Review for Final Fall 2010 James R Burns

Review for Final Fall 2010 James R. Burns

Dimensionless Ratios What do we use them for? ? n What impact do they have on dimensional consistency of an equation? n Why do they make sense? n

Dimensionless Ratios n How is the dimensionless ratio used in the natural gas model?

Construct equations for this model

What kind of behavior is this?

Dimensionality Considerations Rigorously, all models must be _______ n What ever units you use for stocks, the associated rates must have those units divided by ______ n Explain what the SYNTHESIM tool does in VENSIM n

What if Dimensionless Ratios Don’t give us the effect we want? n Is there another way to pull in information? n Let’s look at the Forrester World Model

What we see here is the use of table functions—Dimensionless Multipliers n Birth Rate = Birth Rate Normal * Population * Births Material Multiplier * Births Pollution Multiplier * Births Food Multiplier * Births Crowding Multiplier The last four multipliers are dimensionless table functions

Establishing units for unquantified variables n How did Forrester do this in his world model?

More ratios n Food ratio = Food/ Food normal – Again, Food normal is the amount of food available in the year 1970, in Food units n Crowding ratio = Population density normal/Population density – again, Population density normal is the population density in the year 1970, say

Explain this picture

What does it take to create a table lookup function in VENSIM? Do table lookups ever have connectors (arrows) directed toward them? n What point do we generally expect to see on a table lookup function? n Why? n How is the table lookup used in the function it impacts? n

More about table lookups n Table lookups use ______ between data points, by default

Comment about Table Lookups To find the ordinate value corresponding to a particular abscissa value that is given, let b = ordinate desired, a given abscissa. Then b = bi + (a – ai)*(bi+1 – bi) / (ai+1 – ai) Where a has been determined to lie between abscissas ai and ai+1 n

Delays Where do they appear? n Name some delays n n n aging populations, mail delays, perception delays, shipping delays, appearance delays, adjustment delays, scheduling delays and queue delays Name two delay types

Why 3 rd-order exponential delays? n Why 1 st-order exponential delays?

Some Flow Delays that we’ve already looked at

Comment about delays The modeler must ask… How do physical processes in the actual system create lagged behavior? How much disaggregation is necessary to represent the delay accurately

Simulation Time Step n n Should be between. 5 and. 25 of the shortest time constant (delay) in the model Look at all of the time constants – – – n n Adjustment time Perception time Delivery delay time Construction time Lifetime Find smallest Set simulation time step appropriately

Integration Method Euler for models with discrete events n RK 4 for models with oscillation n

Dynamic Test Inputs n Purpose – Reveal inherent behavior – Create extreme conditions n Examples – Pulse – Step – Ramp—one we didn’t look at – Exponential growth – Noise—randomness

Extreme Conditions n Purpose – Reveal weaknesses – Generate insight n Methods – Remove contents of stock with PULSE function – Cut off inflows or outflows – Artificially force variables to 0 or to infinity

Partial Model Testing n Purpose – Divide and Conquer – Develop understanding of subsystems – Test response of subsystems to driving data n Methods – Cut & paste structures into a new model – Use data variables or test inputs to drive behavior

Feedback Elimination n Purpose – Identify feedback loops that are causing behavior n Methods – Sever flow connections – Replace variables with constants or test inputs – Insert 0*… in equations – Flatten lookups

Parameter Sensitivity Analysis n Purpose – Link behavior to feedback loop structure – Identify leverage points – Search for equilibria n Methods – Vary parameters and initial conditions – Stretch and shift lookup table shapes

Types of Sensitivity n Insensitive – Pendulum always comes to rest at bottom n Numerical – Numerical values change, but behavior “looks” the same n Behavior mode – Shift from s-shaped growth to oscillation n Policy – Policy conclusions change

Policy Evaluation n Purpose – Develop effective policies – Identify conditions for effectiveness – Identify weakness in formulation of existing policies n Tools – Sensitivity Analysis – Optimization – Gaming

