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The Basics of System Dynamics: Discrete vs. Continuous Modelling of Time
Abstract
System Dynamics deals with modelling of processes over time. In this paper we discuss two ways to model changes over time: finite vs. infinitesimal. This leads to two different concepts of time: discrete time as a succession of time points and time intervals vs. continuous time. Although the System Dynamics concept of distinguishing between stocks and flows suggests a discrete modelling of time, System Dynamics is considered mostly a modelling technique based on continuous time. In the paper we argue to see System Dynamics modelling compatible with both the continuous and the discrete concept of time. We will show that this "hybrid" potential makes System Dynamics a superior technique for modelling time, which combines the advantages of continuous and discrete time concepts.
... System dynamics deals with the modeling of processes over time [21]. Two different concepts of time are: continuoustime and discrete-time [21]. ...
... System dynamics deals with the modeling of processes over time [21]. Two different concepts of time are: continuoustime and discrete-time [21]. The continuous-time models are described by differential equations while the discrete-time models are expressed by difference equations. ...
In this paper, we attempt to mathematically formulate a susceptible-exposed-infectious-recovered-susceptible (SEIRS) epidemic model to study dynamical behaviors of malware propagation in scale-free networks (SFNs). In the proposed discrete-time epidemic model, we consider defense mechanism of software diversity to limit epidemic spreading in SFNs. Dynamical behaviors of the SEIRS epidemic model is determined by basic reproductive ratio, which is often used as a threshold parameter. Also, the impact of the assignment of diverse software packages on the propagation process is examined. Theoretical results show that basic reproductive ratio is significantly dependent on diverse software packages and the network topology. The installation of diverse software packages on nodes leads to decrease reproductive ratio and malware spreading. The results of numerical simulations are given to validate the theoretical analysis.
... As the time unit commonly used to report epidemiological data and describe clinical characteristics of COVID-19 in the literature is daily, the ABM modules Network and Temporary Staff use a daily time step. The stochastic SD module Intra-facility is theoretically in continuous time, with the time step dt representing an infinitesimally small interval (Allen, 2008;Ossimitz & Mrotzek, 2008). In practical implementation, the module operates with a finite time step dt of ½ 7 days to ensure that numerical outcomes are as close as possible to those of a continuous model without the burden of carrying out too many calculations. ...
The growing complexity of systems and problems that stakeholders from the private and public sectors have sought advice on has led systems modellers to increasingly use multimethodology and to combine multiple OR/MS methods. This includes hybrid simulation that combines two or more of the following methods: system dynamics (SD), discrete-event simulation, and agent-based models (ABM). Although a significant number of studies describe the application of hybrid simulation across different domains, research on the theoretical and practical aspects of combining simulation modelling methods, particularly the combining of SD and ABM, is still limited. Existing frameworks for combining simulation methods are high-level and lack methodological clarity and practical guidance on modelling decisions and elements specific to hybrid simulation that modellers need to consider. This paper proposes a practical framework for developing a conceptual hybrid simulation model that is built on reviews and reflections of theoretical and application literature on combining methods. The framework is then used to inform and guide the process of conceptual model building for a case study in controlling the spread of COVID-19 in care homes. In addition, reflection on the use of the framework for the case study led to refining the framework itself. This case study is also used to demonstrate how the framework informs the structural design of a hybrid simulation model and relevant modelling decisions during the conceptualisation phase.
... Changing conditions within the system are reflected by the interaction of different stocks and flows based on stock levels. This leads to balancing and reinforcing loops within the system, which are not present in other simulation approaches (Ossimitz and Mrotzek, 2008;Rahmandad and Sterman, 2008). As the not mainly forward interaction is one of the main characteristics of CEBMs, System Dynamics provides a very good fit for CE simulations (Angerhofer and Angelides, 2000;Schieritz and Gr€ oßler, 2003). ...
