An Adaptive Statistical Data Processing Algorithm Applied to SD
Modeling of Iran’s Demographic Transition
Hamed Shakouri G.!, Shakib Taheri?, Ayyub Ansarinejad?, M. Sadegh Shahmohammadi*
Department of Industrial Engineering, Faculty of Engineering, University of Tehran, Iran
Thshakouri@ ut.ac.ir
*shakib_taheri@ yahoo.com
Sansarinejad@ gmail.com
‘sadegh_shahmohammadi@yahoo.com
Abstract:
There are different official estimations about current and future growth rate of Iran’s
population. Inadequacy and unreliability of data in addition to usage of unsuitable forecasting
methods are the main reasons for existence of this variety. To have accurate estimates for year
on year growth rate, in this research, a population system dynamics model is implemented. To
run the model, total fertility rate and other needful fertility parameters are calculated by
processing raw data. In the next step and to resolve the statistical inconsistencies in census data
which have been revealed by calculation of survival fractions and death rates, an appropriate
adaptive process is proposed and applied to modify the parameters. The result of applying model
shows that the next ten-year average growth rate will be about 1.9. Finally, simulation results of
three possible scenarios on the fertility factor are obtained that warns on exceeding of
population over 100m by 2020.
Keywords: System Dynamics Modeling, Population Dynamics, Uncertain Data Processing,
Census Data Correction, Parameter A daption.
1-Introduction
"Perhaps no single factor is more important for local government planning than the size and
composition of a region's population and the way it will change in the future. Changes in
Population composition can fundamentally alter the need for public facilities and services."
(Klosterman 1990). Demographic forecasting has a long history (De Gans 1999) and has
important effects. Population, household’s number and related forecasts form the basis of social
and economic planning and are fundamental to many other forecasting exercises (Booth 2006).
To provide necessary detail in demographic forecasting, the population must be disaggregated by
age and sex. To achieve this, the three components of population change (mortality, fertility and
migration) must be separately forecasted and appropriately combined (Booth 2006). Population
forecasting is thus a highly complex and difficult undertaking (Keyfitz 1985). During the
twentieth century, fertility was the most important component in determining population size.
The historical booms and busts in childbearing have to a large degree provided the urges for the
more recent renewal of interest in demographic forecasting. The uneven and transitionary age
structure created by past fertility instabilities is the dominant feature of present day demography
in the developed world (Booth 2006).
Several useful research and studies have previously done on demographic forecasting (Lutz,
Goldstein, and Prinz 1996; Ahlburg 1982). Walonick remarked that many scholars have
proposed a variety of ways to categorize forecasting methodologies. And the following
classification is a modification of the schema developed by Gordon over two decades ago to
forecasting: Genius forecasting, Trend extrapolation, Consensus methods, Simulation methods,
Cross-impact, Matrix method, Scenario and Decision trees (Walonick 2006). Booth categorized
approaches to forecasting demographic processes to three parts: extrapolation, expectation
(individual-level birth expectations or population-level opinions of experts), and theory-based
structural modeling involving exogenous variables (Booth 2006). Also there are several methods
to forecast population growth. The following methods were reviewed to find out which is most
applicable to forecasting the Iran population for the short and long term. These methodologies
are:
* Cohort Component Model: Need for more comprehensive and more in-depth projections in
population Demographics detail have led to the development of the cohort-component projection
technique. Cohort Component Model is a system of demographic accounting in which the
population is advanced forward in time through the application of time specific survivorship
ratios by age and sex and the derivation of births from time-specific fertility rates of women by
age; migration by age and sex can also be incorporated (Preston, Heuveline, and Guillot 2001).
This method can be quite accurate when forecasting population up to ten or twenty years into the
future where in-migration is not the major growth factor (Van Buskirk and Associates 2004).
* Simple Curve fitting or Extrapolation Model: Simple Curve fitting or Extrapolation Model
assumption is that the future will be a continuation of the past. This method is the most common
approach in demographic forecasting and widely used (Schmitt 1954; Smith, Tayman, and
Swanson 2001). The most commonly-used method of extrapolation is univariate ARIMA
modeling (Box, Jenkins, and Reinsel 1976). Simply extended linear curve into the future is not
an exact estimate of future growth. For the reason that communities in Iran is in their mid-stage
of growth the extrapolation of the growth curve into the future greatly overestimate future
growth. Therefore, this model is not the most appropriate one for Iran.
+ Exponential Model: An exponential trend is one where the trend is increasing at a constant rate
of change each year. This compounding effect of a constant rate of growth can result in
astronomical increases in forecasted population in the long term. While this type of trend in
growth may exist for a period of five years or even ten years, it cannot sustain itself for longer
terms (Van Buskirk and Associates 2004). This model would be misleading for forecasting long-
term growth for Iran.
* Gompertz (Sigmoid or Logistic) Model: Many biological populations (including cities) tend to
grow at a rate over time that simulates a logistic or Sigmoid Curve. Population growth increases
at an increasing rate over time until it reaches an inflection point, then the increase in population
growth is at a decreasing rate until it reaches upper growth limit. One of the key variables in this
growth equation is its upper growth limit (build-out).As an example, the upper limit for large-
scale pre-platted communities such as bounded city can be precisely defined by calculating the
total number of housing units that can be built on platted lots, and un-platted lands. The housing
units can be translated to population. The Sigmoid Model is a more scientifically sophisticated
variation of an extrapolation model and should be more accurate than other methods for
forecasting short and long term growth for small zone given the larger role of in-migration and
estimated “build-out” population (Van Buskirk and Associates 2004; Capece). But for a country
with enough amounts of resource and vast land like Iran, this model is not fit with situations.
An efficient tool to study the population transition is System dynamics (SD). System dynamics is
an approach to understanding the behavior of sophisticated systems over time and firstly
introduced by Forrester (Forrester and Wright 1961). The importance of all research in
population statistics can be understood by considering concepts of Planning, Employment,
Poverty and Wealth, Health factors and Education. There is no doubt that having precise
population statistics is very helpful in the fields of better economical planning and social
development. The population model is developed using an object-oriented modeling software
package called Vensim (Ventana Systems, Inc., 2002). This software is designed for use in
collaborative model building projects and has a graphical interface that allows model participants
to concentrate their attention on symbolic objects, rather than numbers and equations. The model
objects symbolize system elements such as stocks, processes, material and information flows.
The software employs coupled systems of finite difference equations as a modeling framework
(Cole and Flenley 2008).
In this study a theory-based structural cohort component model, involving both endogenous and
exogenous variables (SD model) is implemented to observe Iran’s demographic transition. Then
a novel combined adaptive process is proposed and applied to modify unreliable data using the
SD model. If a reliable and precise set of raw data exists (a complete census statistics plus death
and fertility rate of each age group, etc.) then employing a system dynamics model would have
lots of profits like: accurate and trustworthy results, ability to study population transitions in
different cohorts, evaluate effects of exogenous variables, population policies, and so on.
Unfortunately, existing data, which is available on the Statistical Center of Iran (sci.org.ir) is not
adequate and/or accurate.
To solve the problem and to obtain reliable data an adaptive statistical data processing algorithm
is designed. The algorithm applies the implemented SD model to obtain reliable parameters
essential to run the model and achieve valid simulation results.
The paper is organized as follows. Section 2 briefly describes the system dynamics model
structure and different variables used in population projection. Section 3 explains mathematical
relations used in the SD model. Section 4 discusses on statistical data and explains the lack of
accuracy in the official data. Then by processing data we have estimated the parameters related
to fertility. Section 5 proposes an adaptive statistical data processing algorithm using the SD
Model for data correction. The designed adaptive algorithm is a novel method by which the
problem of data inconsistency is resolved. Model validation and some simulation results that can
be obtained by the model are represented in Section 6, including population growth rate forecasts
for three different scenarios on fertility factor. Section 7 concludes the paper.