Integration What does RK 4 assume in terms of step size? n Does RK 4 like small step sizes? n What is the problem with small step sizes? n

Global Warming How much warming is likely over the next century? n What changes in climate patterns, rainfall, growing season, storm incidence and severity, and sea level might ensue? n How much damage would these changes cause to humanity? n

All the models show the climate system to possess enormous inertia The implication here is that if we had shut off all GHG emissions in the year 2000, TEMPERATURES WOULD CONTINUE TO RISE FOR ANOTHER 25 YEARS and then fall very slowly n This was an extreme condition test, of the type we talked about yesterday n

Would you describe the global warming system as…. n STABLE n UNSTABLE

n Warming reduces the winter snow cover and shrinks the highly reflective polar ice caps, thus increasing heat absorption and leading to further melting, less snow cover and still greater absorption. This positive loop will cause much greater warming at the poles than in the tropics and more warming in the winter than summer

This, in turn releases more methane and carbon dioxide into the atmosphere from decayed biomass in the frozen tundra, resulting in still another positive feedback loop ALL THE MODELS AGREE THAT STABILIZING THE GHG EMISSIONS WILL NOT STABILIZE TEMPERATURES OR THE CLIMATE ANYTIME SOON n

Barry Richmond’s Terrorism Model n Name some characteristic archetypes

n In addition to the escalation archetype, what other archetype comes to mind when you consider Barry Richmond’s model of terrorism

Maturity Contrast the concept of Maturity with the Senge concept of learning n Who created the capability maturity model? n What are the five levels of the capability maturity model? n How long does it take to go from one level to the next? n

The Five levels of the CMM 1. 2. 3. 4. 5. INITIAL REPEATABLE DEFINED MANAGED OPTIMIZING

Goldratt’s Thinking process What three questions does it address? n What are the five steps in Goldratt’s TOC? n

THEORY OF CONSTRAINTS: GOLDRATT 1. Identify the system constraints 2. Decide how to exploit the system constraints 3. Subordinate everything else to that decision 4. Elevate the system constraints 5. When this creates new constraints, go back to step 1

What to change? Team constructs a current reality tree (CRT) n Team starts by listing all undesirable effects (UDE’s) n Team inter-relates these by use of a tree, called a CRT n In the current reality tree, the team traces UDE’s back to a core problem (CP) n

Symptoms, Root Causes & a Core Problem Rather than reacting to symptoms, we should be finding root causes n We consider undesirable effects to be symptoms n We look for a “common cause” that is the source for most of the undesirable effects n

Trees and such n Which tree do we use to address the question

How do we read and interpret the following structure? Software Development Projects take too long Fixing changes takes time n There are many latebreaking changes to requirements How are these structures different from CLD’s

Evaporating Cloud [EC] The EC is used to address what question? n How does it work? n What is an injection? n What do we do next? n

The Future Reality Tree How do we construct it? n What is it used for? n

The last question is… n What trees do we use to address this question?

The prerequisite tree n The Transition tree

The Prerequisite Tree Place INJECTIONS at the top n List the obstacles that are expected n For each obstacle that is overcome, an intermediate objective is achieved n – Each obstacle gives rise to an intermediate objective The intermediate objectives need to be sequenced n The prerequisite tree does the sequencing n

OBSTACLE INTERM. OBJECTIVE n No well-defined ES Architecture n Pick an appropriate ES Architecture n There are many commerciallyavailable ES Shells n Select an appropriate ES Shell

The Prerequisite Tree, Cont’d Takes an impediment or obstacle approach n This approach enables dissection of the implementation task into an array of interrelated, well-defined, intermediate objectives n

The Prerequisite Tree Our Example Create Project Management Expert System Test Project Management Expert System A Objective