This research paper is concerned with potential barriers to the transition to a circular economy business model (CEBM) on the firm-level. Using a case study in the electronics manufacturing industry, we identify and analyze barriers in terms of their impact along the value chain (VC) as well as the level of difficulty required to overcome them. This allows us to map barriers to managerial responsibilities, thus improving the organizational transition process. The key findings of this research are: (1) To scale up CEBM on the firm-level, additional changes need to be implemented next to the oft-cited and discussed changes towards a Product-Service-System (PSS) and reverse logistics. Based on literature research and our case study, we put forward an extensive list of 29 potential barriers. (2) As managerial and financial resources are limited, we also suggest a priority ranking for barriers. Specifically, we show that barriers should be prioritized along the dimensions of their organizational resistivity and their impact on the VC. Organizational resistivity refers to the estimated effort along managerial time, financial resources, and cultural resistance for change, while VC impact refers to the ability of the barrier to influence and re-direct product, parts, and material flows along the foreword and reverse supply chain. This type of barrier assessment is new to the literature. (3) We argue that the proposed method for barrier prioritization, which we term the Circular Economy Matrix, can be readily transferred to manufacturing firms in other industries. (4) Clustering the barriers along managerial responsibilities (sets of barriers) is shown to lead to a more efficient and effective transition, as gauged by incurred transaction costs.
... The adaptation of the Static AHP to an environment which changes over time is generally called Dynamic AHP. 4,[22][23][24][25][26][27][28][29][30] In the light of these considerations, the aim of this paper is to propose a dynamic view of the AHP methodology for the assessment of tangible and intangible elements in a long-term decision-making scenario. This can be done by considering the longterm evolution of an assessment, 2 in order to take into account the changes (time by time) of AHP weights criteria. ...
The Analytic Hierarchy Process (AHP) is a methodology, based on both mathematical and psychological approaches, exploited to analyze and solve complex problems, in order to make the best decision. AHP is also widely employed for the evaluation of healthcare systems. It works by splitting the decision problem into a hierarchy of more easily-comprehended sub-problems, each of which can be independently analyzed. Starting from these assumptions, our work aims to implement a dynamic framework for the AHP methodology, able to overcome the static nature of the technique, taking into account the evaluations associated with criteria and sub-criteria as a function of time. In the context of this paper, the Dynamic AHP is implemented as a tool for Health Technology Assessment (HTA). Indeed, the proposed case study concerns the evaluation of a new health technology for the thyroglobulin assay in patients with differentiated thyroid cancer. To this aim, we have defined the decision problem and formalized criteria and sub-criteria hierarchically; then, in order to deal with the problem from a dynamical point of view, i.e., to take into account the time dependence of criteria and sub-criteria, we developed several System Dynamics models, one for each criterion. In this context, it is shown that the Dynamic AHP approach provides a dynamic evaluation of the system, which allows to identify the best decision by exploiting the information on the possible evolution of the problem due to its time behavior, rather than taking the decision at a fixed time point, as the Static AHP does.
... In System Dynamics models the main variable is time. However this type of modeling is considered mostly as based on continuous type, can be used in models with the discrete concept of time [10]. Applications of System Dynamics paradigms in manufacturing processes are presented in publications: e.g., [11][12][13][14][15]. ...
The paper describes advantages of teaching and application of modeling manufacturing systems. Two paradigms of modeling: Discrete Event (DE) and System Dynamics (SD) are briefly presented and compared. A few possibilities of teaching these approaches worldwide are presented. Furthermore, a combined way of teaching these two methods, with a focus on the modeling and simulating selected basic processes of manufacturing systems, is proposed in briefly described exercises. The concept provides division of this method depending on student’s education level.
... One of the representations is integral equation. The integral equation describes that new Stock (t) is defined through initial Stock (to) plus all Inflow (s) subtracted by all Outflow (s) between time to and time t as follows [9]: ...
Jeneberang River is mined in order to fulfill construction materials demand of Gowa Regency and Makassar City. The aim of this study were to develop the dynamical system for supply-demand model suitable for prospecting the future of construction materials and using the model to explore effects of parameter uncertainty by using sensitivity analysis, and to know how changing in parameters cause change in dynamic behavior of supply and demand. Primary data were collected through field survey and secondary data were obtained from Central Bureau Statistics of Gowa Regency and Makassar City, and Department of Mines and Energy of Gowa Regency. The supply-demand model was built based on multiple regression analysis, validated against field data, and proved well-performed. This study presented a new prediction model of construction materials supply and demand in dynamical system through simulation by using sensitivity analysis. The model is beneficial to learn the behavior of supply-demand interaction and very useful to provide information about future supply and demand sensitivity based on uncertain parameters. © 2006-2017 Asian Research Publishing Network (ARPN). All rights reserved.
... As shown in Figure 3, the underlying system dynamics model with discrete time steps (dt = 1) can reproduce the theoretical cobweb behavior. However, system dynamics models usually aim at continuous simulation by minimizing the integration steps (Ossimitz and Mrotzek, 2008). Therefore, the model in Figure 3(b) should be regarded as a special case rather than a typical system dynamics model. ...
