherent way to incorporate less‐than‐perfect prior information about the in‐control mean. In this paper, we introduce a Bayesian procedure that can incorporate prior information, allow online inference, and should be particularly attractive for short‐run settings where large Phase I calibration exercises are impossible or unreasonable.