A Construct Project Management Expert System No well-defined PM Body of Knowledge Codify PM Body of Knowledge into Expert System Shell No well-defined ES Architecture Decide upon Obtain PM Body of Knowledge Select Expert System Shell Expert System Architecture

The Transition Tree We know where we stand n We identified the core problem n We found an injection (one or more) that produces the desired effects n We found the milestones of the journey--the intermediate objectives (IO’s) n The question now is What specific actions must we take? n

The Transition Tree, Cont’d We must focus, not on what we plan to do but on what we plan to accomplish n For each IO, a specific action or set of actions are determined and initiated n Causing a specific change in reality is the imperative n The transition tree provides a ROAD MAP for getting from here to there! n

The Four-Element Transition Tree Expected effect Condition of reality Unfulfilled need Specific action

Expected effect Condition of reality Unfulfilled Unfilled need Unfulfilled need Specific action

Discrete Stochastic Simulation What is meant by MONTE CARLO? ? n How does the computer do that? n

Computer-generated random numbers Are they truly random? n Why do we need them? n

What are the basic building blocks of discrete stochastic simulation? Activities n Events n Entities n Their attributes n

Must also identify Locations—points assoc with the starting and stopping events of an activity n Path network—the network the entity travels n Resources—permanent entities that act on ordinary temporary entities n Processes—the activities n

PROMODEL SELECT BACKGROUND--optional n BUILD-->locations n BUILD-->entities n BUILD-->PATH NETWORK n BUILD-->resources n BUILD-->processes and routing n BUILD-->arrivals n RUN IT n

Locations n Places where an event of importance to the model occurs – Like an arrival – A beginning of customer checkout – An ending of customer checkout

Entities These are the temporary items that pass through the model of the system n Chits n Mail pieces n Piece parts n Students n Cars n People n

Path network n The network that will be followed by the entities and/or the resources

Resources n Mobile permanent entities that can move over a network

Processes A process is required everywhere the entity undergoes an operation n A process is an activity n An exit process is always required n

Routing You must specify how the entities move through the model n Usually you inform PROMODEL what path network to use n

Arrivals n The statistics of the arrival process for each entity type must be communicated to PROMODEL

Now let’s look at PROmodel

n Exercise 1. (15 points) A local convenience store has a self-service island from which it dispenses gasoline. Two lines of cars may form on either side of the island. The island will accommodate no more than two cars being filled with gas on a single side. There is space for no more than three cars in each of the two queues of cars waiting for each of the two service areas.

n Cars arrive at the rate of one every minute with a distribution that is exponential. Service times are normal with a mean of seven minutes and a standard deviation of two minutes. Cars will drive away if more than six cars total are either waiting or in service (regardless of the line they are in). Once cars have entered the store’s gasoline facility, they will en-queue themselves into the shortest queue. Formulate a model in BLOCKS to determine how many cars are turned away in a day. For BRANCH/ TRANSFERS, be sure to indicate the type, such as UNCONDITIONALLY to block 12. Assuming the store is open 24 hours, setup the model to determine how many cars are turned away in one 24 -hour day.

Promodel What do we need to know? ?

What the following are Locations n Entities n Path networks n Resources n Processes n Arrivals n

What has to be specified before resources can be specified n Path networks

In order to get more than one arrival, the freq must be set to n INFINITE

In order to double the capacity of the number of turning machines and machining centers you would n Go to locations and increase the capacity from 1 to two for both of these locations

Failed Arrivals means n Arrivals that could not even get their foot in the door, in this case because the pallet was full

The important measures for this model were… Throughput for the product n Utilization of the resource n Utilization of the locations n Failed arrivals n Amount of blocked time there is n

On the final you may be given a scenario like the ones above and asked to determine Locations n Entities n Path networks—may be asked to draw these n Resources n Processes (ACTIVITIES) n Arrivals n

You will also need to know what events and activities are n How random numbers are generated n How random variates (non-uniform) are generated n What is meant by MONTE CARLO n

That is all n I enjoyed having ya’all in the class