Global industrial metal markets have experienced a drastic price decline over the past years. In this paper we link the dynamics of raw material markets and commodity price fluctuations to a delayed adjustment of supply. Drawing on the classical cobweb theorem we show how the implementation of this theorem using system dynamics may yield a valuable explanation, not only for the recent price decline, but also for possible future price movements. Starting from a simple cobweb model of general industrial markets, we couple the price-adjusting mechanics to the global copper market and demonstrate how a simple market model can be merged with a physical material flow model. This model captures both market dynamics and technical aspects of raw material processing, recycling and substitution and adds an explanation for the widely accepted fact that the cost structure of the copper industry cannot explain current price levels. Finally, we compare the system dynamics forecasting model with a traditional econometric forecasting method and found the system dynamics model to be more intuitive and better suited to capture and convey the structural market fundamentals. Copyright
... Thus we designed a mathematical model to interpret and fit the data obtained from the experimental cytometry bi-dimensional dot plots. To model system dynamics and the variation of " stocks " of cells as a function of time, equivalent representations can be proposed: the hydraulic metaphor, stock-flow/transition diagrams, integral equations, and differential equations[33]. We chose to explain our model with a state-transition diagram (Fig 3), a visual language that is accessible to biologists and provides an equivalence to a system of ODEs[34,35]. ...
Cell proliferation is the common characteristic of all biological systems. The immune system insures the maintenance of body integrity on the basis of a continuous production of diversified T lymphocytes in the thymus. This involves processes of proliferation, differentiation, selection, death and migration of lymphocytes to peripheral tissues, where proliferation also occurs upon antigen recognition. Quantification of cell proliferation dynamics requires specific experimental methods and mathematical modelling. Here, we assess the impact of genetics and aging on the immune system by investigating the dynamics of proliferation of T lymphocytes across their differentiation through thymus and spleen in mice. Our investigation is based on single-cell multicolour flow cytometry analysis revealing the active incorporation of a thymidine analogue during S phase after pulse-chase-pulse experiments in vivo, versus cell DNA content. A generic mathematical model of state transition simulates through Ordinary Differential Equations (ODEs) the evolution of single cell behaviour during various durations of labelling. It allows us to fit our data, to deduce proliferation rates and estimate cell cycle durations in sub-populations. Our model is simple and flexible and is validated with other durations of pulse/chase experiments. Our results reveal that T cell proliferation is highly heterogeneous but with a specific “signature” that depends upon genetic origins, is specific to cell differentiation stages in thymus and spleen and is altered with age. In conclusion, our model allows us to infer proliferation rates and cell cycle phase durations from complex experimental 5-ethynyl-2'-deoxyuridine (EdU) data, revealing T cell proliferation heterogeneity and specific signatures.
... It is noteworthy that the models are typically introduced as continuous-time and discrete-time models. The continuous-time models lead to solving a system of linear differential equations of the system parameters while the discrete-time models solve a system of difference equations[32]. In recent years, the discrete-time epidemic models have received more attention[13]; the reasons are as follows[12]: (1) statistical data on epidemics is obtained in discrete time; it is more convenient and accurate to illustrate epidemics using discrete-time models than the continuous-time models[33], (2) the numerical simulation results using discrete-time models are more accurate, (3) the numerical simulations of continuous-time models are obtained by discretizing the models, (4) the discrete-time models have more wealthy and complex dynamical behaviors. ...
In this paper, we propose a discrete-time susceptible–exposed–infected–recovered–susceptible (SEIRS) epidemic model of malware propagation in scale-free networks (SFNs) with considering software diversity. We study dynamical behavior of the SEIRS model, which is determined by a threshold (i.e., basic reproductive ratio). With this threshold, we can predict whether the malware propagates or not. Also, using a coloring algorithm, the number of diverse software packages installed on nodes is calculated and used as a parameter to prevent malware spreading. Furthermore, we investigate global dynamics of the model and analyze the stability of the malware-free equilibrium. The dynamics of malware propagation is evaluated using the results of numerical simulations. Simulation results show that the proposed model, which considers software diversity, is more effective than other existing epidemic models. We have compared different immunization mechanisms, and have shown that the targeted immunization is better than the random immunization for controlling malware spreading in SFNs.
