System Dynamics Modeling and Simulation

System Dynamics Modeling and Simulation
An Overview of Booz Allen Hamilton’s System Dynamics
Modeling Capability
by
Chip Jansen
[email protected]
2
1. Overview of System Dynamics
System Dynamics (SD) is an advanced simulation methodology that helps improve understanding of complex system
and causal structures by focusing on system behavior over time and system behavior in response to stimuli. Originally
developed in the United States at the Massachusetts Institute of Technology’s Sloan School of Business in the 1950s
and 1960s, SD applies the mathematics of feedback control to business or mission systems.
SD helps link policies to their impacts by simulating system responses to policy changes. This furthers
knowledge about the causal mechanisms within a complicated system, allowing for better policy decisions.
SD models can be rapidly built and modified to increase understanding of the simulated system. The primary
language of SD is stocks and flows. Stocks are accumulations, such as stores of cash, inventory levels, or
quality-adjusted life years. Flows are simply the rates at which those stocks accumulate or deplete, and can
include a variety of inputs to their calculation. One aspect of complicated systems that SD handles more
gracefully than some other methodologies is the notion of system feedback, which describes how even
seemingly simple systems display baffling nonlinearity. A sample model architecture is illustrated in Exhibit 1.
Exhibit 1 | System Dynamics Modeling
Number of Parts (Parts)
Current [+OT]
Casual Tracing - Backlog Queue (System, Maintenance)
Current
maintenance complete
S
Experience Level
Through Put or
Availability Issue
S
Experience Loss $$
Backlog Queue (System 1, Overhaul)
8
actual final inspection time
reorder
4
percent rework required
0
Backlog Queue (System 1, Repair)
8
actual initial inspection time
4
percent pass initial inspection
Backlog Queue
tagged for shop work
0
Backlog Queue (System 1, Modification)
8
tagged for inspection
4
Training
S
Attrition
(Backlog Queue)
0
to shop
shop work constraints
Backlog Queue (System 2, Overhaul)
8
4
Uses of current variable
S
Training $$
Variable Definition
Select a new variable to trace
Change subscript selection
Return to Analysis Control
Backlog Queue (System 2, Repair)
8
8
4
4
0
Help?
0
Backlog Queue
0
Backlog Queue (System 2, Modification)
8
1
2
1
2
3
4
5
6
3
4
5
6
7
8
9
10
4
0
0
2.5
5
7.5
10
YEARS
Source: Booz Allen Hamilton
2. Booz Allen Hamilton’s Approach to System Dynamics Modeling and Simulation
Booz Allen Hamilton, a leading strategy and technology consulting firm, uses a systematic approach to
developing our SD models. This approach revolves around a combination of qualitative, quantitative, and
systems thinking analysis, including appropriate combinations of statistical analysis techniques and data
mining. Systems thinking focuses on the whole view of a complex system, enabling analysts, for example, to
identify non-intuitive behavior or results. Systems thinking has its foundations in SD. Our SD model design
process is depicted in Exhibit 2 on the next page.
This approach provides a powerful method for blending qualitative and quantitative data, as well as systems
thinking techniques together with traditional analysis techniques, to better understand and model the
complexities of systems across a variety of domains.
3
2.1 Define Goals, Objectives, and
Desired End-State
Exhibit 2 | System Dynamics Modeling Approach
2
SELECTED
MODEL THEMES
IDE
Risk Mitigation
Training & Education
Personnel Management
Acquisition Decisions
Organizational Re-structuring
Technology/Capability Assessment
Incident Management
Strategy Formulation
Informative Surveys
Tactical Response
Collaboration
3
G
L O O E NE R A
TE
PS
& IN CASUAL
ITIA L D
ESIG N
REVI
EW
& R OUT
EPO PU
RT T
7
E GOAL, OBJEC
DEFIN RED END TIVES
-STATE
& DESI
NS,
PTIO
UM S
ASS AINT
IFY STR
NT CON
&
2.2 Identify Assumptions and Constraints
1
SIS
NALY
D E S IG N A X E C U T E
E
PLAN &
Booz Allen Hamilton works with clients to define
principal goals and strategic priorities that drive
towards a desired end state. In addition, both
Booz Allen Hamilton and clients will work together
in defining mission success indicators against
core operational requirements, identification and
prioritization of risks, validation of mission priorities,
and identification of possible stress test scenarios.