2-The Model
An aging chains model of population dynamics is developed according to the well known basic
definitions such as state (stock) variables, rate (flow) variables, auxiliary variables, and cohort
component (Sterman 2000). The population in Iran is divided to males and females in 5-year age
groups, having results of the 10-year census and the population pyramid. For the range of new
babies to more than 100 years old people, we have 21 state variables in the aging chain. There
are many structural and practical reasons for using cohorts; for example, mortality rate is high in
early childhood birth, which reduces for children and young people, and then increases for older,
finally reaching one in the aged people (Figure 1).
wee
es CCE a rates) a a a Ss a“
. - qe 2
"i
8 \
{Death ratel4 [Death rate15 i Death rate16 fDeath ratel7 {Death rate1§
("| C : (| (
> aa es f } + ]
[Population!4|_+ [Populationt5| + Population’ 6| [Popuiation’§| [Poy
65-69 | | 70-74 78-79 4
Maturation rate |
f _ Ci.CIS C15-C16 C16-C17
\iNet Immigrationl 4 [Net Immigration 5 [Net Immigration16 [Net Immigration!7 [Net Immigration18
Figure 1: A part of the SD model built by Vensim the Cohorts
Women between the ages of 15 to 50 years have ability to give birth. Birth rate in these years
doesn’t have a uniform distribution and is affected by various biological, social and economic
factors (Figure 2).
These cohorts are required and useful for studying the diversity of population behavior according
to different cohorts and also to forecast and then plan for meeting special needs of the different
groups.
‘NetInmigations
TE
ee —
Sams a
/ fo distin ot
x os
om we, ff a -- ann
aS Ly ee ae
puto a” oF ae “nh
‘Net innigatonl |_54°_ = patted z fb fp Paani Free fatoat
Figure 2: A part of the SD model; distribution of women in childbearing cohort and the Health
Factor as an exogenous variable.
Considering phenomenon such as increasing population growth ratio in 1980’s (so called baby
boom) and consequently effects of this event, on need to educational facilities, employment,
social welfare and retirement, with a delay emphasize importance of the cohort model.
Moreover, impact of birth-giving age groups on the dynamics of the system by repeating this
event and rebuilding next generation, which leads to future growth of the population, is the main
object of building such a model.
Health F:
Figure 3: A part of the SD model; birth rate, growth rate exogenous variables like: policy, GDP,
culture and health.
As mentioned, in this article the proposed model is used to forecast population growth rate;
however, for further researches this model can be utilized in several fields such as labor market,
housing market, education, social welfare and health. In addition, the interaction of each
mentioned field with socio-economic factors like GDP, oil price, recession, inflation, per capita
income and other political and cultural factors and/or health and population control policies can
be separately considered. This section will not cover the benefits and reason of using this specific
model or the possibility of construction of different casual diagram in different perspectives. In
this model and for long or short perspectives, the abovementioned factors are considered as
exogenous variables (Figure 3). We can run different scenarios within the current system
boundary by changing some of these variables.
3- Mathematical relations
According to the pyramid of age groups known in demographics, states variables are used to
demonstrate different age-sex groups and these variables increase or reduce with their related
flow variables. For the first cohort, newbom babies up to 4 years old (5 years minus 1 day) are
considered as infant cohort.
t
Psa) = Psa (Co) +{ (BO + Is10) — Ds) — Ms ©)at
to
Here, P;,,(t) is the population in the first cohort, B,(t) is the birth rate, /, (t) is net immigration
to this group that migration out will be deducted from migration to country. M,,(t) is the rate of
growth which shows the number of people going from the first Cohort to the second Cohort.
Birth rate is the sums of children are born during the reproductive years of women.
t
Pri(t) = Prilto) + [ (Moja) + Isi(8)— Dei —Myi(O)dt— For i € (2, .20))
to
et
Psai(t) = Psai(to) + i (Ms20(t) + Is,21 (0) — Dai (t)) dt
to
P, {(to)Is initial population in moment of ty and cohort i and P, ;(t) is population in cohort i and
M,;-1(t) is the rate of population entered from previous cohort. also M, ;(t) is the rate of
growing up and going from cohort i to cohort i+1 and D, ;(t) is mortality rate in the cohort of i
and the amount of it is calculated using the survival factor of cohorts, /, ;(t) is the net migration
to the current group which described above. Other variables except /,;(t) are endogenous
variables. Index s, in all variables is used to separation of gender to male and female groups.
Cyr
Bs = 75. TF P.
's = s(ey= ey +1) » w(@)Pfem(@)
CY¢
> w(a) =
a=Cy;
In this formulation Pyem(a) is the population of women in cohort of a, and TF (total fertility) is
the total number of children per women during childbearing years. First and last years of fertility
is calculated and multiplier 7 shows number of cohorts considered for the time of fertility.
Consequently "amy is the average baby’s birth per each woman, during the
fT OYE
childbearing years. w(a) is a coefficient of weight that dependent to each cohort, actually shows
births than occur in any of the childbearing years. Weight coefficients depend on two factors,
including biological factors such as maturity and nutrition and social economic factors such as
the role of women in the community, age of marriage and education. Coefficient of gender is the
ratio of each gender in all births and is generally close to 0.5. This ratio in all societies and over
time is not constant and the preferences of people and using technology could be change this
ratio a little.
Exit Rate(i), = DELAYI(Mg(i- 1) + I,(i), YPC@)
x Pi
= ee
Auxiliary exit rate variable represents that each population which entered a state variable finally
will be out with a maximum first degree of delay which is composed of two parts, first transfer to
the next cohort and the second one, is death.
Mg (i) = Exit Rate(i), * SK(i)
D,(i) = Exit Rate(i), * (1 — SF,(i)
SF,(i) or survival fraction shows the coefficient of population which transfer to the next cohort.
Survival fraction can be calculated through different method such as life table, survival
distributions for the population. (Keyfitz and Caswell 2005; Rosner 2006; Lee 1992) Describe
the mathematics of life tables and survival analysis in discrete and continuous time.
6
By using survival factor, probability of death per year, or annual death rate of each cohort, is
calculated through equation below:
FOR. = =InBO/, yPC(i)
SF,(i) = exp(—FDR,(i) * YPC(i))
These equations are obtained due to geometric growth and multiplying survival factor for each
year in the remaining population of previous year. YPC(i) is the range of ages in each cohort i
and in our model the range of ages in each cohort except the ages above 100 years, is 5 years.
Till here the structure of our model is described. In long-term perspective other auxiliary and
exogenous variables in model are considered. Such as cultural effects (Auxiliary variable) which
continuously and over time reduces the fertility rate and health factors that considered in three
categories (Health Factor A, B, C). These three regulatory variables utilized as a result of policy
making in the model and potentially can affect survival fractions and death rate in different
cohorts.
4-Discussion on Statistic Data
Iran's dynamic population model after reviewing relationships among variables was constructed.
In the next step by entering data and parameters into the model and utilizing Vensim, simulation
process was done. It is important to mention that unfortunately in Iran statistics data and
population census, even 10 years interval population and housing census data, is not consistence
and reliable. One of the clear mistakes that happen in general census is reporting the number of
infants and babies lower than actual numbers. The actual number of infants and babies will
report in the next ten years general census. The elderly and single households also will be
counted lower than reality. Because of various reasons, including the lack of people cooperation
and lack of efficient and accurate statistics system, also statistics about dead people, is not
accurate.
Next section will show that available SF (i)'s which are derived from census data is not precise
and reliable consequently an adaptive statistical data processing algorithm combined with SD
model, will apply to modify SF (i)'s parameters.
Also fertility parameters are not clearly available. To achieve reliable statistics about fertility
data processing methods used. w(a)'s or weighted coefficient of each woman childbearing in
specific cohort, which is described above, calculated according to statistics published by the
United Nations population division and the impact of two biologic and social-economical
factors. First column (in the left) of each cohort in Figure 4 is derived from United Nation
Population Division and shows the distribution of birth by mothers’ age.
Second, third and forth columns of each cohort in Fig. 1 show the result of w(a) calculated by
using data obtained from United Nation 2008 and A bbasi (A bbasi-Shavazi and McDonald 2005).
These processed results are shown in table 1.
World Average W(a) 2008 m Calculated W(a) for 2006
Calculated W(a) for 1996 jm Calculated W(a) for 1986
0.350
0.300
0.250
0.200
0.150
0.100
0.050
0.000 T T T T
19-15 24-20 29-25 34-30 39-35 44-40 49-45
Figure 4: Iran Data Processing Result for w(a).
