System Dynamics Models: MCQs part III

Small System Dynamics Models

forBig Issues

Triple Jump towards Real-World Dynamic Complexity

Erik Pruyt

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Chapter 11

MCQs Part III

‘[A]ll models are wrong, but some are useful’ (Box and Draper 1987)

Which of the following statements are right and which are wrong?

1. The smaller the smoothing time, the smaller the oscillations in the smoothed response are.

2. A seed is a number from which a pseudo-random number is generated.

3. The number of feedback loops in a CLD equals the order of the system being modeled: e.g.a feedback loop system with 2 loops corresponds to a 2nd order system.

4. In models containing discrete functions, Euler is the most appropriate integration method.

5. For a given step size, Runge-Kutta(4) will always outperform Euler in a purely continuousmodel with oscillatory tendencies.

6. SD models are continuous models: a model with discrete functions cannot be called a SDmodel since it is not continuous.

7. In SD models, using softmin/softmax structures is always better than min/max functions.

8. It is possible that the same real-world system element –for various levels of aggregation andtime horizons of interest– is modeled as a constant, a stock, a flow, or an auxiliary.

9. A softmin is a smoothed min function in a soft variable.

10. Two step functions can substitute a pulse function, and a pulse function in an inflow plus astock variable can substitute a step function.

11. Using random sampling is a substitute for using randomizers.

12. Unexpected runaway behavior could be caused by a sign error in a stock equation, e.g.INTEG(-inflow, initial) or INTEG(+outflow, initial).

13. Floating point errors indicate that even though all equations can be computed, values to becomputed are too big. They are often caused by positive feedback loops or divisions by 0.

14. If the eigenvalues of a 2nd order SODE are complex with a negative real part, then thebehavior is asymptotically stable in the equilibrium points.

15. PULSE TRAINS can be replicated with a combination of Time, Modulo and PULSE func-tions.

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HOP: MCQs Part III c⃝ 2013 by Erik Pruyt

Multiple Choice Question 1

Consider the cash balance model of a companyon the left. Receipts (blue –1–) flow into the bal-ance at a particular rate, and expenditures (red–2–) flow out at a particular rate as is displayedon the right. The graph on the right shows theevolution of the receipts and expenditures overtime. Given this information and assuming thatthe initial cash balance equals e100, what is thebehavior of the firm’s cash balance?

(a) (b)

(c) (d)


Using a simplistic SD model one can foresee that the currently known gas reserves will be depletedwithin 40 years if the demand for gas keeps on increasing by 2% per year.Suppose that gas reserves are just half as large as expected. How many years would it take thenbefore the gas reserves are depleted if the demand for gas keeps on increasing by 2% per year?

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c⃝ 2013 by Erik Pruyt HOP: MCQs Part III

a. ± 16 years; b. ± 23 years; c. ± 30 years; d. None of the previous answers.


Consider the behavior over time of the stockvariable on the right. This stock variable has 1outflow and no inflow. By which of the outflowbehaviors displayed below could the behavior ofthe stock variable be caused?

(a) (b)

(c) (d)


Given the model on the depletion of ‘natural gas’ displayed on the left, what are the units of thevariable demand gas growth if the units of gas use are m3/Y ear?

a. m3/Y ear

b. m3/Y ear2

c. m3

d. None of these answers is correct

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Consider the behavior of an input (blue curve)and its delayed output (red curve) in the graphon the right. The input increases according toa STEP function at t = 5 and the delay timevaries following the green curve. Which type ofdelay of which order could cause this behavior?

a. a 1st order information delay

b. a 3rd order information delay

c. a 3rd order material delay

d. none of them could cause this behavior


Consider the graph below. A step function input (1) is delayed with variable delay time (2).Which of following statements related to the delayed responses (3) and (4) could be true?

a. (3) is a 3rd order material delay,(4) is a 1st order information delay

b. (3) is a 3rd order information delay,(4) is a 1st order material delay

c. (3) is a 1st order material delay,(4) is a 3rd order information delay

d. (3) is a 1st order information delay,(4) is a 3rd order material delay


Consider the SFD on the right. Whichof the following statements concerningthis model could possibly be correct?