6
4
Critical to any modeling and simulation effort is a
T
RU C
REF TE ST &
T
S
clear understanding of the assumptions that drive
N
IN E
C O D EL
MOD
MO
EL
5
the model and the constraints under which it will
operate. Working with clients and key stakeholders,
Source: Booz Allen Hamilton
we develop a candidate set of assumptions and
constraints that will govern the model’s behavior.
This candidate list is then subjected to a detailed review against the requirement, goal, or objective it impacts
to ensure it is in line with mission priorities and operational requirements.
2.3 Cause-and-Effect Diagramming
Starting with system relationships, Booz Allen Hamilton utilizes facilitated sessions with subject matter
experts and relevant stakeholders, to develop relationship maps between system entities using Causal
Loop Diagrams (CLDs), as illustrated in Exhibit 3. From these CLDs we can then begin defining the primary
system variables and critical interactions. Primary system variables serve as “levers of change,” which allow
stakeholders to vary the conditions under which the system operates in order to observe its response. Critical
interactions define specific interactions among all the different system components and serve as a basis
for completing multi-factor scenario analysis of the identified primary system variables. In addition, critical
interactions allow for the definition of feedback loops and for the examination of multi-order effects.
Exhibit 3 | Causal Loop Diagram
+
–
= Change in SAME Direction
= Change in OPPOSITE Direction
A
B = Delayed Effect
&
= Change in EITHER Direction Possible
Implement
Stop/Loss
Pressure to
Implement
Stop/Loss
Sea Tour
Length
Resignations
Shore Tour
Length
Readiness
Accessions
Source: Booz Allen Hamilton
4
Training
Throughput
Training
Turbulence
Mandated
Requirements
2.4 Data Collection and Model Construction
Utilizing data mining, authoritative data sources, and other data gathering techniques, we gather and
analyze information supporting the primary elements of the system. Logical relationships defined in 2.3 are
broken down into further system sub-components, inputs and outputs are finalized, and business rules and
quantitative equations that regulate system behavior are defined. Next, a quantitative model is constructed
that will serve as the platform for performing multi-factor scenario analysis and stress testing the impacts to
the overall system. While typically these models have been built using Ventana System’s Vensim application,
Booz Allen Hamilton has also constructed SD models in isee systems’ iThink and the AnyLogic Company’s
AnyLogic.
2.5 Test and Refine Model
Testing ensures that all functional requirements, as specified in 2.1, have been met and verifies the accuracy
of the data employed and the operation of the model. Clients, key stakeholders, and users play an important
role in this step and often serve as the final validation check of the model. Any changes, discrepancies,
or additional refinements captured during this phase are quickly addressed and incorporated into the final
version of the model.
2.6 Design Analysis Plans and Execution
System shocks, what-if analysis, tradeoff evaluation, decision making, and scenario analysis are just a few
of the varied outputs of this phase in the process. Working in conjunction with clients and key stakeholders,
Booz Allen Hamilton brings together the strategic factors, identified in 2.1 and 2.2, and combines them
with the quantitative processes of the model, developed during phases 2.3 to 2.5, to develop and execute
analysis plans against organization goals. Utilizing the developed model, we draw out system/organizational
characteristics, positive and negative correlations, risk/non-risk factors, and trade-offs affecting the system/
organization.
2.7 Review Output and Report
Results are then examined and summarized, recommendations are collected, and detailed analysis of the
model’s results are captured and presented to both clients and key stakeholders. This includes an overview
of analysis plans executed, key findings from the model and any identified future issues that an organization
may need to consider. In addition, as illustrated in Exhibit 2, this does not necessarily have to be the end of
the overall process. Insights gained through the analysis of model data can be injected back into previous
process stages for further refinement of objectives, goals, assumptions, constraints, data, and even the
model itself. As such, clients and stakeholders can go through this process multiple times, further refining the
end product or products.
