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# System Dynamics Models

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### System Dynamics Models

1. 1. Small System Dynamics Models for Big Issues Triple Jump towards Real-World Dynamic Complexity Erik Pruyt | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |\$| | | First time readers: start with the preface | |
2. 2. Chapter 7 MCQs Part II ‘It’s so much easier to suggest solutions when you don’t know too much about the problem.’ Malcolm Forbes Which of the following statements are right and which are wrong? 1. The value of a stock variable can only be changed, during a simulation, by its ﬂow variables. 2. An inﬂow cannot be negative. 3. The behavior of a stock is described by a diﬀerential equation. 4. If two causally linked variables show exactly same behavior as a function of time, then one of these variables is a stock. 5. A stock variable always needs to be embedded in at least one loop. 6. Plugging a SD model with correction factors that do not have any relation to the real world system is not considered good SD practice. 7. If a hypothetical sheet of paper that could be folded inﬁnitely is about 0.1mm thick and the maximum distance between the earth and the moon is 405500 km, then folding the paper 42 times more than bridges the maximum distance between earth and moon. 8. The units of inﬂow variables and outﬂow variables of the same stock variable always have the same units. 9. Non-linear functions, feedback loops, or their combination can generate non-linear dynamics. 10. Underlying SD models, there is exactly one diﬀerential equation for each feedback loop. 11. Diﬀusion and transition models always have the same feedback loop structure consisting of one + or R and one - or B . 12. Quantitative System Dynamics simulation results need to be interpreted qualitatively. 13. If A →+ B, both variables A and B were increasing until time t, and variable A starts to decrease at time t, then variable B may either start to decrease or keep on increasing but at a reduced rate of increase. 14. If a potentially important variable is not reliably quantiﬁable, it should be omitted from a SD model. 15. In SD studies, conclusions can only be drawn validly if they are based on simulations. 102
3. 3. c⃝ 2013 by Erik Pruyt RUN-UP: MCQs Part II Multiple Choice Question 1 The equation for the CLD on the right –with p(t) = size of the rat population, g the annual number of births per rat, and s the annual number of deaths per rat– is: a. p(t) = gp(t) − sp(t) b. p(t) = g(t)/s(t) c. dp(t)/dt = gp(t) d. dp(t)/dt = gp(t) − sp(t) Multiple Choice Question 2 Consider the SD model displayed on the right, with c > 0, d > 0, A0 > 0, en B0 > 0. The formula of the ﬂow variable is equal to c.d.A.B/(A + B). Which behavior corresponds to (stock) variable B? (a) (b) (c) (d) Multiple Choice Question 3 Many European countries consider raising the retirement age to keep the social security system ﬁnancially healthy. To study this issue in its most basic form (that is: all adults work, only the retired die, ﬁrst-order delays are good approximations, etc.), three groups need to be discerned: the kids K, adults younger than the retirement age A, and retirees R (see the incomplete stock-ﬂow diagram below). | | | | | | | | | | | | | | | | | | | | | | |STOP | 103 | | | | | | | | | | | | | | |\$| | |
4. 4. RUN-UP: MCQs Part II c⃝ 2013 by Erik Pruyt Which of the following systems of diﬀerential equations is best suited for studying the sustain- ability of the security systems? [death rate of the Retired = m; birth rate per adult = b; average residence time in group K = t1 and in group A = t2]. a.    dK(t) dt = bK(t) − t1K(t) dA(t) dt = t1K(t) − t2A(t) dR(t) dt = t2A(t) − R(t)/m b.    dK(t) dt = K(t) t1 − A(t) t2 dA(t) dt = K(t) b − K(t) t1 dR(t) dt = A(t) t2 − mR(t) c.    dK(t) dt = bA(t) − K(t) t1 dA(t) dt = K(t) t1 − A(t) t2 dR(t) dt = A(t) t2 − mR(t) d.    dK(t) dt = bK(t) − K(t) t1 dA(t) dt = K(t) t1 − A(t) t2 dR(t) dt = A(t) t2 − mR(t) Multiple Choice Question 4 The graph on the right contains data and projections of the CBS (Dutch Central Bureau of Statistics) concerning the births (blue) and deaths (red) in the Netherlands