Table 1: The processed results for Fertility Ratio and w(a)
Women Population (thousand Person) Fertility Ratio (per woman) w(a)
Cohort
2006 1996 1986 2006 1996 1986 WorldData 2006 19961986
15-19 4283.9 3535.7 2531.8 0.02339 0.05554 0.13853 0.095 0.056 0.088 0.113
20-24 4499.6 2655.5, 2090.1 0.13045 0.16542 0.27146 0.29 0.311 0.262 0.221
25-29 3564.8 2343.3, 1812.7 0.13575 0.16928 0.26766 0.28 0.324 0.268 © 0.218
30-34 2715.6 1967.3 1446.5 0.07862 0.12227 0.24443 0.18 0.187 0.193 0.199
35-39 2409.6 1754.2 1073.4 0.03637 (0.07389 (0.18415 0.095 0.087 0.117 0.15
40-44 2007.5 1381 821.6 0.01172 0.03378 0.09835 0.04 0.028 0.053 0.08
45-49 1730.3 1022.9 766.2 0.0031 0.01182 0.02539 0.02 0.007 0.019 0.021
Total Fertility 24 32 61
Total Population 70495.8 600555 494450
As previously mentioned to calculate the death rate per each cohort (D), survival factor (SF) is
used. Review of Population and Housing Statistics Center of Iran Census; reveal that there are
problems in process and results of census and these problems should be modified.
5-The proposed adaptive algorithm for data correction
These problems in census are described by an example. Let’s consider first 0 to 4 years cohort, in
the census of 1996. This cohort should be transferred to 10 to 14 years cohort in census of 2006.
If we assume that all people in the first cohort during these 10 years, transferred to 10 to 14 years
8
cohort, or in other word if we assume that during these years population didn’t change (increase
or reduce), then population ratio of first census to second on in 2006, must be exactly equal to 1.
Obviously this assumption is not true because in reality during these 10 years numbers of people
have died also due to migration numbers of population have changed (increase or reduce).
Especially when we notice that mortality rate in early birth is significant. So the survival ratio,
without considering of net migration rate, must be between 0 and 1.
The other important point is that the population in the third cohort in 2006, consists of people
remained alive during 10 years ago or the first cohorts in 1996 plus immigrants entered the
country, minus migrants from this cohort. According to the statistics and information (Iran
Yearbook of Statistics in 2007), if we assume that all immigrants during these 10 years add up
top third cohort in 2006, the number of immigrants will be equal to 66,421. But according to
census of 2006, third cohort in this year is 545,570 people more than first cohort in 1996 census
data. This result means that survival fraction is greater than 1 and this is clearly not correct and
rational. Probably this result is a consequent of low counting people in 1996 census or high
counting people in census of 2006.
Table 2: Inconsistent SF; Related to C ohorts
i Cohort $F2006/1996 SF96/91 SF96/86 SF91/86
1 0-4 1.088523 1.041831 1.003964 0.998965
2 ee 1.028875 1.005005 0.945475 1.002822
3 10_14 0.992373 0.942815 0.884587 1.000949
4 15-19 1.015375 0.883748 0.906967 0.952825
5 20-24 1.063491 0.951871 0.949053 0.955065
6 25-29 1.045012 0.993705 0.977954 0.959456
7 30-34 1.02741 1.019279 0.960417 0.979059
8 35-39 0.986276 0.980959 0.950798 0.96234
9 40-44 0.979849 0.988006 0.923718 0.953262
10 45-49 0.937876 0.969008 0.862072 0.99068
11 50-54 0.957735, 0.870183 0.864872 0.902384
12 55-59 0.876217 0.95843 0.804617 0.974318
13 60-64 0.809372 0.825826 0.714575 0.747132
14 = 65-69 0.644871 0.956424 0.634577 0.810684
15 70-74 0.525759 0.782768 0.42825 0.543807
16 75-79 0.350601 0.787503 0.276003 0.667117
17-80-84 0.268847 0.456868 0.569051
18 = 85-89 0.207178
It is notable that this conclusion was regardless of migration abroad, according this fact,
problems in survival fraction (SF) Statistics from census will appear clearly. To obtain net
migration rates per cohort, accurate statistics is needed, but according to table of page 114 in Iran
Y earbook of Statistics 2007, net migration rate of the population is about zero. In Table 2 shown
SF from 1986 census up to 2006 census, because of SF> 1, and similar problems such as
irrational trends of data and behavioral inconsistency in SF in compare to global statistics of SF,
non-acceptable and unreliable data is specified.
To modify the model parameters, a system dynamics model is used and in an adaptive decision-
making process the following three criteria is considered:
I. SFi’s must be logically and behaviourally consistence with the global statistics
Il. Transfer a cohort in a census to the corresponding cohort in another census
Ill. Total numbers of deaths
Our adaptive algorithm first reads inputs. Then checks the satisfaction of Criterionl, which
explain that SF; 's must be logically and behaviorally consistence with the global statistics. If this
condition satisfied then goes to next level else modifies SF;'s by using world statistics then goes
up. Next step is Inputting Data and Parameters like SF;'s to SD Model of population and
Simulating. Then calculate the error that explains below:
Error SF; = P;(Simulate) — P;(Statistical Data)
RE, = Error $F _
i P; (Statistical Data)
Then checks the second criterion by result of SD model, if absolute value of RE; was greater
than @ then substitutes SF;(new) = SF;(old) — Relative error of SF;, and goes to first. Else in
next step calculates the relative error of total death (RETD) from the data and the simulation
results and checks if RETD was greater than # then checks error sign, if it was positive only
selects SF;'s which are related to positive errors and otherwise only selects SF;’s which are
related to negative errors. Then utilizes selected SF; ’s and for below calculations and goes to first
step:
Wsr, = Pi(Simulate) — P,(Statistical Data)
WsF;
SF,(new) = SF,(old) — x (RETD)
Dselected WsF;
The above process continues from first step until all of SF;’'s satisfy all criteria simultaneously.
Finally the modified parameters and corrected data succeeded.
Following Flowchart shows the adjustment of parameters in the adaptive process (Figure 5):
10
)
Input SF;'s
Parameters
ij
SF;,'s Logical Modification by World
Statistics
Satisfaction of
Criterion I
Input Data and Parameters to SD Model and
Simulate
!
Error SF, = P;(Simulate) — P;(Statistical Data)
) Error SF;
Relative error of i (RE;
/p, (Statistical Data)
Error SF,
| SFi(new) = SF;(old) — Tp, (Statistical Data)
Check Criterion II
|RE;| <a
| Select SF;'s Related to Positive Errors
|
Weighting to Select SF; 's and Modification:
Wsp, = P;(Simulate) — P;(Statistical Data)
Wsr;
SF,(new) = SF,(old) — x (RETD)
Zsetected Wsr,
i
Select SF;’s Related to Negative Errors
Calculation Relative error of Total Death
(RETD)
Check Criterion III
|RETD| < B
All of SF;'s satisfy
all criteria
simultaneously
Figure 5: Adaptive Statistical Data Processing Algorithm Using SD Model
Table 3: Adjusted Parameters of SF,’s Resulted from Adaptive Statistical Data Processing
Algorithm
[Cohort | o4 | 59 | 10.14 | 15-19 | 20-24 | 25-29 | 30-34 | 35-39 | 40-44 | 45-49 | 50-54 |
| SFi_| 0.9402 | 0.982642 | 0.998371 | 0.999648 | 0.999819 | 0.999649 | 0.99839 | 0.996808 | 0.99507 | 0.985694 | 0.966559 |
[Cohort] 55-59 | 60-64 | 65-69 | 70-74 | 75-79 | 80-84 | 985-89 | 90-94 | 95-99 | 100- |
[_ SFi_| 0.901765 | 0.867682 | 0.852311 | 0.79965 | 0.670123 | 0.603504 | 0.568197 | 0.5605 | 0.550449 | 0.549309 |
S © 8 S$ OQ HD BV HB GO OL
pe OP fh 8 x Ss
eae ap a ep? ME ant ap op?
Figure 6: SF; and DR; for Each Cohort Resulted from Adaptive Process
The above shows the results of proposed adoptive algorithm.
6-Model Validation and Simulation Results:
In order to check reliability of model and evaluate the accuracy of outputs assume that we are in
1996 and by using data of that time simulate the model and observe population behavior up to
2006 which its data obtained from census.
Table 4: Model Validation Results
Results | Census Of 2006 | Error Pi gt
Iran Population 70845700 70495872 0.496 %
Deaths in 2006 410541 408566 0.483 %
Average Annual Growth Rate 1996-2006 1.666 1.615 3.1%
Results and low percentage of errors show the validity and accuracy of the model (Table 4).
Answering to this question: “Will be Iran's population growth rate in a few coming years
descending?"
The results of the simulation model to predict annual population growth rate in Iran from 2006 to
2016 is shown below:
Table 5: Average Growth Rate and Forecast
12
10 years Census Intervals Average Growth Rate
1956-66 3.127%
1966-76 2.714%
1976-86 3.905%
1986-96 1.963%
1996-2006 1.612%
2006-2016 (Simulated) 1.813%
The result shows that the ten-year average growth rate from 2006 to 2016 will be equal to 1.896.