2.8 Overcoming Potential Risks
There are many risks associated with the creation of any model. Risks such as diving too deep into the
system and not looking at the system as a whole, or misinterpreting model outputs, by focusing on single
numerical outputs rather than looking at overall trends and behavior, are common in any systems thinking or
SD development process. Booz Allen Hamilton mitigates these risks by ensuring at every stage of the project
that both client and key stakeholders understand the intended goal, objectives, and desired end state of the
project. Our investigative processes are rooted in sufficient analytical rigor to enable complete traceability and
defensibility. We coordinate with stakeholders early and throughout the process to ensure their buy-in and
receive feedback, avoiding the expenditure of time and effort developing items that cannot be successfully or
effectively executed.
5
3. Past Client Engagements
3.1 Diabetes Simulation in the United Arab
Emirates (UAE)
Program Description
Booz Allen Hamilton conducted a proof of concept
for various firms and government agencies in the
UAE to demonstrate the debilitating impact of
diabetes on an individual company.
Technical Approach and Technical Resources Used
We conducted a model-supported game, working on
the game design and building an SD model using
Vensim, as illustrated in Exhibit 4. We developed
and used a seminar game design that included
capture templates for player outputs. These player
outputs were then fed into the model to provide a
deterministic result of the player decisions during
each move.
Program Outcome, Significant Accomplishments,
and Impact
The game demonstrated to UAE business leaders the
impact of diabetes on the workforce of a single company, both from financial and human perspectives.
Exhibit 4 | UAE Diabetes Simulation Model
<UnXPD to NDE>
<UnDXTTH Out>
<UnXTTO Out>
<NEH Out>
New Employees
<NOPD Out>
UnDXPDD
<OPD Out>
<UnDXPD to NDE>
<UDXPDDH Out>
<UnDXTTCH Out>
<UnDXTT to DXTT>
UnDXTTD
UnDXTTCD
<UnDXTTCO Out>
NDE to UnDXPD
UnDXPD to UnDXTT
UnDxTT to UnDxTTC
UnDX
PreDiabetes
UnDXPD to NDE
<Employee Initial
Population>
Non Diabetic
Employees
UnDX
Type Two
UnDX
Type Two
Complicated
<UnDXPDD>
UnDxPD to DXPD
<UDPDR Out>
<DXTTO Out>
UnDXTT to DXTT
<TTSD Out>
UnDXTTC to DXTTC
<TTCSD Out>
<PDSD Out>
Initial DX PD
Initial DX TT
DX
PreDiabetes
DXPD to NDE
<ENDDH Out>
<NDE to UnDXPD>
Source: Booz Allen Hamilton
6
NDE Deaths
DXPDD
<DPDR Out>
UnDX
Type Two
DXTT to DXTTC
DXPD to UnDXTT
<DXPDDH Out>
<DXPD to NDE>
DXTTD
<DXTTH Out>
<DXTTCO Out>
UnDX
Type Two
Complicated
DXTTCD
<DXTTCH Out>
3.2 Financial System Modeling – Central Bank
of Azerbaijan
Program Description
The Central Bank of Azerbaijan (CBA) contracted
with Booz Allen Hamilton for the purpose of understanding the effects of policies and law on financial
transactions and the behavior of citizens when
conducting financial transactions, while at the same
time understanding risk to the financial system.
Technical Approach and Technical Resources Used
We designed and implemented an SD model
of CBA’s financial network using the Vensim
application, as depicted in Exhibit 5.
Program Outcome, Significant Accomplishments,
and Impact
Results of the modeling effort showed CBA where
improvements in efficiency could be made and
where it should focus on keeping customers
interested in bank programs. Those programs,
in turn, need to be carefully managed in order to
ensure the stability of the bank in question.