between 1960 and 2060. Assuming there is no net migration in this period, it means that: a. the Dutch population remained more or less constant be- tween 1980 and 2000 because births and deaths developed more or less in parallel; b. the Dutch population is projected to decrease between 2000 and 2032 because the number of deaths increases faster in that period than the number of births; c. the Dutch population is projected to keep on growing till 2032 – nevertheless with a decreasing growth rate, because the number of deaths remains larger than the number of births; d. none of the statements above is correct. Blue: births x1000; Red: deaths x1000; Source: CBS in NRC Han- delsblad 17/12/2010 p4. Multiple Choice Question 5 The unit of time in a model concerning the large-scale introduction of wind turbines is expressed in months. The production capacity of a company that produces wind turbines is modeled as a stock variable with units expressed in turbine/month. The enormous growth of the demand for new wind turbines, leads to an increase of the production capacity of the company. Which unit needs to be used for the increase of the production capacity of the company? | | | | | | | | | | | | | | | | | | | | | | |STOP | 104 | | | | | | | | | | | | | | |\$| | |
5. 5. c⃝ 2013 by Erik Pruyt RUN-UP: MCQs Part II a. turbine b. turbine/month c. turbine/month2 d. (turbine/month)2 Multiple Choice Question 6 The green curve in the left hand side graph is the only inﬂow ‘in’ into a stock variable, and the red line is the only outﬂow ‘uit’ out of the same stock variable. Which of the behaviors in the right hand side graph corresponds, given the ‘in’ and ‘uit’ ﬂows, with the behavior of the stock variable? a. curve 1 (green) b. curve 2 (red) c. curve 3 (dark blue) d. curve 4 (light blue) Multiple Choice Question 7 The graph below shows the number of parcels entering and leaving a warehouse between 10:00am en 10:35am in time intervals of 5 minutes. It is unknown how many parcels there were in the warehouse before 10:00am. It is unknown how many parcels left the warehouse after 10:35am. In which time interval between 10:00am and 10:35am was the smallest number of parcels inside the warehouse? a. The number of parcels inside was smallest at 10:00am or 10:05am. b. The number of parcels inside was smallest at 10:15am or 10:20am. c. The number of parcels inside was smallest at 10:30am or 10:35am. d. That cannot be determined with the information provided here. | | | | | | | | | | | | | | | | | | | | | | |STOP | 105 | | | | | | | | | | | | | | |\$| | |
6. 6. RUN-UP: MCQs Part II c⃝ 2013 by Erik Pruyt Multiple Choice Question 8 The left hand side graph in the above ﬁgure shows the behavior of two out of three ﬂows of the stock-ﬂow diagram displayed on the right. The third ﬂow is proportional to the Stock. Which of the following ﬁgures displays possible behaviors for the Stock and outﬂow1 that could have been generated with the above structure? (a) (b) (c) (d) Multiple Choice Question 9 What was long predicted, happened in the second quarter of 2010: China’s economy became bigger than Japan’s. The Japanese economy amounted in the second quarter to \$ 1290 billion, against \$ 1340 billion for China. Economists point out that Japanese welfare is still much higher than Chinese welfare. The average Japanese income (\$ 37800 per capita) is about 10 times higher | | | | | | | | | | | | | | | | | | | | | | |STOP | 106 | | | | | | | | | | | | | | |\$| | |
7. 7. c⃝ 2013 by Erik Pruyt RUN-UP: MCQs Part II than the average Chinese income. Measured in Gross Domestic Product per year, the top ﬁve currently looks –according to the ﬁgures of the IMF– as follows: the United States of America are the largest economic power (e10995 billion), far ahead of China (e4319 billion), Japan (e4053 billion), Germany (e2486 billion) and France (e1921 billion). Practically all analysts predict that China will take over the lead from the USA – the only question seems to be when. When will China take over the lead from the USA if China keeps on growing at a rate of 11,9% per year as in the ﬁrst quarter of 2011, and the USA at 2% per year? a. 2019; b. 2021; c. 2023; d. 2027. Multiple Choice Question 10 Given