As aresult of simulation, in the same pattern of Iran population behavior for future, the statement
of “Iran population growth rate in near future years, not only will not descending but also has an
obvious ascending trend” would be confirmed. This confirm by noticing to the baby boom in
1980’s and large population which reaching to the childbearing years seems quite logical. Here
the simulation results from 2006 to 2015 for growth rate are shown:
2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015
1.812 | 1.845 | 1.866 | 1.872 | 1.860 | 1.848 | 1.819 | 1.782 | 1.737 | 1.686
1
Hl
18 1
'
p
ial . J
‘T9990 1995 2000 2005 2010 2015
Figure 7: The year-on-year growth rate obtained by the model
To utilize this model in long term three scenarios for Iran Population is considered:
e First Scenario: Continuing current situation like what resulted from calculation of
table 1.
e Second Scenario: Decreasing the total fertility (TF) to 1.8 based on forecasts from
experts at Population Studies and Research Centre in Asia and the Pacific.
e Third Scenario: Incentive policies of Iranian government to increase the total fertility
(TF), which is optimistically assumed to reach 3.2.
13
Population
200M
165M
¢
i 130 M
95M
60M
2006 2010 2014 2018 2022 2026 2030 2034 2038 2042 2046
Time (Y ear)
Population : Current Scenario
Population : Second Scenario
Population : Third Scenario
Figure 8: Three Scenarios for Iran Population
7-Conclusion
The aim of this research was to calculate current and future Iran population growth rate about
which there are several different official estimations. The main reasons for existence of this
variety are unsuitable forecasting method and insufficient and unreliable data. SD has been
identified as a very powerful device for dealing with complexities at the level of the content of
social and economic systems such as population transition by modeling and simulating them
dynamically. In this study a novel combined adaptive process designed for modification of
unreliable data with theory-based structural modeling involving endogenous and exogenous
variables (SD model) and cohort component model was used to observe Iran demographic
transition.
After literature review, the system dynamics model structure and different variables presented
for population projection were described. Then the mathematical relations used in SD model to
forecast the demographic components were explained. To deal with lack of precise data, these
troubles and statistic data discussed then by processing data reached to useful parameters about
fertility. In section 5 adaptive statistical data processing algorithm using SD model for data
correction was proposed. This adaptive algorithm was a valuable method for solving the problem
of data’s inconsistencies. Parameters resulted from this adaptive method, were used in simulation
and made a very accurate result. Finally model validation was observed and presented part of
simulation results like forecasting population growth rate shows that ten-years average growth
rate from 2006 to 2016 will increase and would be equal to 1.896.Then three different probable
14
scenarios were simulated for Iran population. In this research, despite of some previous reports,
we robustly conclude that Iran population growth rate in near future not only will not be
descending but also has an obvious ascending trend. This fact can affect main planning of
country and authorities should notice this result carefully.
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Walonick, D. S. 2006. An overview of forecasting methodology. Statpac, Inc.
16
shown in Figure 4 (by cities). Time = 0 corresponds to the time when Uber began its first ride-
hailing service in NYC.
Figure 12 shows our comparative simulation result of Uber’s Drivers and active drivers.
Empowered by the reinforcing loops of word of mouth both in supply and demand side, the number
of drivers increases exponentially.
As a result of such business expansion, the model shows that monthly gross revenue
continues to grow at increasing rate. Behaviors of gross revenue and bonus spending are shown in
Figure 13. Uber’s cost structure in NYC, which consists only of bonus spending in the current
model is correspondingly increasing.
Figure 14 shows behavior of Uber’s market share in response to the entrance of its
main competitor, Gett, to NYC at time = 10 months.®, Initially, there was no ride-hailing service
competitor in NYC. Over time the competitor gradually gain market share until it reaches its steady
point. Then at time = 45 months, Uber cuts its service price by 15 %.’ Asa result, Uber regain its
market share. Moreover, at time = 60 months, one of the competitors, Lyft reduces its pickup time
from 6 to 3 minutes.® The loss in market share of Uber is a consequence of its competitor’s service
price change.
Limits to growth
So far, as the model is simulated in default scenario, the number of Uber’s customers could
continue to grow since the industry itself is expanding, supported by two reinforcing loops of word
of mouth. However, when the model is run until 200 months, it reaches a peak and the market
seems to saturate. This is certainly a result of limited capacity in the number of drivers and service
users in NYC. A specific value does not have significance itself. Rather, system structure which
produces certain behavior should be focused.
Scenario Analysis
1. Change in Commission Percentage
In the scenario 1, competitor cuts its commission from 20% to 10% at time = 60 months.
This happened in reality; Gett, one of Uber’s main competitor in NYC, reduced its commission
5 Uber’s competitor, Gett, launched operation in NYC in June 2012. (Mashable, 2012)
7 This change in Uber’s price is based on real case in Golson (2016)
8 “Since May 2016, Lyft has halved its average waiting time for a ride in NYC” (Wieczner, 2016).
Page | 17
Uber's Drivers
50,000
25000
Drivers:
Month
— Uber's Drivers = += Uber's Active Drivers
Figure 12: Behavior of Uber Drivers and Active Drivers
Gross Revenue & Costs
UsDIMonth
Month
— Gross Revenue ~~ Indicated Bonus Spending
Figure 13: Behavior of Financial Performance Indicators
Market Share: Demand Side
unitless
o 5 1 1 2 2 3 35 40 45 50 55 60 65
Month
—1—Perceived Service Value
2 Uber Market Share
Page
Figure 14: Response in Uber’s Market Share
a Price per Ride
2000
3 2500 7 L__,—2
3 3 a 3 2
000
Month: ~23
Effective Price per Ride
287.10
_ Uber's Perceived Price per Ride
29.10
Competitor's STD Price per Ride
**"20.00
Figure 15: Uber’s Service Price per Ride
Ride Halling Customers
Uber's Customers 2a Hts
on
Customers
Month
Month
Ride Haling Customers
— Ubers Customers
Figure 16: Market Saturation
to %10 in May 2016. If Uber will not react to it and just let its commission percentage as it is, this
company loses its drivers and, therefore, also loses service capacity, and ultimately will go out of
the business due to further decrease in service demand. Figure 18 shows dramatic change of
Uber’s service capacity and demand. Therefore, Uber loses its entire market share and will go out
of the business in NYC. This simulation results can be used to argue that the model produces
realistic system behavior in such a case.
2. When Competitor Cuts Service Price.
Competitor cuts its Service Price per Ride at time = 80 months for $10 (Figure 19). In
this scenario, If Uber does not react to competitor’s cut in service price, it loses large portion of
customers reflected in Uber’s loss in market share (Figure 20).
Page | 19
a Commission Graph
0.20 }s 212}. -.
0.10 j lotarrenig earns
00 i
o 4 2 30 4 50 60 70 80 90 100 110 120
Month
Uber Commission Percentage
Competitor Commission Percentage
Figure 17: Change in Commission Percentage
Capacity vs. Service Demand Market Share: Demand Side
om 10‘
5 . 8 oso
sg \. $ ft /
& a cas
oo BS
oo en) eo Ta o 0 m 0 «0 % 6 70 m0 mw vO) 10 120
Month Month
—'— Uber's Available Capacity (Rides/Months) ='— Perceived Service Value
‘Service Demand for Uber (Rides/Months) Uber Market Share
Figure 18: Uber’s loss of service capacity and market share
Policy Analysis
In this section, policies for each scenario case is presented and explained:
1. Policy for Scenario of War on Commission
Suppose that we introduce a policy where Uber adjusts “commission percentage” in response to a
change in competitor’s commission. In scenario 1, at time = 60 months, as competitor cuts its
commission from 20% to 10%, Uber perceives such move in competitor and adjusts its
commission with a small delay.
Page | 20
sm
Customers
USDIRides.
Price per Ride
50.00
12 1—2
25.00
8 = 5.