... In contrast, changes occur continuously and smoothly in the continuous simulation technique. Ossimitz and Mrotzek (2008) argue that although SD is generally considered to be a methodology based on continuous time; it is compatible both with the continuous and the discrete concept of time. This conclusion is similar to that of Huggett (1993), who found that, although continuous aggregated models of environmental systems have their uses, more complex discrete disaggregated models are usually preferred. ...
This paper details a system dynamics model developed to simulate proposed changes to water governance through the integration of supply, demand and asset management processes. To effectively accomplish this, interconnected feedback loops in tariff structures, demand levels and financing capacity are included in the model design, representing the first comprehensive life-cycle modelling of potable water systems. A number of scenarios were applied to Australia’s populated South-east Queensland region, demonstrating that introducing temporary drought pricing (i.e. progressive water prices set inverse with availability), in conjunction with supply augmentation through rain-independent sources, is capable of efficiently providing water security in the future. Modelling demonstrated that this alternative tariff structure reduced demand in scarcity periods thereby preserving supply, whilst revenues are maintained to build new water supply infrastructure. In addition to exploring alternative tariffs, the potential benefits of using adaptive pressure-retarded osmosis desalination plants for both potable water and power generation was explored. This operation of these plants for power production, when they would otherwise be idle, shows promise in reducing their net energy and carbon footprints. Stakeholders in industry, government and academia were engaged in model development and validation. The constructed model displays how water resource systems can be reorganised to cope with systemic change and uncertainty.
... In contrast, changes occur continuously and smoothly in the continuous simulation technique. Ossimitz and Mrotzek (2008) argue that although SD is generally considered to be a methodology based on continuous time; it is compatible both with the continuous and the discrete concept of time. This conclusion is similar to that of Huggett (1993), who found that, although continuous aggregated models of environmental systems have their uses, more complex discrete disaggregated models are usually preferred. ...
This paper details a system dynamics model developed to simulate proposed changes to water governance through the integration of supply, demand and asset management processes. To effectively accomplish this, interconnected feedback loops in tariff structures, demand levels and financing capacity are included in the model design, representing the first comprehensive life-cycle modelling of potable water systems. A number of scenarios were applied to Australia's populated South-east Queensland region, demonstrating that introducing temporary drought pricing (i.e. progressive water prices set inverse with availability), in conjunction with supply augmentation through rain-independent sources, is capable of efficiently providing water security in the future. Modelling demonstrated that this alternative tariff structure reduced demand in scarcity periods thereby preserving supply, whilst revenues are maintained to build new water supply infrastructure. In addition to exploring alternative tariffs, the potential benefits of using adaptive pressure-retarded osmosis desalination plants for both potable water and power generation was explored. This operation of these plants for power production, when they would otherwise be idle, shows promise in reducing their net energy and carbon footprints. Stakeholders in industry, government and academia were engaged in model development and validation. The constructed model displays how water resource systems can be reorganised to cope with systemic change and uncertainty.
... According to Frenkiel and Goodall (1978), who identified the relationships between major simulation techniques, a discrete simulation is often appropriate for situations where the system being studied contains a number of separate items, and each item has its own characteristics and period of existence within the system, whereas, changes occur continuously and smoothly in the continuous simulation technique. Ossimitz and Mrotzek (2008) argue that, although it is generally considered to be a methodology based on continuous time, SD is compatible both with the continuous and the discrete concept of time. ...
Water supply and demand planning is often conducted independently of social and economic strategies. There are presently no comprehensive life-cycle approaches to modelling urban water balances that incorporate economic feedbacks, such as tariff adjustment, which can in turn create a financing capacity for investment responses to low reservoir levels. This paper addresses this gap, and presents a system dynamics model that augments the usual water utility representation of the physical linkages of water grids, by adding inter-connected feedback loops in tariff structures, demand levels and financing capacity. The model, applied in the south-east Queensland region in Australia, enables simulation of alternatives and analysis of stocks and flows around a grid or portfolio of bulk supplies including an increasing proportion of rain-independent desalination plants. Such rain-independent water production plants complement the rain-dependent sources in the region and can potentially offer indefinite water security at a price. The study also shows how an alternative temporary drought pricing regime not only defers costly bulk supply infrastructure but actually generates greater price stability than traditional pricing approaches. The model has implications for water supply planners seeking to pro-actively plan, justify and finance portfolios of rain-dependent and rain-independent bulk water supply infrastructure. Interestingly, the modelling showed that a temporary drought pricing regime not only lowers the frequency and severity of water insecurity events but also reduces the long-run marginal cost of water supply for the region when compared to traditional reactive planning approaches that focus on restrictions to affect demand in scarcity periods.