is the fully displayed sub- model of a company with a large number of employees on the left. The model is about gain and loss of experience, which is mea- sured in weeks. The SD model aggregates the experience of all employees in the company. All relevant variables are displayed; no constants or parameters are used that are not shown. Employees gain experience over the course of time. If an employee leaves the company, then it is assumed that the employee leaves with his/her experience which equals the average experience. The formula for loss of experience is equal to the ﬁring and attrition of employees times the aver- age experience of employees. The formula for average experience is equal to the total experience of employees divided by number of employees in the company. The number of employees is expressed in ‘person’, the unit of time is expressed in ‘week’. What units should be used for the average experience of employees and the total experience of employees? a. week; person * week; b. Dmnl; person; c. week; person; d. Dmnl; week/person. Multiple Choice Question 11 The green line in the graph on the left is the only inﬂow ‘in’ into a stock variable. The blue line with the positive slope is the only outﬂow ‘uit’ out of this same stock variable. Which of the patterns of behavior on the right could, given the ‘in’ and ‘uit’ ﬂows, correspond to the stock variable? a. pattern 1 (green) b. pattern 2 (blue) c. pattern 3 (orange) d. pattern 4 (red) | | | | | | | | | | | | | | | | | | | | | | |STOP | 107 | | | | | | | | | | | | | | |\$| | |
8. 8. RUN-UP: MCQs Part II c⃝ 2013 by Erik Pruyt Multiple Choice Question 12 The SD model below could be used to calculate demographic scenarios. Suppose one uses the model to project the expected demographic developments in Germany starting from following assumptions about the ﬂow variables (see also the graph below): The net immigration decreases from 300000 in 2000 to 0 in 2008 and remains constant at that level until the year 2025 after which an annual amount of immigrants equal to 500000 are admitted. The birth rate decreases linearly from 0.0083 in 2000 to 0.0075 in 2050. The death rate increases linearly from 0.01 in 2000 to 0.02 in 2050. Given these assumptions and the model displayed above, what would be the expected evolution of the stock variable ‘Inhabitants’? | | | | | | | | | | | | | | | | | | | | | | |STOP | 108 | | | | | | | | | | | | | | |\$| | |
9. 9. c⃝ 2013 by Erik Pruyt RUN-UP: MCQs Part II Multiple Choice Question 13 Consider the model below. Assume that it is in equilibrium. Inventory is measured in ‘item’, the time unit of the model is days. The variable X is deﬁned as X = inventory/shipment rate. What is the unit of X? What would be a good name for X? a. dimensionless, average residence time b. day, average residence time c. day, residence coeﬃcient d. 1/day, day Multiple Choice Question 14 Pattern 1 in the graph on the left shows the only inﬂow ‘in’ into a stock variable and pattern 2 its only outﬂow ‘out’. Which pattern of behavior on the right belongs to the stock variable? a. pattern 1 (blue) b. pattern 2 (red) c. pattern 3 (pink) d. pattern 4 (orange) Multiple Choice Question 15 Diﬀerent parts of the Dutch housing market have been under attack from diﬀerent sides for the past few years. The social housing market too. According to the European Commission, the rules and organization of the Dutch corporation system did not correspond to the purpose of social housing. That is, the social rental market was not restricted to the poor. Although nobody complained, the European Commission argued that the Dutch rental market did not comply with the rules of free competition, creating a situation of unfair competition with the private rental market, resulting in a distorted housing market. After long negotiations, the Dutch government and the European Commission agreed that after 1/1/2011, 90% of all social housing vacancies would be allocated to families with incomes up to e28475 per year – which is below modal. However, no agreement was reached about the majority of above modal income families in the social housing sector, resulting in the situation that above modal income families were not allowed to move (upward or sideways) inside the social housing sector any more. For them, moving meant, from then on, leaving the social housing sector, i.e. buying or renting on the (excessively expensive) private market. Before 1/1/2011, the housing market was a pull system: after an attractive house had become vacant, another social housing family would soon move to the vacant house, freeing up their own house, which would soon be ﬁlled up by yet another social housing family, until ﬁnally, a ‘starters house’ | | | | | | | | | | | | | | | | | | | | | | |STOP | 109 | | | | | | | | | | | | | | |\$| | |