Exhibit 5 | CBA Financial System Model
Domestic Loans in Good Standing to Past Due Process Flow
<Domestic LL to GSL>
<PD NToG>
<Domestic UL to GSL>
Domestic PDL to GSL Pulse
<Domestic DL to GSL>
Loans to Performing
<Domestic New
Loan Demand>
<Domestic GSL to PDL>
<Domestic
Lending Funds>
<Domestic PDL to UL>
<Domestic PDL to GSL
Warmup Amount>
<Past Due Rate>
New Domestic GSL
Clear Domestic PDL
Initial
Domestic
GSL
Domestic GSL Sold
Domestic GSL to PDL
Initial Domestic PDL
<Domestic Principle
Payments>
Domestic
PDL to UL
Time
<Domestic Principle
Interval Payment>
Domestic
Unsatisfactory Loans
Domestic
PDL to UL
Domestic PDL
to UL Pulse
Domestic GSL Repayment Window
<Domestic GSL Sold>
Initial Domestic UL
Domestic GSL
Interest Paid
Total Domestic
GSL Payments
<Domestic Good Standing Loans>
<Bank Has Failed>
Doubtful Loans
Domestic UL
to DL Time
<UN NToG>
<Bank Has Failed>
<Domestic
GSL Sold>
Domestic UL
to DL
Domestic DL
to LL Time
Domestic UL to DL
Warmup Amount
Domestic DL
to LL Pulse
Initial IBL
Clear
Domestic DL
<PD NToG>
<Time>
<Domestic
GSL to PDL>
<Domestic PDL to UL>
<Domestic UL to DL Time>
Domestic DL
to LL
Domestic UL to LL
Warmup Amount
<DO NToG>
<Time>
<Domestic DL
to GSL>
<Loan
Default Rate>
<Domestic UL to DL>
<Time>
<Domestic PDL
to UL Time>
Domestic PDL to GSL Warmup Amount
Inter Bank
Loans
<Domestic DL to GSL
Warmup Amount>
<Clear Bank
Values>
Initial
Domestic DL
Domestic UL to GSL
Warmup Amount
Domestic DL to GSL
Warmup Amount
<Domestic DL
to LL Times>
Interbank Lending Process Flow
Bank Failure IBL
Domestic DL
to GSL
<Bank Has Failed>
Domestic UL
to DL Pulse
Domestic PDL to UL
Warmup Amount
<Domestic GSL Interest Rate>
<Bank Has Failed>
<Domestic UL
to LL Time>
<Domestic UL to GSL Warmup Amount>
<Domestic UL to GSL>
<Domestic PDL to GSL>
Domestic Past
Due Loans
Domestic GSL
Principle Payments
Clear Domestic GSL
<Domestic UL to DL Time>
<Bank Has Failed>
Daily Past Due Rate
Domestic Good
Standing Loans
Domestic UL to GSL
Clear Domestic UL
<Domestic
UL to DL>
Domestic DL
to GSL Pulse
<DO NToG>
<UN NToG>
Domestic UL to GSL Pulse
<Clear Bank Values>
Domestic PDL to GSL
<Bank has Become
Non Bank Entity>
<Bank Has
Failed>
<Clear Bank Values>
Domestic Non Performing and Default Process Flow
<Domestic PDL to UL Time>
Domestic
Loss Loans
<Domestic Good Standing Loans>
DGSL Minus Provision
<GSL Provision>
<Domestic Past Due Loans>
DPDL Minus Provision
<PDL Provision>
<Domestic Unsatisfactory Loans>
DUL Minus Provision
<UL Provision>
<Doubtful Loans>
DDL Minus Provision
<DL Provision>
<Domestic Loss Loans>
DLL Minus Provision
<LL Provision>
<Bank Has Failed>
Daily Default Rate
Clear Domestic LL
<Clear Bank
Values>
Domestic Defaults
Initial
Domestic LL
Domestic
LL to GSL
<Bank Has
Failed>
Daily Non Performing
to Performing Rate
Source: Booz Allen Hamilton
7
3.3 Armenia Tax Improvement Program –
USAID/Armenia
Program Description
Booz Allen Hamilton developed a simulation model
to assist the United States Agency for International
Development (USAID) and the Government of
Armenia in investigating ways to increase tax
revenue collected as a percentage of gross
domestic product (GDP) through more effective,
equitable, and transparent tax administration. A
pilot regional inspectorate was identified to test new
procedures, policies, and systems prior to roll out at
a national level. A Modeling & Simulation software
program and workshop were used to evaluate the
impact from a range of potential changes.
Technical Approach and Technical Resources Used
We designed and implemented an SD model of
Armenia’s Tax Service using the Vensim application,
as illustrated in Exhibit 6.
Program Outcome, Significant Accomplishments,
and Impact
Expected results include increased collection of tax
revenues as a percentage of GDP with a broader
tax base, reduced reliance on value-added tax, improved administration of direct taxation, and enhanced
information management systems. The study also showed achievement of these objectives will also improve
the overall transparency and consistency of tax collection.