This paper presents a model to predict the market penetration of autonomous cars for passenger transportation, focussing on autonomous taxis without a steering wheel. For this, a discrete system dynamics model was created and evaluated where the input parameters have been taken from the literature and a survey. In this survey, user demands were investigated among 873 participants. It showed that gender, age, job situation, city size and monthly income have an impact on the trust in the technology of autonomous driving as well as on the willingness to use autonomous taxis. In contrast, no evidence of an impact was found for the respondent’s education or the numbers of adults or children in the household.
The results indicate that the majority of autonomous driving vehicles will be private and will have a steering wheel within the scope of this study, which covers the time frame until 2040. These are expected to reach 12.4 million units. At the same time, autonomous taxis will enter the market. These are expected to be mainly non-controllable (without a steering wheel), reaching a maximum of 2.4 million units by 2038. This maximum mainly depends on the trust in the technology as well as on people’s willingness to give up their own car due to cost or usage factors. As an autonomous taxi supports more people on average, the total number of vehicles is expected to drop from 45.1 million to around 41.7 million by 2040. Furthermore, the percentage of people travelling primarily by taxis and public transport is expected to increase from today’s 20.0% to about 32% in 2040. Then, about 19% will use autonomous taxis at least occasionally. Lastly, the vehicle miles travelled are expected to increase by 25% with people switching from public transport to autonomous taxis.
The utilization of Computer-aided Manufacturing has allowed for rapid growth in the automotive and aerospace industries; however, effects of such advancements have not been fully realized in modern day construction. Even in the case of automated solutions, there are relatively few studies available in the literature which describe such systems. This paper introduces a prototype machine for fastening light-gauge steel framed wall-panels, proposing a framework for transferring manufacturing information outputted from building information models (BIM) to an open source file format readable by the programmable logic controller used to control the introduced machine. The proposed framework generates collision-free tool trajectories through the implementation of collision detection and avoidance modules. These modules are designed to intelligently plan operations for safe tool movement and easy integration of in-shop modifications. Real-world results from various panel configurations are presented to validate the accurate information transfer between the 3D-BIM outputs and the prototype machine.
In this paper, we propose a susceptible-exposed-infected-recovered-susceptible (SEIRS) epidemic model in scale-free networks (SFNs). The aim has been to model the impact of software diversity and a defense mechanism to reduce malware propagation in SFNs. The dynamics of network topology was considered during the propagation process. During the malware propagation, the network topology varies considering leaving and joining of nodes. Reproduction ratio as a measure of epidemics plays an important role in dynamic behavior of discrete-time SEIRS models. The number of diverse software packages installed on nodes is calculated and used as a parameter to prevent malware propagation. The accuracy of the model is investigated by comparing the numerical results of the analytical solution and simulation outputs.
The proliferation of a diversity of capable ManPADS missiles poses a serious threat to civil and military aviation.
Aircraft self protection against missiles requires increased sophistication as missile capabilities increase. Recent
advances in self protection include the use of directed infrared countermeasures (DIRCM), employing high power
lamps or lasers as sources of infrared energy. The larger aircraft self-protection scenario, comprising the missile,
aircraft and DIRCM hardware is a complex system. In this system, each component presents major technological
challenges in itself, but the interaction and aggregate behaviour of the systems also present design difficulties
and performance constraints. This paper presents a description of a simulation system, that provides the ability to model the individual components in detail, but also accurately models the interaction between the components, including the play out of the engagement scenario. Objects such as aircraft, flares and missiles are modelled as a three-dimensional object with a physical body, radiometric signature properties and six-degrees-of-freedom kinematic behaviour. The object’s physical body is modelled as a convex hull of polygons, each with radiometric properties. The radiometric properties cover the 0.4–14 μm spectral range (wider than required in current technology missiles) and include reflection of sunlight, sky radiance, atmospheric effects as well thermal self-emission. The signature modelling includes accurate temporal variation and spectral descriptions of the object’s signature. The object’s kinematic behaviour is modelled using finite difference equations. The objects in the scenario are placed and appropriately orientated in a three-dimensional world, and the engagement is allowed to play out. Low-power countermeasure techniques against the missile seekers include jamming (decoying by injecting false signals) and dazzling (blinding the sensor). Both approaches require knowledge of the missile sensor and/or signal processing hardware. Simulation of jamming operation is achieved by implementing the missile-specific signal processing in the simulation (i.e. accurate white-box modelling of actual behaviour). Simulation of dazzling operation is more difficult and a parametric black-box modelling approach is taken. The design and calibration of the black-box dazzling behaviour is done by heuristic modelling based on experimental observations. The black-box behaviour can later be replaced with verified behaviour, as obtained by experimental laboratory and field work, using the specified missile hardware. The task of simulating a DIRCM system is scoped, by considering the threats, operational requirements and detailed requirements of the respective models. A description is given of the object models in the simulation, including key performance parameters of the models and a brief description of how these are implemented. The paper closes with recommendations for future research and simulation investigations.
