This document contains a final exam for an advanced simulation course. It consists of 6 questions. Question 1 asks to discuss the steps of the modeling process in detail. Question 2 provides rate graphs and asks to draw the behavior of a stock given the input and output rates. Question 3 provides a scenario about adjusting daily food consumption to reach a weight goal and asks to model it with diagrams and a graph. Question 4 describes a population model divided into age cohorts and asks to diagram the stocks and flows and write the equations. Question 5 asks about the T21 model, its use by government officials, an example of a feedback loop between sectors, and comparisons to other approaches. Question 6 asks to diagram and write equations for the Bass diffusion model,

1. Cairo University
Faculty of Computers & Information
Department of Decision Support
Advanced Simulation
Final Exam 2007/2008
Duration: 2 hours
Question 1:
Discuss in-details the steps of the modeling process.
Question 2:
Consider a stock with a single inflow rate R1 and single outflow rate R2. Draw the
behavior of the stock given the behavior of the two rates shown below. The initial value
of the stock is 56.
12
R1
10
8
6
4
2
0
0
10
20
30
40
50
60
70
80
90
100
70
80
90
100
Time
15
R2
10
5
0
-5
-10
0
10
20
30
40
50
60
Time
Question 3:
Assume that today (1. January 2008) your weight is 40 kg.
You think you are too thin, and you want to be a new person in 2008.
So you developed a plan to reach your desired weight of 56 Kg.
This can be done be adjusting your daily food consumption.
a. Draw a simple causal loop diagram that captures this process
b. Draw a simple stock and flow diagram that captures this process
c. Draw a time-graph representing your expected weight in the whole year 2008.
(Assume that the half-life time of this process is equal to 3 month; i.e. the gap
is halved every 3 months).
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2. Question 4:
a. Draw a simple stock and flow diagram for the model described below.
b. Write all equations for the model.
The Population (in a certain country) is divided into three cohorts (age groups):
- Children (from 0 years, till around 30 years)
- Reproductive Adults (from around 30 years, till around 60 years)
- Old People.
Hint: represent each cohort by a stock, in the model.
The model assumptions are as follows:
- Only Reproductive Adults can contribute to the increase of population; moreover, it is
assumed that (on average) every 56 reproductive adults give birth to 1 baby each
year.
- Only Old People die. And in this population, the average life time is 90 years.
- No migration (into the country or out of the country).
- No differentiation between male and female.
Question 5:
During the course you have studied the T21 model.
a. Explain why government officials use the T21 model.
b. T21 is divided into 3 main sectors: economy, environment and social sectors.
These sectors are integrated together through feedback loops.
Give an example of a feedback loop connecting any 2 sectors together.
(i.e. the variables of this feedback loop belong to these 2 different sectors)
c. Explain why the developers of the T21 model used the system dynamics (SD)
approach. (Hint: Compare and contrast SD with other approaches.)
d. From your point of view, what are the main limitations of the T21 model?
e. How can you enhance the T21 model?
Question 6:
a) Draw the Stock and flow diagram of the Bass Diffusion Model.
b) Write all equations of the model
c) Even though the Bass model often works well, the model invokes a number of
restrictive assumptions. List as many restrictive assumptions as you can
1) Homogeny
2) Assume that the pop are only (P - A)
3) Assume that there is not immigration nor birth nor death.
4) assume that you can purchase single time there is no repurchasement process.
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