3
0.00
o 4 2 30 4 50 60 70 8 00 100 10 120
Month
== Effective Price per Ride
~ 2 ~ Uber's Perceived Price per Ride
5- Competitor's STD Price per Ride
Figure 19: War on Service Price per Ride
Ubers Customers
Market Share: Demand Side
10
|
ons] |
8 oso \
5 Weng Fy
028
oo
o 0 2 9 40 8 6 70 8 @ 100 110 120
Month
— Uber's Customers
unitless
Perceived Service Value
Uber Market Share
Month
Figure 20: Competitor’s cut in Service Price takes customer from Uber
‘Commission Graph
020 }4——
oo
Month
—1— Uber Commission Percentage
2- Competitor Commission Percentage
Figure 21: War on Commission Percentage
Page | 21
Gross Revenue & Costs
aay Market Share: Demand Side
| /
eM | |
[Vv
Lusbintontn
vunitless
0 1 2 30 4 50 0 70 e o 100 110 120
Month
Month Perceived Service Value
~~ indicates Bonus Spencing Uber Market Share
Figure 22: Behavior of gross revenue and market share during War on Commission
2. Policy for Scenario of War on Service Price
We note that for this policy, commission ratio of Uber and its main competitor set to be equal;
otherwise, one of them will go out of business very soon.
This policy is a reactive policy since Uber adjusts its service price in response to a cut
in competitor’s price. This policy structure is so-called War on Service Price. As a result of this
policy, Uber will be able to keep its customers who have remained interested in using Uber
(Figure 24). Another interesting consequence is the reaction of Uber’s drives to this policy by
showing less on the streets and as a result, decreasing the capacity for Uber platform (Figure 25).
Price per Ride
50.00
USD/Rides
|
|
o |
|
1
|
|
|
hark
0.00
Month
—!— Effective Price per Ride
- 2 - Uber's Perceived Price per Ride
3. Competitor's STD Price per Ride
Figure 23: War on Service Price per Ride
Page | 22
Market Share: Demand Side bers Customors
unitless
customers
2
on a 6 0 © & % 8 8 OD 0 120 “Caw 6 8 @ 8 www We tw
Month
—1— Perceived Service Value
Uber Market Share
— uber Customers
Figure 24: Uber’s customers’ reaction to policy of cutting service price
Capacity vs. Service Demand
200M
2
£
S 100m
2
8 1
ZB
z
00 |, P eT
0 1 2 3 40 50 60 7 8 90 100 110 120
Month
—1— Uber's Available Capacity (Rides/Months)
~2- Service Demand for Uber (Rides/Months)
Figure 25: Uber’s driver’ reaction to policy of cutting service price
Concluding Remarks
This paper aims to explore how the dynamic performance management approach could be applied
to a case study of Uber Inc. in NYC and to further explore how such a methodology helps to
capture holistic view of performance management inherently embedded in complex system. First,
the model structure is briefly presented with the help of Dynamic Performance Management Chart
to foster understandings of the relationship between performance drives and end results; those end
results in turn affect strategic resources of the firm. Then, underlying structure of business system
is analyzed and illustrated. The model assumes the word of mouth diffusion mechanism for both
customer acquisition and driver-partnership structure of the model. Our default case scenario
Page | 23
showed exponential growth of the ride-hailing service industry and number of Uber driver-partners.
The behavior is consistent with what has been observed in the real world. Based on the same
explanatory model and assumptions, 2 scenario cases and policies to each scenario examined. Each
scenario case produced different behaviors, including the worst case of bankruptcy.
Furthermore, limitations in the model are also highlighted, indicating rooms for further
improvements in our current research. Particularly, it is an important question to ask whether any
policy is sustainable or not. In this respect, one of our limitations would be that our scenario and
policy analysis suffers from lack of financial structure.
Our research particularly contributes to the relatively less explored research domain of
ride-hailing service market. It provides a holistic view to such a rising on-demand economy and
hypothetical mechanisms which explain the rapid growth behind the business. We acknowledge
that our model is simplified due to the lack of credible data, but we believe that the real value of
our approach would be realized when business people who are working closely within the system
every day, incorporate a similar approach with a more detailed managerial task.
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Page | 26
Appendix 1: Complete Model View
Page | 27
Appendix 2: Model Documentation
Adaption Fraction = 0.005
UNITS: unitless
DOCUMENT: Our Assumption
Adaption Fraction by WoM = 0.0041
UNITS: unitless
DOCUMENT: Our Assumption
Average Monthly Working Hours = 15600
UNITS: Minutes/Month
DOCUMENT: {60 minutes = | hour, 65 hours/week per driver* 4 weeks/month, 60*65*4 = 15600}
Average Preparation Time = %
UNITS: Months
DOCUMENT: {4 month /2 weeks} {We assume that it takes 2 weeks to pass the background and vehicle check}
Average Time to Make Decision = 5
UNITS: Minutes
DOCUMENT: Our Assumption
Awaiting Drivers(t) = Awaiting Drivers(t - dt) + (Tempting Drivers - Becoming Drivers) * dt
INIT Awaiting Drivers = INITIAL Awaiting Drivers
UNITS: Drivers
INFLOWS:
‘Tempting Drivers = (Contacts Between Potential Drivers and Uber Drivers* Adaption Fraction by WoM + Transition Realized by
Bonus)*Effect of Commission on Tempting Drivers
UNITS: Drivers/Months
OUTFLOWS.
Page | 28
Becoming Drivers = Awaiting Drivers/Average Preparation Time
UNITS: Drivers/Month
DOCUMENT: limited capacity for mentioned checks
Bonus Effectiveness = 0.0003
UNITS: Drivers/USD
DOCUMENT: Our Assumption
Bonus Incentives Spending Percentage = 0.3
UNITS: unitless
DOCUMENT: Our Assumption
Bonus Spending(t) = Bonus Spending(t - dt) + (Change in Bonus Spending) * dt
INIT Bonus Spending = INITIAL Bonus Spending
UNITS: USD/Month
INFLOWS:
Change in Bonus Spending = (Indicated Bonus Spending-Bonus Spending)/Bonus Spending Adjustment Time
UNITS: USD/Month/Month
Bonus Spending Adjustment Time = 1
UNITS: Months
DOCUMENT: Our Assumption
Capacity Demand Ratio = Uber's Available Capacity/Service Demand for Uber
UNITS: unitless
Commission Adjustment Time = 0.5
UNITS: Months
DOCUMENT: Our Assumption
Page | 29
Commission Goal = Effect of Indicated Coverage Ratio on Commission
UNITS: unitless
Competitor Commission Percentage = REAL DATA Competitor Commission + Scenariol Competitor's Commission Changes*Scenariol
Switch
UNITS: unitless
DOCUMENT: http://www.theverge.com/2016/5/12/11664422, de“hail-new-yorketith
Competitor Pickup Time = REAL DATA Competitor PT + Scenario2 Competitor's Pickup Time Changes*Scenario2 Switch
UNITS: Minutes
DOCUMENT: Since May 2016 (month 60 in our model), “Lyft has halved its average wait time for a ride in New York from six
minutes to three minutes”. i s-uber-new-york/
‘Competitor's Standard Price per Ride = REAL DATA Competitor Price + Scenario3 War on Price Parameters*Scenario3 Switch
UNITS: USD/Rides
DOCUMENT: https://en.wikipedia.org/wiki/Gett and http://mashable.com/2012/06/07/gettaxi/
Contaet Frequency of Drivers = 18
UNITS: I/Month
DOCUMENT: Our Assumption
Contact Frequency of Ride Hailing Customer = 30
UNITS: I/Month
DOCUMENT: Our Assumption
Contacts Between Potential and Ride Hailing Customer = Fraction of Potential Customers*Total Contacts by Ride Hailing Customer
UNITS: Customers/Months.
Contacts Between Potential Drivers and Uber Drivers = Total Contacts by Uber Drivers*Fraction of Potential Drivers
UNITS: Drivers/Months
Page | 30
Demand Capacity Ratio = Service Demand for Uber/Uber's Available Capacity
UNITS: unitless
Effect of Commission on Drivers Attrition = GRAPH(Relative Commission)
(0.000, 0.1), (0.250, 0.3), (0.500, 0.4), (0.750, 0.6), (1.000, 1.0), (1.250, 50.0), (1.500,
100.0), (1.750, 150.0), (2.000, 200.0), (2.250, 250.0), (2.500, 300.0), (2.750, 400.0),
(3.000, 500.0)
UNITS: unitless
DOCUMENT: The logic here is that as competitor offers less commissions (more
gain for Drivers), more and more drivers leave Uber and join its competitor.