10. 10. RUN-UP: MCQs Part II c⃝ 2013 by Erik Pruyt would become vacant and would be occupied by young entrants into the social housing system. Due to these regulations, higher income families stay put, which brought the dynamics on the social renting market to a halt. Consider the SFD of a Dutch social housing simulation model displayed above. Which of the following CLDs corresponds to this SFD? (a) (b) (c) (d) | | | | | | | | | | | | | | | | | | | | | | |STOP | 110 | | | | | | | | | | | | | | |\$| | |
11. 11. c⃝ 2013 by Erik Pruyt RUN-UP: MCQs Part II Multiple Choice Question 16 Consider the detailed CLD on the outbreak of a disease displayed above. Which of the following SFDs corresponds best to this CLD? (a) (b) (c) (d) | | | | | | | | | | | | | | | | | | | | | | |STOP | 111 | | | | | | | | | | | | | | |\$| | |
12. 12. RUN-UP: MCQs Part II c⃝ 2013 by Erik Pruyt Multiple Choice Question 17 Consider the above simulation model and behavior of the ﬂow variable. What is the corresponding behavior of the stock variable? (a) (b) (c) (d) Multiple Choice Question 18 What is wrong with the SFD on the right? a. There are too many inﬂows into the stock. b. There is a variable in the diagram that is not inﬂuenced by other variables, hence it should have been modeled as a constant. c. There is a loop in the diagram without a stock variable, which is not allowed. d. The diagram is correct. | | | | | | | | | | | | | | | | | | | | | | |STOP | 112 | | | | | | | | | | | | | | |\$| | |
13. 13. c⃝ 2013 by Erik Pruyt RUN-UP: MCQs Part II Multiple Choice Question 19 Suppose a stock variable displays the behavior over time displayed above. If the stock variable only has one ﬂow variable, more precisely an inﬂow, then what is the corresponding behavior of the inﬂow? (a) none of the behaviors below (b) (c) (d) Multiple Choice Question 20 Suppose you made the model on the left. By simulating the model, you obtained the behavior on the right. What can you say about the link between model and behavior? a. You found the critical variable values that make model behave chaotically. b. It is impossible to obtain this behavior with that model since it is a model with only one independent stock variable. c. You have chosen a bad time step: the output shown is due to a numeric solution error. d. The model has complex eigenvectors. Link to the answers to the 15 right/wrong questions & 20 multiple choice questions in this chapter. Links to web based quizzes: | | | | | | | | | | | | | | | | | | | | | | | | | | |STOP | 113 | | | | | | | | | | | | | | |\$| | |
14. 14. Flexible E-Book for Blended Learning with Online Materials Although this e-book is ﬁrst and foremost an electronic case book, it is much more than just a set of case descriptions: it is the backbone of an online blended-learning approach. It consists of 6 concise theory chapters, short theory videos, 6 chapters with about 90 modeling exercises and cases, many demo and feedback videos, feedback sheets for each case, 5 overall chapters with feedback, 5 chapters with multiple choice questions (with graphs or ﬁgures), hundreds of online multiple choice questions, links to on-site lectures, past exams, models, online simulators, 126 slots for new exercises and cases, and additional materials for lecturers (slides, exams, new cases). The fully hyperlinked e-version allows students (or anybody else for that matter) to learn –in a relatively short time– how to build SD models of dynamically complex issues, simulate and analyze them, and use them to design adaptive policies and test their robustness. ISBN paperback version: ISBN e-book version: