1. Why simulation?
There is an essential dependence upon time that must be considered
There is change, complexity, and causality involved in the original problem

2. Simulation vs optimization
with Simulation, the question is usually “What if”
This is called the “descriptive mode”
with optimization (math programming, decision theory) the question is “What’s best”
This is called the “prescriptive mode”

3. Purposes of Simulation
To explore alternatives
To improve the quality of decision making
To enable more effective planning
To improve understanding of the business
To enable faster decision making
To provide more timely information
To enable more accurate forecasts
To generate cost savings

4. Simulation Usage
One of the most widely used model paradigms in all of management science

5. Simulation gestalts Discrete versus continuous
Stochastic versus deterministic
Steady state versus transient
Mathematical versus physical
Causal versus correlative

6. Continuous-deterministic simulation
Forrester’s system dynamics
Fits well for large scale models where variables assume large values, taken in relation to the change in value of those variables
Many public-sector problems are best modeled with this type of approach
Problems involving energy, resources, water, pollution, food, the economy, population
Can be used to find leverage points where just a little twiking will move the entire system in the right direction

7. Methodological Overview
Collect information and sources thereof--books, articles, internet, PEOPLE
Construct causal models representing what the written material would suggest is causally correct
Use knowledgeable people to refine and validate these models
Transform these causal models into schematic models
Use VENSIM, STELLA, or POWERSIM to implement the schematic model and execute the associated simulation

8. Discrete-stochastic simulation
Pritsker/Kiviat were initial developers
Most BPR simulators are of this variety
Fits well where probabilistic considerations come into play significantly
variables are largely binary or at least their values are small taken in relation to their change

9. Overview of system dynamics and its sister, Systems Thinking
World wide push to inculcate systems thinking into K-16 education
Andersen teaches it to all of their consultants and sees it as the next major wave in consulting
Peter Senge is Forrester’s student

10. Systems Thinking basics
Peruse relevant literature
Talk to people knowledgeable about the problem
List relevant variables
Describe causal interactions between variables
Fully delineate the causal diagram
Draw behavior over time graphs

11. Examples Itch--scratch population and growth rate of population
revenues, sales force size, sales
inventory, order rate, desired inventory,

12. Definitions and Terms ST--Systems Thinking SD--Systems Dynamics
CLD--Causal Loop Diagram
BOT--Behavior Over Time Chart
SFD--Stock & Flow Diagram
Also called Forrester Schematic, or simply “Flow Diagram”
quantity--any variable, parameter, constant, or output
edge--a causal link between quantities

13. Stock and Flow Notation--Quantities
RATE
Auxiliary

14. Stock and Flow Notation--Quantities
Input/Parameter/Lookup
Have no edges directed toward them
Output
Have no edges directed away from them

15. Inputs and Outputs
Inputs
Parameters
Lookups
Outputs

16. Stock and Flow Notation--edges
Information
Flow

17. Some rules relative to causal diagrams
There are two types of causal links in causal models
Information
Flow
Information proceeds from stocks and parameters/inputs toward rates where it is used to control flows
Flow edges proceed from rates to states (stocks) in the causal diagram always

18. Robust Loops In any loop involving a pair of quantities/edges,
one quantity must be a rate
the other a state or stock,
one edge must be a flow edge
the other an information edge

19. CONSISTENCY
All of the edges directed toward a quantity are of the same type
All of the edges directed away from a quantity are of the same type

20. Rates and their edges

21. Parameters and their edges

22. Stocks and their edges

23. Auxiliaries and their edges

24. Outputs and their edges

25. STEP 1: Identify parameters
Parameters have no edges directed toward them

26. STEP 2: Identify the edges directed from parameters
These are information edges always

27. STEP 3: By consistency identify as many other edge types as you can

28. STEP 4: Look for loops involving a pair of quantities only
Use the rules for robust loops identified above

31. Distinguishing Stocks & Flows by Name
NAME UNITS Stock or flow
Revenue
Liabilities
Employees
Depreciation
Construction starts
Hiring
material standard of living

32. System Dynamics Software
STELLA and I think
High Performance Systems, Inc.
best fit for K-12 education
Vensim
Ventana systems, Inc.
Free from downloading off their web site:
Robust--including parametric data fitting and optimization
best fit for higher education
Powersim
What Arthur Andersen is using

33. What is system dynamics
A way to characterize systems as stocks and flows between stocks
Stocks are variables that accumulate the affects of other variables
Rates are variables the control the flows of material into and out of stocks
Auxiliaries are variables the modify information as it is passed from stocks to rates

34. A Simple Methodology Collect info on the problem
List variables on post-it notes
Describe causality using a CLD
Translate CLD into SFD
Enter into VENSIM
Perform sensitivity and validation studies
Perform policy and WHAT IF experiments
Write recommendations

35. Causal Modeling A way to characterize the physics of the system
Lacking: a Newton to describe the causality in these socioeconomic systems

36. A single-sector exponential growth model
Einstein said the most powerful force in the world was compound interest
interest taken in relation to principal
Each stock requires an initial value

37. Let’s DO IT Create the stock principal Include the rate interest
Include the information connector
Initialize the stock
Simulate

38. John vs. Jack Each works for 30 years before retiring
John makes $2000 contributions to his IRA each year for the first five years and none there after.
Jack makes $2000 contributions to his IRA each year beginning in year six and continuing through year 30
Each IRA yields a 15% compounded return
Which turns out to be larger?

39. John vs. Jack--two interest accounts.mdl

42. A single-sector Exponential growth Model
Consider a simple population with infinite resources--food, water, air, etc. Given, mortality information in terms of birth and death rates, what is this population likely to grow to by a certain time?

43. Key Benefits of the ST/SD
A deeper level of learning
Far better than a mere verbal description
A clear structural representation of the problem or process
A way to extract the behavioral implications from the structure and data
A “hands on” tool on which to conduct WHAT IF

44. Senge’s Five Disciplines
Personal Mastery
because we need to be the very best we can be
Mental Models
because these are the basis of all decision-making
Shared Vision
because this galvanizes workers to pursue a common goal
Team Learning
because companies are organized into teams
Systems Thinking
because this is only tool for coping with complexity

45. Relating behaviors to structures
Reinforcing loops create exponential growth
Balancing loops create exponential goal-seeking or decay

46. The VENSIM User Interface
The Time bounds Dialog box

50. Exponentially growing population model
In 1900 there were just 1.65 billion people on the planet. Today, there are more than 6 billion people on the planet. Every year there are .04 births per capita and .028 deaths per capita.
The .04 births per capita shall be referred to as a parameter called BIRTH RATE NORMAL

51. Experiments with growth models
Models with only one rate and one state
Average lifetime death rates
cohorts
Models in which the exiting rate is not a function of its adjacent state
Including effects from other variables
ratios and table functions

52. A single-sector Exponential goal-seeking Model
Sonya Magnova is a television retailer who wishes to maintain a desired inventory of DI television sets so that she doesn’t have to sell her demonstrator and show models. Sonya’s ordering policy is quite simple--adjust actual inventory I toward desired inventory DI so as to force these to conform as closely as possible. The initial inventory is Io. The time required for ordered inventory to be received is AT.

53. The Sector Approach to the Determination of Structure
What is meant by “sector?”
What are the steps
to determination of structure within sectors
to determination of structure between sectors

54. Definition of sector All the structure associated with a single flow
Note that there could be several states associated with a single flow
The pect sector in the pet population model has three states in it

55. Sector Methodology, Overall
Identify flows (sectors) that must be included within the model
Develop the structure within each sector of the model.
Use standard one-sector submodels or develop the structure within the sector from scratch using the steps in Table 15.5
Develop the structure between all sectors that make up the model
Implement the structure in a commercially available simulation package

56. Steps Required to Formulate the Structure for a Sector from Scratch
Specify the quantities required to delineate the structure within each sector
Determine the interactions between the quantities and delineate the resultant causal diagram
Classify the quantity and edge types and delineate the flow diagram

57. A Two-sector Housing/population Model
A resort community in Colorado has determined that population growth in the area depends on the availability of housing as well as the persistent natural attractiveness of the area. Abundant housing attracts people at a greater rate than under normal conditions. The opposite is true when housing is tight. Area Residents also leave the community at a certain rate due primarily to the availability of housing.

58. Two-sector Population/housing Model, Continued
The housing construction industry, on the other hand, fluctuates depending on the land availability and housing desires. Abundant housing cuts back the construction of houses while the opposite is true when the housing situation is tight. Also, as land for residential development fills up (in this mountain valley), the construction rate decreases to the level of the demolition rate of houses.

59. What are the main sectors and how do these interact?
Population
Housing

60. What is the structure within each sector?
Determine state/rate interactions first
Determine necessary supporting infrastructure
PARAMETERS
AUXILIARIES

61. What does the structure within the population sector look like?
RATES: in-migration, out-migration, net death rate
STATES: population
PARAMETERS: in-migration normal, out-migration normal, net death-rate normal

62. What does the structure within the housing sector look like?
RATES: construction rate, demolition rate
STATES: housing
AUXILIARIES: Land availability multiplier, land fraction occupied
PARAMETERS: normal housing construction, average lifetime of housing
PARAMETERS: land occupied by each unit, total residential land

63. What is the structure between sectors?
There are only AUXILIARIES, PARAMETERS, INPUTS and OUTPUTS

64. What are the between-sector auxiliaries?
Housing desired
Housing ratio
Housing construction multiplier
Attractiveness for in-migration multiplier
PARAMETER: Housing units required per person

65. Ratios and Table Functions
Concept of normality
Attenuation
Acceleration or Enhancement

66. Shifting loop Dominance
Rabbit populations grow rapidly with a reproduction fraction of .125 per month
When the population reaches the carrying capacity of the area, the net growth rate falls back to zero, and the population stabilizes
Run for 100 months with time step of 1 month
(This model has two loops, an exponential growth loop (also called a reinforcing loop) and a balancing loop)