Exhibit 6 | Armenia Tax Service Model
<Time>
Annual
Requested Audits
Monthly Timer
Supervision Management
Capture Possible Audits
Additional Info Process Time
Total Requests
per Month
Requests In
Use Variable
Audit Workload
Requests Out
Total Requests
Inspectorate Staff
Requests for
Information
Information
Generation
Generate Requests
Send Requests
<Final Report>
Liquidation
Request
Rate
Budget
Relationship
Requests
DP
Information
Production
Delay
Information Provided
Goods
Registration
Requests
Other
Requests
Audit
Requests
Impact of S and P
adoption on
process rates
Annual
Requested Audits
Final Information Collected
Receive All Requests
Impact of S and P
adoption on Info Rates
Average Audit
Workload
Sys and Proc
Improvements
Head of TI Info
Assignment Delay
Audits to be
Considered
Consider for Audit
Use Capacity
Audit Workload
Impact of S and P
adoption on
Productivity
<Audit Capacity>
Green parameters are user inputs, Red are graphical lookups, Gold are used for debugging logic.
Set Constant Defaults
Source: Booz Allen Hamilton
8
Next
Previous
Copy to Clipboard
Impact of S and P
adoption on
Staff Use
<Send Request>
Print
<Shared Assess Switch>
Return
3.4 Measuring Shocks to Ethiopia’s
Agriculture System
Program Description
Booz Allen Hamilton conducted a proof of concept
study to enable more robust analyses to determine
the multiple impact of inputs (e.g., climate, conflict,
geography, and natural resources) on a wide
range of micro-indicators (e.g., farmer livelihood)
and macro-indicators (e.g., GDP, exports, and
employment).
Technical Approach and Technical Resources Used
As depicted in Exhibit 7, we designed and
implemented an SD model, using the Vensim
application, of the agricultural system in Ethiopia
to test shocks to commodities and the agriculture
sector by shifting “levers” such as climate and
conflict, to identify vulnerabilities in areas such as
food security and trade.
Program Outcome, Significant Accomplishments,
and Impact
The simulation demonstrated to public policy
makers the effects on individual livelihoods that
various shocks on a country’s agricultural system
can have, including changes in income and
kilocalories available to be consumed.
Exhibit 7 | Ethiopia Agriculture System Model
Income Sources - NHB (Very Poor)
1.0
0.8
0.6
0.4
0.2
0.0
Yemen
Sudan
Djibouti
Series
Somalia
0
0
0
0
0
Cash
Sub
Crop
Income
Labor
Income
Other
Cash
Livestock
income
Vensim Model Directory
C:Documents\020456\Desktop
Vensim Model Name
AAIP_v17.vpm
Vensim Simulation End Time (Days)
12
Report Results Out By
Month (30 Days)
Simulation Start Date
01/01/2012
Simulation Run Name
AAIPBaseline
Run Simulation
Food Sources - NHB (Very Poor)
Current Date
10/17/2012
12/06/2014
09/07/2014
06/09/2014
03/11/2014
12/11/2013
09/12/2013
06/14/2013
03/16/2013
12/16/2012
09/17/2012
06/19/2012
03/21/2012
12/22/2011
WMB
09/23/2011
SWB
12
10
8
6
4
2
0
06/25/2011
Better Off
0
Other
Food
03/27/2011
Middle
SME
0
Purchased
Food
12/27/2010
Poor
NWE
0
Grown
Food
09/28/2010
NMC
0
Food
Aid
06/30/2010
Wealth Bands
NHB
Date
NHB
NMC
NWE
SME
SWB
WMB
0
01/01/10
100%
100%
100%
100%
100%
100%
395
01/31/11
10%
10%
10%
10%
10%
10%
696
11/28/11
10%
10%
10%
10%
10%
10%
1097
01/02/12
100%
100%
100%
100%
100%
100%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
Series 1
0%
0%
0%
0%
0%
0%
Series 2
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
Household Consumption - NHB (Very Poor)
Livelihood Zones
Very Poor
0
Livestock
Food Income
04/01/2010
Kenya
Rainfall Modifier
Sim Time
Series
01/01/2010
Uganda
1.0
0.8
0.6
0.4
0.2
0.0
END
Source: Booz Allen Hamilton
9
3.5 Financial System Modeling – 2008 US
Financial Market Collapse
Program Description
Booz Allen Hamilton conducted a brief study
in 2008 on ways to mitigate the impact to the
economy of the ongoing US financial crisis. This
study analyzed the impact on the overall financial
system of key decisions the US government could
make with regard to the Troubled Asset Relief
Program (TARP). The study also looked at the
counter-party exposure risk between the top 30 US
banks and the effect of one bank’s failure on the
rest of the banks in the system.