Figure Al:
Effect of Comm...vers Attrition
Relative_Commission 3
Effect of Commission on Drivers Attrition
Effect of Commission on Tempting Drivers = GRAPH(Relative Commission)
(0.000, 2.000), (0.200, 2.000), (0.400, 1.930), (0.600, 1.825), (0.800, 1.572), (1.000,
1,000), (1.200, 0.611), (1.400, 0.419), (1.600, 0.288), (1.800, 0.148), (2.000, 0.070)
UNITS: unitless
DOCUMENT: The logic here is that as competitor offers less commissions (more
gain for Drivers), it becomes more difficult to tempt drivers to join Uber.
Effect of Com...pting Drivers
Relative_Commission 2
Figure A2: Effect of Commission on Tempting Drivers
Effect of Demand Capacity Ratio on Pickup Time = GRAPH(Demand Capacity Ratio)
(1.000, 1.00), (1.100, 1.10), (1.200, 1.17), (1.300, 1.24), (1.400, 1.40), (1.500, 1.66), (1.600, 2.14), (1.700, 2.88), (1.800, 4.25), (1.900,
6.65), (2.000, 10.00)
UNITS: unitless
DOCUMENT: An assumption behind this effect is that when service demand becomes (for example, twice as) higher than service
delivery capacity of Uber, Effective Pickup Time becomes nearly ten times longer than normal time. In other words, having twice as service
Page | 31
demand than service capacity does not simply mean that Uber’s pickup time becomes twice of normal times. In fact, we assumed the effect
would be much stronger until it hits certain threshold’. Our reasoning is as follows:
is twice as many as what the company can deliver, each Uber driver in NYC has two
people waiting for a ride at the same time. But some of the drivers need to refill the
gas or even they may get into traffic jam, etc. Therefore, the effect should be
increasingly stronger as Demand-Capacity ratio increases.
Why the maximum is the specific value of 10? Because this is the period between the
moment a customer hails a ride and the driver arrives. In NYC, considering the number
of available Uber driver, we assume that it will not exceed Uber's MIN Pickup Time
(=3 minutes) * Max value of the Effect (= 10) = 30 minutes.'°
vhen the service demand for Uber at a specific period
Effect of Demand ..jo on Pickup Te
Demand Capacity Ratio 2
Figure A3: Effect of Demand Capacity Ratio on Pickup Time
Effect of Indicated Coverage Ratio on Commission
(0.000, 0.2000), (2.000, 0.0100)
UNITS: unitless
DOCUMENT: Our Assumption
Effect of Pickup Time on Service Value = GRAPH(Relative Pickup Time)
(0.000, 1.000), (0.200, 0.983), (0.400, 0.930), (0.600, 0.843), (0.800, 0.677), (1.000,
0.500), (1.200, 0.271), (1.400, 0.157), (1.600, 0.092), (1.800, 0.039), (2.000, 0.022)
UNITS: unitless
INPUT = Relative Waiting Time
RAPH(Indicated Capacity Demand Ratio)
Effect of Pelup Time on Sarvice Value
° Ralatve Pidap_Tine 2
Figure A4: Effect of Pickup Time on Service Value
® Specifically, the maximum value is set to be 10.
10 For example, Uber car hailing service can be considered as a super-efficient version of ambulance in a sense that many available cars
are ready at a specific moment in NYC.
Page | 32
DOCUMENT: The assumption made behind this structure is that the longer Uber drivers make their customers wait, the more they
lose market share (to its competitors such as Get, Lyft, Yellow cab). The degree of the effect is subjective since, on the shadow of lack of
information, we have not conducted regression analysis whatsoever. However, the curve of the graphical function is determined by our
logics based on our mental model. The horizontal line in the graph means that there will be no effect if “Relative Pickup time” is 1.
Effect of Price on Service Value = GRAPH(Relative Price) Fi
(0.000, 1.000), (0.200, 0.983), (0.400, 0.930), (0.600, 0.843), (0.800, 0.677), (1.000,
0.500), (1.200, 0.271), (1.400, 0.157), (1.600, 0.092), (1.800, 0.039), (2.000, 0.022)
UNITS: unitless
3
DOCUMENT: Our Assumption
° Reatve Price 2
Figure AS: Effect of Price on Service Value
Effect of Price Threshold Ratio on Closing App = (Price Threshold Ratio/10) - 0.1
UNITS: unitless
10
DOCUMENT: 1 0. O01 0)
2 02 O1 O41
3 03 O41 02
4 04 o.1 03
5 05 oO. 04
6 0.6 O11 05
ay 07 O. 0.6
8 08 O41 07
9 09 O41 08
9 09 O1 08
10 1 0. 09
Figure A6: Effect of Price Threshold Ratio on Closing App
Page | 33
Effect of Price Threshold Ratio on Active Drivers = GRAPH(Price Threshold Ratio {We assume that in normal situation, price ratio of 1
leads to 40% of drivers availability})
(0.00, 0.000), (1.00, 0.400), (2.00, 0.502), (3.00, 0.590), (4.00, 0.664), (5.00, 0.721), (6.00, 0.790), (7.00, 0.834), (8.00, 0.882), (9.00, 0.921),
(10.00, 0.978)
UNITS: unitless
DOCUMENT: This effect is used to describe the change in active Uber drivers
when service price increase and becomes higher than normal rates. When Uber drivers
see service rate is surging, more and more drivers start turning on their car engines and
become involved actively. This concept of rise in service capacity is observed in real
case study. A case study of Hall, Kendrick and Nosko (2015) shows that the service
Effect of Price... Active Drivers
capacity can get to be 150% higher than normal times during surge period in the event
of sold-out musical concert in NYC. {We assume that in normal situation, price ratio o
° Threshold Ratio {We a.
of I leads to 40% of drivers’ availability}
Figure A7: Effect of Threshold Ratio on Active Drivers
Effect of Service Value on Customer Acquisition = Perceived Service Value
UNITS: unitless
DOCUMENT: This variable is an intermediate one and it is equal to Perceived Service Value.
Effective Price per Ride = Uber's Normal Price per Ride*Surge Pricing Effect
UNITS: USD/Rides
Fraction of Potential Customers = Potential Customers/Total Ridership
UNITS: unitless
Fraction of Potential Drivers = Potential Drivers/Total Drivers
UNITS: unitless
Fraction of Uber's Active Drivers = Effect of Price Threshold Ratio on Drivers
UNITS: unitless
Page
Gross Revenue = Uber Commission Percentage*Giving a Ride*Uber's Perceived Price per Ride
UNITS: USD/Month
Indicated Bonus Spending = Gross Revenue*Bonus Incentives Spending Percentage
UNITS: USD/Month.
Indicated Capacity Demand Ratio = Policy4 Desired Capacity Demand Ratio - Capacity Demand Ratio
UNITS: unitless
Indicated Uber's Customers = Ride Hailing Customers*Effect of Service Value on Customer Acquisition
UNITS: Customers
INITIAL Awaiting Drivers = 0
UNITS: Drivers
INITIAL Bonus Spending = 10*26850 {10 Bonus * Average price of new passenger cars sold and leased in 2010}
UNITS: USD/Month
DOCUMENT: Average price of new passenger cars sold and leased, in 2010: 26850 USD
1990/
Sf Coe ere ens
hitp:/Avww.statist ics/18374:
INITIAL On Decision =
UNITS: Rides
INITIAL On Service = 0
UNITS: Rides
INITIAL POTENTIAL DRIVERS = 51398 + 1400000
UNITS: Drivers
DOCUMENT:
As of March 14, 2014, in New York City, there were 51,398 men and women licensed to drive medallion taxicabs.
in existence, 368 of them having been auctioned by the City of New
There were 13,605 taxicab medallion licenses
Page | 35
York between November 2013 and February 2014.
https://en.wikipedia.org/wiki/Taxicabs_of New_York City
“According to the data, only 1.4 million households in the City out of the total 3.0 million owned a car”
ip: nycede.comvbl ‘kers-and-cars) Here, in our model, we ignore the fact that some car
‘owners may have more than one car!
