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

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”

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

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

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

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

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

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

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

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

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

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

Stock and Flow Notation--Quantities RATE Auxiliary

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

Inputs and Outputs Inputs Parameters Lookups Outputs

Stock and Flow Notation--edges Information Flow

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

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

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

Rates and their edges

Parameters and their edges

Stocks and their edges

Auxiliaries and their edges

Outputs and their edges

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

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

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

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

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

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: www.vensim.com Robust--including parametric data fitting and optimization best fit for higher education Powersim What Arthur Andersen is using

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

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

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

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

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

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?

John vs. Jack--two interest accounts.mdl

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?

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

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

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

The VENSIM User Interface The Time bounds Dialog box

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

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

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.

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

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

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

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

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.

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.

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

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

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

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

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

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

Ratios and Table Functions Concept of normality Attenuation Acceleration or Enhancement

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)