a. This structure combines a first-order material delay with a second-order material delay,which together make a 3rd order material delay. The final outflow is therefore a 3rd ordermaterial delay of the inflow.

b. This structure combines a first-order material delay with a second-order material delay, butby means of blue information arrows, which does not make a 3rd order material delay. Thefinal outflow is therefore not a 3rd order material delay of the inflow.

c. This structure combines a first-order material delay with a second-order material delay, butis not a 3rd order material delay. This structure can generate oscillatory behavior of thefinal outflow even if the inflow is not oscillatory.

d. None of the statements above could possibly be correct.

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Suppose you are asked to turn the 1st order delaystructure on the left –without too many changes(e.g. by using a function)– into a 3rd order de-lay structure. Which of the following adaptedstock-flow structures could be used to simulate a3rd order delay if all variables –except for someconstants– are visualized?

(a) (b)

(c) (d)


Consider the following model in which inStock2 = inStock1 = in and out = outStock1 =outStock2. What does this structure correspond to?

a. The first tier in a bull-whip structure

b. A negative feedback loop with a delay

c. A 1st order material delay

d. None of the previous answers is correct


A 3rd order material delay structure is given below. The system with a Delay Time of 5 monthsis observed to be in equilibrium. If the Input Flow to this structure is 10 cars/week, which of thefollowing is true about the Output Flow and/or the value of the stock variables?

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a. The stock values cannot be calculated.

b. All stock values are equal.

c. The output flow is equal to 2 cars/week.

d. Stock 3 has a value of 2 cars.


Consider following graph representingthe behavior of an input (dashed green)and the behavior of the delayed output(red). The input steps up at t = 2, andthe time constant changes abruptly att = 4. What order and type of delaycould cause this behavior?

a. a 1st order material delay

b. a 3rd order material delay

c. a 1st order information delay

d. a 3rd order information delay


The simple SD model below is about the outbreak of pneumonic plague in an isolated com-munity (more precisely a remote Chinese village with 10000 inhabitants). The behavior on theright hand side of the Stock-Flow Diagram is generated with this model. Which of the followingstatements is correct?

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a. The model is wrong because of a specification error: the infection flow must be modeled asnon-negative.

b. The model is wrong because of a numeric integration error: it looks as though the Eulerintegration method is used with too big a time step.

c. The model is wrong because of a numeric integration error: it looks as though the Runge-Kutta4 integration method is used with too small a time step.

d. The model is wrong because of a specification error: the recovery flow and deaths flow shouldhave been modeled as non-negative flows.


Which of the following statements regarding the table function displayed below is incorrect?

a. If this graph represents an additive effect,the reference point is (0,0).

b. The modeler should check whether this sin-gle graph function can be modeled as thecombination of two different effects.

c. This graph cannot represent a multiplica-tive effect.

d. If this graph represents a multiplicative ef-fect, then it has two reference points.


Examine the behavior of a stock variable on theleft (assume the stock converges to a level of 20in the long-run). What is the constant doublingtime or half-life time?

a. A constant half-life of 3.5 time periods

b. A constant half-life of 7 time periods

c. A constant doubling time of 17.5 periods

d. None of these answers is correct


Which of the following statements concerning stock variables is wrong?a. Stocks allow flows to be decoupled.

b. A stock can be increased by decreasing its outflow rate.

c. Stocks change relatively slowly, even when their flows change suddenly and/or rapidly.

d. Stocks would become nil or would cease to exist if systems would be paused.

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Suppose you made a SD model (as displayed above) concerning the large herbivores population inthe ‘Oostvaardersplassen’ (OVP), and that you used the carrying capacity calculation displayedin Figure 10.1 on page 134.

The graph on the left shows the 3rd or-

der smoothed response of the flow vari-ables (in blue: smoothed info on largeherbivores births; in red: smoothed infoon large herbivores deaths). Which ofthe following graphs could then be thegraph of the corresponding smoothedstock variable smoothed info on largeherbivores?