INITIAL POTENTIAL Customers = 8175133/3
UNITS: Customers
DOCUMENT: 8175133 Initial population of NY City in 2010; we assume that just one third of them are potential customers
http: Lnye, ps fi pe
INITIAL PT =3
UNITS: Minutes
INITIAL Requested Rides
UNITS: Rides
INITIAL Ride Hailing Customers = 200
UNITS: Customers
INITIAL Uber Commission Percentage = 0.2
UNITS: unitless
INITIAL Uber Drivers = 100
UNITS: Drivers
INITIAL UBER PRICE per RIDE = 29 {We assume it is equal to INITIAL Uber’s Normal Price per Ride.}
UNITS: USD/Rides
INITIAL Uber's Normal Price per Ride = 29
Page | 36
UNITS: USD/Rides
DOCUMENT:
After Jan 2016:
$2.55 Base Fare + $0.35 per minutes *30 minutes + $1.75 per mile * 6.5 miles from Manhattan to East Brooklyn
= $24.425 = 25
http://wwi Ahi +h-does-uber-cost-uber-fare-estimator/ and c (o
York-City/ )
Before Jan 2016:
$3.00 Base Fare + $0.40 per minutes *30 minutes + $2.15 per mile * 6.5 miles from Manhattan to East Brooklyn
= $28.975 = 29
“Uber is slashing prices in New York City The base fare on UberX will go from $3 to $2.55, with the per mile rate going from
$2.15 to $1.75. The per minute rate will go from $0.40 to $0.35. UberXL will see drops of similar levels.”
(http://www. theverge.com/201 6/1/28/108645 16/uber-cutting-uberx-rates-new-york-city)
Matched Rides(t) = Matched Rides(t - dt) + (Requesting a Ride - Free Cancellation - Ride Arriving) * dt
INIT Matched Rides = INITIAL Requested Rides
UNITS: Rides
INFLOWS:
Requesting a Ride = On Decision/(Average Time to Make Decision/Time Converter)
UNITS: Rides/Months
OUTFLOWS:
Free Cancellation = SMTHI (Requesting a Ride*0.001, 5/Time Converter)*0 +0
UNITS: Rides/Months
Ride Arriving = MIN(Matched Rides/(Uber's Average Pickup Time/Time Converter), Uber's Available Capacity)
UNITS: Rides/Months
‘Normal Regreters per Month = 5
UNITS: Customers/Month
Page | 37
On Decision(t) = On Decision(t - dt) + (Opening App - Requesting a Ride - Closing App Crazy Prices - Discarding Late Services) * dt
INIT On Decision = INITIAL On Decision
UNITS: Rides
INFLOWS:
Opening App = Service Demand for Uber
UNITS: Rides/Months
OUTFLOWS:
Requesting a Ride = On Decision/(Average Time to Make Decision/Time Converter)
UNITS: Rides/Months
Closing App Crazy Prices = Opening App*Effect of Price Threshold Ratio on Closing App
UNITS: Rides/Months
Discarding Late Services = IF (Uber's Effective Pickup Time > 60) THEN SMTHI((Opening App - Requesting a Ride), 1/30)
ELSE 0 {If effective waiting time exceeds [Hours (~ 60 minutes), customers cancel their rides (requests)}
UNITS: Rides/Months
On Service(t) = On Service(t - dt) + (Ride Arriving - Giving a Ride) * dt
INIT On Service = INITIAL On Service
UNITS: Rides
INFLOWS:
Ride Arriving = MIN(Matched Rides/(Uber's Average Pickup Time/Time Converter), Uber's Available Capacity)
UNITS: Rides/Months
OUTFLOWS:
Giving a Ride = On Service/(Standard Riding Time/Time Converter)
UNITS: Rides/Months
Perceived Price Adjustment Time = 1/4 {about a week}
UNITS: Months
Perceived Service Value(t) = Perceived Service Value(t - dt) + (Change in Perceived SV) * dt
INIT Perceived Service Value = Service Value
Page | 38
UNITS: unitless
INFLOWS:
Change in Perceived SV = (Service Value - Perceived Service Value)/Time to Change Perceives
UNITS: I/month
Pickup Time Weight = 0.25
UNITS: unitless
Policy! Switch = IF TIME > 80 THEN 1*0 ELSE 0 {0= off, 1 =on} {Change 1*0 to | to activate this switch} {Tnis scenario is very
sensitive to time, if it is activated late, company will fail; here 80 is too much! }
UNITS: unitless
Policy2 Change in MIN Pickup Valu
UNITS: Minutes
Policy2 Switch = 0 {0 =
1=on}
UNITS: unitless
Policy2 Time = 80 {month}
UNITS: Months
DOCUMENT: Timing of policy implementation has significant effect on the performance of the business; Test these values: Change
in MIN Waiting Time = -3; Policy2 Time = 1 vs 30
Policy3 Adjustment Time = 1/2 {half'a month}
UNITS: Months
Policy3 Switch = IF TIME > 80 THEN 1*0 ELSE 0 {0 = off, 1 = on} {Change 1*0 to I to activate this switch}
UNITS: unitless
Policy4 Desired Capacity Demand Ratio = 3
UNITS: unitless
Page | 39
Policy4 Switch = IF TIME > 70 THEN 1*0 ELSE 0 {0 = off, 1 = on} {Change 1*0 to | to activate this switch}
UNITS: unitless
Potential Customers(t) = Potential Customers(t - dt) + (Net Change in Potential Customers + Regreters - New Customers) * dt
INIT Potential Customers = INITIAL POTENTIAL Customers
UNITS: Customers
DOCUMENT: An important assumption: We assume that the population of the NY City is constant during the 5 years period of
simulation,
INFLOWS:
Net Change in Potential Customers = 0
UNITS: Customers/Months
Regreters = Surge Pricing Effect*Normal Regreters per Month
UNITS: Customers/Months
OUTFLOWS:
New Customers = Contacts Between Potential and Ride Hailing Customer*Adaption Fraction
UNITS: Customers/Months.
Potential Drivers(t) = Potential Drivers(t - dt) + (Drivers Leaving Uber + Net Change in Potential Drivers - Tempting Drivers) * dt
INIT Potential Drivers = INITIAL POTENTIAL DRIVERS
UNITS: Drivers
INFLOWS:
Drivers Leaving Uber = Standard Drivers Attrition*Effect of Commission on Drivers Attrition
UNITS: Drivers/Month
Net Change in Potential Drivers = 0
UNITS: Drivers/Months
OUTFLOWS:
‘Tempting Drivers = (Contacts Between Potential Drivers and Uber Drivers* Adaption Fraction by WoM + Transition Realized by
Bonus)*Effect of Commission on Tempting Drivers
UNITS: Drivers/Months
Page | 40
Price Threshold Ratio = SMTH I (Effective Price per Ride/Uber’s Normal Price per Ride, DT, 1) _ {smoothing time = one DT}
UNITS: unitless
Price Weight = 0.75
UNITS: unitless
REAL DATA Competitor Commission = 10000 + STEP(-10000+0.2, 10) + STEP(-0.1, 60) {To make sure that before arrival of our first
competitor in March 2012 (Month 10), all of market share goes to Uber}
UNITS: unitless
REAL DATA Competitor Price = 10000 + STEP(-10000+20, 12) {To make sure that before arrival of our first competitor in March 2012
(Month 10), all of market share goes to Uber} {we assume Gett entered the NYC market with $20 per ride}
UNITS: USD/Rides
REAL DATA Competitor PT = 10000 + STEP(-10000+6, 10) + STEP(-3, 60) {To make sure that before arrival of our first competitor in
March 2012 (Month 10), all of market share goes to Uber}
UNITS: Minutes
DOCUMENT:
Since May 2016 (moth 60 in our model), Lyft has halved its average wait time for a ride in New York from six minutes
to three minutes, the spokesperson added by way of explaining the 500% ridership growth. Both Lyft and Uber have
also been aggressively slashing their prices in New York and other cities as they compete with each other to win
customers. s-uber-new-york/
REAL DATA Uber Commission = PULSE(0.05, 52,0) _ {in September 2015, increased to 25%; September 2015 = Month 52 in our model}
UNITS: I/month
REAL DATA Uber Price = PULSE(-4, 43, 0)
UNITS: USD/Rides/Month
DOCUMENT: in Jan. 2016, Uber slashed its prices by 15% in NYC and some other markets. Jan 2016 = Month 43 in our model.