Technical Approach and Technical Resources Used
We designed and implemented an SD model of the
US financial network using the Vensim application,
as illustrated in Exhibit 8.
Program Outcome, Significant Accomplishments,
and Impact
Results of the modeling effort showed the inherent
dangers associated with counter-party risk among
the top 30 banks to include system-wide failure due
to a large bank collapse. In addition, the study also
provided policy makers the means to gauge levels
of effectiveness, with regard to TARP, given various
system conditions and trends.
Dollars
Total Bank Failures
0
150
300
Total Bank Failures: Test Run
600
750
Loan Delinquency To Default Control
Fed Lending Threshold
00
0
Derivative Scaler
00
0
0
Fed Ratio
00
0
AIG Losses On/Off
00
0
Fed On/Off
00
0
AIG Loss Time
00
Inter Bank Lending Controls
Commercial Loan Default Percentage
00
0
Consumer Loan Default Percentage
00
0
Real Estate Loan Default Percentage
00
Receivership Controls
00
0
Receivership Return on Asset Sale
00
0
Consumer Loan Default Percentage
00
0
Time to Forget Financing Denied
00
0
Receivership Delinquency Modifier
00
0
Commercial Buyer Modifier
00
0
Real Estate Buyer Modifier
00
General Lending Controls
0
01
0
TARP Repayment Start Time
00
0
TARP Repayment Window
00
Source: Booz Allen Hamilton
0
Starting TARP Value
0
150
300
4
3
2
1
0
1.75M
0
Short Term Funding Availability
450
Time (Day)
600
750
900
750
900
750
900
Total Bank Failure Asset
0
150
300
Total Bank Failure Asset: Test Run
450
Time (Day)
600
Total Bank Failure Equity
Inter Bank Lending Threshold
TARP Repayment On/Off
Total Bank Failures Liability
Loan Asset Sale Controls
0
TARP Controls
10
900
4
3
2
1
0
Total Bank Failure Liability: Test Run
Losses Controls
FED Controls
0
450
Time (Day)
Dollars
4
3
2
1
0
Dollars
DMNL
Exhibit 8 | 2008 US Financial Network Model
4
3
2
1
0
0
150
300
Total Bank Failure Equity: Test Run
Commercial Loan Controls
00
0
0
Commercial Loans Delinquency %
450
600
Time (Day)
Consumer Loan Controls
100
Commercial Loans Nondelinquency % 100
0
0
Consumer Loans Delinquency %
Real Estate Loan Controls
100
Consumer Loans Nondelinquency % 100
0
0
Real Estate Loans Delinquency %
100
Real Estate Loans Nondelinquency % 100
11
International Office Locations
Principal Headquarters
Office
Principal Offices
OperatingOperating
OfficeOffices
Global Headquarters
About Booz Allen Hamilton
Booz Allen Hamilton has been at the forefront of strategy and technology consulting for nearly a century. Today,
the firm provides services to US and international governments in defense, intelligence, and civil sectors,
and to major corporations, institutions, and not-for-profit organizations. Booz Allen Hamilton offers clients
deep functional knowledge spanning strategy and organization, engineering and operations, technology, and
analytics—which it combines with specialized expertise in clients’ mission and domain areas to help solve their
toughest problems.
Booz Allen Hamilton is headquartered in McLean, Virginia, employs approximately 25,000 people, and had revenue
of $5.86 billion for the 12 months ended March 31, 2012. To learn more, visit www.boozallen.com. (NYSE: BAH)
For more information contact
Daniel Whitehead
Senior Associate
[email protected]
+971-50-442-8634
Chip Jansen
Lead Associate
[email protected]
+971-2-691-3600
To learn more about the firm and to download digital versions of this article and other Booz Allen Hamilton
publications, visit www.boozallen.com.
www.boozallen.com/international
©2013 Booz Allen Hamilton Inc.
01.001.13