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Case 10.13 on page 133 and the previous MCQ deal with massive starvation in the OVP. In theguiding questions, one is asked to simulate the model with different ‘seeds’ for the two randomizers.What could be concluded from these simulations with different seeds?

a. The significant difference in dynamics show this model is strongly behavior pattern sensitiveand policy sensitivity for changes in the values of these seeds. It could therefore be concludedthat changing the seed is an interesting policy measure.

b. The simulated dynamics are numerically different which indicates that the model is numer-ically sensitive to changes in the values of the seeds, but not behavior pattern sensitive. Ifthe model is an appropriate model of the dynamics of large herbivores in the OVP, then itcould be concluded that the situation in the OVP could not have been foreseen.

c. The simulated behavior patterns are hardly different in a qualitative sense: the model is notnumerically sensitive to changes of the seeds.

d. None of the previous conclusions is correct.


Following up on the previous two MCQs regarding the OVP model (case 10.13 on page 133) dis-played above: which of the following specifications does not allow –if applied to a further correctlyspecified model– to generate this behavior? In other words, which formula is surely wrong?

a. births large herbivores = DELAY FIXED(large herbivores * percentage birth rate * birthseason / length birth season * randomizer births, 2, large herbivores * percentage birth rate* birth season/length birth season * randomizer births)

b. percentage birth rate = WITH LOOKUP(large herbivores ; ((0, 0.05), (1000, 0.075), (3000,0.2), (4000, 0.3), (5000, 0.45), (6000, 0.75)) )

c. birth season = PULSE TRAIN(1982.5, length birth season, 1, FINAL TIME); with lengthbirth season = TIME STEP

d. smoothed info large herbivores = SMOOTH3I(large herbivores, 1, initial number of largeherbivores)


The normal death rate of inhabitants of a country amounts to 6 deaths per1000 inhabitants per year. However, the future death rate may increasedue to significant deterioration of the drinking water quality. Large quan-tities of chloride per liter drinking water are harmful to public health: thedeath rate is 1 per 1000 inhabitants higher in countries with 50mg chlo-ride per liter drinking water than in countries without chloride-polluteddrinking water, and is even 5 deaths per 1000 inhabitants higher in coun-tries with 100mg chloride per liter drinking water.Suppose you included this effect in the model displayed on the right. The‘additional death rate through chloride lookup’ function connects followingcouples: (0,0), (50,0.001), (100,0.005). Which of following specificationsfor the deaths flow is then best?

a. deaths = inhabitants * (normal death rate + additional death rate through chloride lookup);with additional death rate through chloride lookup a function of chloride in drinking water

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b. deaths = inhabitants * normal death rate * (1 + additional death rate through chloride lookup;with chloride in drinking water being the argument of additional death rate through chloridelookup

c. deaths = inhabitants * normal death rate + additional death rate through chloride lookup *chloride in drinking water

d. deaths = inhabitants * normal death rate + additional death rate through chloride lookup;with additional death rate through chloride lookup a function of chloride in drinking water


Consider the fisheries model displayed above. Which Fish stock behavior could be expected if themodel starts with a very small number of ships, the ship building rate is always ≥ 0, all ships areused to fish, ships are not decommissioned, and the Fish stock starts far below equilibrium?

a. continuous exponential growth

b. sustainable S-shaped growth

c. growth, overshoot, and collapse

d. continued cyclic behavior

Link to the answers to the 15 right/wrong questions & 20 multiple choice questions in this chapter.

Links to web based quizzes: | | | |

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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 justa set of case descriptions: it is the backbone of an online blended-learning approach. It consistsof 6 concise theory chapters, short theory videos, 6 chapters with about 90 modeling exercisesand cases, many demo and feedback videos, feedback sheets for each case, 5 overall chapters withfeedback, 5 chapters with multiple choice questions (with graphs or figures), hundreds of onlinemultiple choice questions, links to on-site lectures, past exams, models, online simulators, 126slots 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 arelatively short time– how to build SD models of dynamically complex issues, simulate and analyzethem, and use them to design adaptive policies and test their robustness.

ISBN paperback version:

ISBN e-book version:

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System Dynamics Models: MCQs part III