Page | 41
Relative Commission = Uber Commission Percentage/Competitor Commission Percentage
UNITS: unitless
Relative Pickup Time = Uber's Perceived Pickup Time/Competitor Pickup Time
UNITS: unitless
Relative Price = Uber's Perceived Price per Ride/Competitor's Standard Price per Ride
UNITS: unitless
Reported Uber's Customers(t) = Reported Uber’s Customers(t - dt) + (Change in UC) * dt
INIT Reported Uber's Customers = Indicated Uber's Customers
UNITS: Customers
INFLOWS:
Change in UC = (Indicated Uber’s Cus s-Reported Uber's Ci Time
UNITS: Customers/Months
Reporting Time = 1
UNITS: Months
Ride Hailing Customers(t) = Ride Hailing Customers(t - dt) + (New Customers - Regreters) * dt
INIT Ride Hailing Customers = INITIAL Ride Hailing Customers
UNITS: Customers
INFLOWS:
New Customers = Contacts Between Potential and Ride Hailing Customer*Adaption Fraction
UNITS: Customers/Months
OUTFLOWS:
Regreters = Surge Pricing Effect*Normal Regreters per Month
UNITS: Customers/Months
Scenariol Competitor's Commission Changes = STEP(-0.09, 80) {Change in Value, Time in Month}
Page | 42
UNITS: unitless
Scenario] Switch = IF TIME > 70 THEN 1*0 ELSE 0 {0= off, 1=on} {Change 1*0 to | to activate this switch}
UNITS: unitless
Scenario2 Competitor’s Pickup Time Changes = STEP(-3, 100) {Change in Value, Time in Month}
UNITS: Minutes
Scenario2 Switch =0 {0 =off, 1= on}
UNITS: unitless
Scenario3 Switch = IF TIME > 80 THEN 1*0 ELSE 0 {0= off, 1=on} {Change 1*0 to | to activate this switch}
UNITS: unitless
Scenario3 War on Price Parameters = STEP(-10, 80) {Change in Value, Time in Month}
UNITS: USD/Rides
Service Demand for Uber = Reported Uber's Customers" Standard Rides Need per Customer
UNITS: Rides/Months
Service Value = Price Weight*Effect of Price on Service Value + Pickup Time Weight*Effect of Pickup Time on Service Value
UNITS: unitless
Shock Test Switch =0 {0 off, 1 =on}
UNITS: unitless
Shock Time =23 {month}
UNITS: Months
Shock Value =0.1 {The Pulse Value is very sensitive to DT. So, a tiny value of 0.1 will be divided by DT = 0.0001 which result in 100}
UNITS: Rides/Customers
Page | 43
Standard Driver per Ride = 1
UNITS: Drivers/Rides
Standard Drivers Attrition = 5
UNITS: Drivers/Month
Standard Rides Need per Customer = 10 + PULSE(Shock Value, Shock Time, 0)*Shock Test Switch
UNITS: Rides/Months/Customers
DOCUMENT: _ 10 rides per week, 4 weeks in a month {The Pulse Value is very sensitive to DT. So, a tiny value of 0.1 will be divided
by DT = 0.0001 which result in 100}
Standard Riding Time = 45 {0.75 hour:
45 minutes}
UNITS: Minutes
Surge Pricing Effect = GRAPH(Demand Capacity Ratio)
99
(1.000, 1.000), (1.100, 1.100), (1.200, 1.300), (1.300, 1.500), (1.400, 2.074), (1.500,
2.598), (1.600, 3.279), (1.700, 4.459), (1.800, 5.897), (1.900, 7.918), (2.000, 9.900) ”
&
UNITS: unitless zg
&
a
1
1 Demand_Capacity Ratio 2
Figure A8: Surge Pricing Effect (Effect of Demand Capacity Ratio on Service Price)
DOCUMENT:
When the demand for Uber rides peaks, Uber applies a policy called surye pricing. This happens when demand increases
largely. However, the algorithm for this policy is not revealed. Information reveals that it can be 2.8x or even 7x of normal rates on New
Year's Eve in 2011 (Moon, 2016). At times, it can go even further:
Page | 44
Surge pricing is one of Uber's most widely hated features. Just look at social media the day after any big holiday
and you'll see a flood of screenshots complaining of rates up to 9.9 times the company's normal price. (Kulp, 2016).
Based on this information, we assumed that company’s surging price algorithm features a quite steep slope when demand exceeds service
capacity as shown in the Figure A8. This effect lies in the center of interaction of supply and demand side of the model.
Time Converter = 43800
UNITS: Minutes/Month
Time to Adjust Perceived Pickup Time = 1/4 {1 weeks / 4 weeks in a month}
UNITS: Months
Time to Change Perceives = |
UNITS: Months
Total Contacts by Ride Hailing Customer = Contact Frequency of Ride Hailing Customer*Ride Hailing Customers
UNITS: Customers/Months
Total Contacts by Uber Drivers = Uber's Drivers*Contact Frequency of Drivers
UNITS: Drivers/Months
Total Drivers = Potential Drivers + Uber's Drivers
UNITS: Drivers
Total Ridership = Potential Customers + Ride Hailing Customers
UNITS: Customers
Transition Realized by Bonus = Fraction of Potential Drivers*Bonus Spending*Bonus Effectiveness
UNITS: Drivers/Months
Page | 45
Uber Commission Percentage(t) = Uber Commission Percentage(t - dt) + (Change in Commission Percentage) * dt
INIT Uber Commission Percentage = INITIAL Uber Commission Percentage
UNITS: unitless
DOCUMENT: hittp://www.forbs 10 15/09/1 L/uber-raises-ub 25-percent-in-five-more-markets/
INFLOWS:
Change in Commission Percentage = REAL DATA Uber Commission + Policy4 Switch*(Commission Goal-Uber Commission
Percentage)/Commission Adjustment Time +Policy1 Switch*War on Commission/Commission Adjustment Time
UNITS: 1/Month
Uber Market Share = Indicated Uber's Customers/Ride Hailing Customers
UNITS: unitless
Uber's Active Drivers = Uber’s Drivers*Fraction of Uber’s Active Drivers
UNITS: Drivers
Uber's Available Capacity = ((Uber's Active Drivers/Standard Driver per Ride)*Average Monthly Working Hours)/Standard Riding Time
UNITS: Rides/Months
Uber's Average Pickup Time = Uber's MIN Pickup Time*Effect of Demand Capacity Ratio on Pickup Time
UNITS: Minutes
Uber's Drivers(t) = Uber's Drivers(t - dt) + (Becoming Drivers - Drivers Leaving Uber) * dt
INIT Uber's Drivers = INITIAL Uber Drivers
UNITS: Drivers
INFLOWS:
Becoming Drivers = Awaiting Drivers/Average Preparation Time
UNITS: Drivers/Month
DOCUMENT: Later we may add more detail
imited capacity for mentioned checks
OUTFLOWS:
Drivers Leaving Uber = Standard Drivers Attrition*Effect of Commission on Drivers Attrition
Page | 46
UNITS: Drivers/Month
Uber's Effective Pickup Time = (Matched Rides/Ride Arriving)*Time Converter
UNITS: Minutes
Uber's MIN Pickup Time = 3 + STEP(Policy2 Change in MIN Pickup Value, Policy2 Time)*Policy2 Switch
UNITS: Minutes
DOCUMENT: “Uber CEO explains why arrival time on the app is never accurate... Kalanick said that the average wait time in major
cities for an ordered Uber is about 3 minutes.” ( 2016/01/04/uber-arrival-time-late/)
Uber's Normal Price per Ride(t) = Uber's Normal Price per Ride(t - dt) + (Change in Normal Price) * dt
INIT Uber's Normal Price per Ride = INITIAL Uber’s Normal Price per Ride
UNITS: USD/Rides
INFLOWS:
Change in Normal Price = REAL DATA Uber Price + Policy3 Switch*(War on Price/Policy3 Adjustment Time)
UNITS: USD/Rides/Month
Uber's Perceived Pickup Time(t) = Uber's Perceived Pickup Time(t - dt) + (Change in Pickup Time) * dt
INIT Uber's Perceived Pickup Time = INITIAL PT
UNITS: Minutes
INFLOWS:
Change in Pickup Time = (Uber's Effective Pickup Time-Uber's Perceived Pickup Time)/Time to Adjust Perceived Pickup Time
UNITS: Minutes/Month
Uber's Perceived Price per Ride(t) = Uber's Perceived Price per Ride(t - dt) + (Uber’s Change in Price) * dt
INIT Uber's Perceived Price per Ride = INITIAL UBER PRICE per RIDE
UNITS: USD/Rides
INFLOWS:
Uber's Change in Price = (Effective Price per Ride - Uber's Perceived Price per Ride)/Perceived Price Adjustment Time
UNITS: USD/Rides/Month
Page | 47
War on Commission = Competitor Commission Percentage - Uber Commission Percentage
UNITS: unitless
War on Price = Competitor's Standard Price per Ride - Uber's Normal Price per Ride
UNITS: USD/Rides
{The model has 139 variables. Stocks: 15; Flows: 21; Converters: 103; Constants: 47; Equations: 77; Graphicals: 8}
Page | 48