This paper proposes a cartography investigation on diagnostics and prognostics techniques accomplished in order to setup the health management for complex vehicle systems in accordance with IVHM (Integrated Vehicle Health Management) principles. Relevant reviews and surveys of the existing approaches are generally realized as statements of the achievements in these fields; however they rarely tackle both diagnostics and prognostics. As classic criteria do not respond to current needs in IVHM, this paper has isolated several main features in order to formally prove the accordance and the effective choice between the system-of-interest, its maintenance system and diagnostics and prognostics algorithms. Thus, the proposed criteria are oriented on the target and on the maintenance systems. The investigated classification established through a multi-criteria selection reveals new orientations which should be considered in IVHM and it also enables further research on future pertinent methods for building a smart multi-model vehicle health assessment reasoner.
This paper describes the process of optimizing a 450 volt shipboard power plant model. The model is developed in MathWorks® Simulink® and used for software-in-the-loop (SIL) simulation of real-time control systems. At a total block count in excess of 135,000, the model complexity reached the point it could not be compiled. Additionally, one of the project requirements was to maintain soft real-time execution when compiled. Through the use of a number of optimization techniques, these goals were achieved. The key optimizations discussed are architectural changes, legacy code conversion, and continuous to discrete conversion.
Dynamic modeling of lymphocyte behavior has primarily been based on populations based differential equations or on cellular agents moving in space and interacting each other. The final steps of this modeling effort are expressed in a code written in a programing language. On account of the complete lack of standardization of the different steps to proceed, we have to deplore poor communication and sharing between experimentalists, theoreticians and programmers. The adoption of diagrammatic visual computer language should however greatly help the immunologists to better communicate, to more easily identify the models similarities and facilitate the reuse and extension of existing software models. Since immunologists often conceptualize the dynamical evolution of immune systems in terms of “state-transitions” of biological objects, we promote the use of unified modeling language (UML) state-transition diagram. To demonstrate the feasibility of this approach, we present a UML refactoring of two published models on thymocyte differentiation. Originally built with different modeling strategies, a mathematical ordinary differential equation-based model and a cellular automata model, the two models are now in the same visual formalism and can be compared.
In a world of accelerating change, educators, business leaders, environmentalists and scholars are calling for the development of systems thinking to improve our ability to take effective actions. Through courses in the K-12 grades, universities, business schools, and corporations, advocates seek to teach people to think systemically. These courses range from one-day workshops with no mathematics to graduate level courses stressing formal modeling. But how do people learn to think systemically? What skills are required? Does a particular type of academic background improve one's ability to think systemically? What systems concepts are most readily understood? Which tend to be most difficult to grasp? We describe initial results from an assessment tool or systems thinking inventory. The inventory consists of brief tasks designed to assess particular systems thinking concepts such as feedback, delays, and stocks and flows. Initial findings indicate that subjects from an elite business school with essentially no prior exposure to system dynamics concepts have a poor level of understanding of stock and flow relationships and time delays. Performance did not vary systematically with prior education, age, national origin, or other demographic variables. We hope the inventory will eventually provide a means for testing the effectiveness of training and decision aids used to improve systems thinking skills. We discuss the implications of these initial results and explore steps for future research. Copyright © 2000 John Wiley & Sons, Ltd.
Can Students Learn Stock-Flow-Thinking? An Empirical Investigation International System Dynamics Conference, System Dynamics Society Stock-Flow Thinking and Reading Stock-Flow-Related Graphs: An Empirical Investigation in Dynamics Thinking Abilities
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Stock-Flow Thinking and Reading Stock-Flow-Related Graphs: An Empirical Investigation in Dynamics Thinking Abilities
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Das Metanoia-Prinzip: Eine Einführung in systemisches Denken und Handeln
- G Ossimitz
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Denken und Handeln. Hildesheim: Franzbecker Verlag.