Including Additional Information Using Table Functions in Modeling

1. TODAY: Recitation Lecture Hands-on tutorial

2. Functions to stress the system • Three functions that can be used to “stress” the model of the system • STEP(,) • PULSE(,) • RANDOM UNIFORM(,,)

3. Which of these will produce an input that looks like…

4. Bringing in the Effects of Additional Information Jim Burns

6. REVIEW: Previously we have used dimensionless ratios to do this • Natural gas model • Gas usage / Gas usage normal • Rabbits model • (Carrying capacity – rabbits) / carrying capacity

8. Equations • Fraction of Reserves Remaining = gas reserves remaining / Initial gas reserves • Gas Consumption Rate = Gas consumption per capita per year * population * Fraction of reserves remaining Is this dimensionally consistent??

10. Equations for Rabbits model • Effect of Resources = (Carrying capacity - Rabbits)/Carrying capacity • Net Rabbit Growth rate = Normal Rabbit Growth Rate * Rabbits * Effect of resources

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

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

14. Similarly for Death Rate • Deaths = Death Rate Normal * Population * Deaths Material Multiplier * Deaths Pollution Multiplier * Deaths Food Multiplier * Deaths Crowding Multiplier

15. Here’s another view of the same basic idea

16. Quantifying the Un-quantified

17. How to Include • Customer Satisfaction • Market Attractiveness • Quality of Life • Consumer Confidence • Faculty Morale • Material Standard of Living • IN YOUR MODEL

18. Often these are Un-quantified • Begin by defining what one unit of any of these would be • Consider Quality of Life • In the Forrester World Model, one unit of Quality of Life is the level of life quality enjoyed in the year 1970 • Define this to be a Parameter called Quality of Life Normal • Quality of Life Normal = QLN = 1

19. What sort of things affect Quality of Life on a global scale? • Pollution • Material Standard of Living • Food • Population density

20. For each of these, construct a ratio • Pollution ratio = Pollution normal/Pollution • Here pollution normal is the amount of pollution experienced in the year 1970, in pollution units • MSL ratio = MSL/MSL normal • Here, MSL normal is the amount of MSL experienced in the year 1970, in MSL units

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

22. What about Units? • For some of our soft variables the units are undefined • Meaning no one has defined them • We have to define them • For example, one unit of pollution could be defined as “the average aggregate level of pollution experienced by a “typical” earthling in the year 1970” • One unit of Quality of Life could be “the average aggregate level of quality of life experienced by a ‘typical’ earthling in the year 1970.”

23. Under Normal Conditions, • What is true about all of these ratios? • What is the dimensionality of these ratios? Under “Normal Conditions” the ratio assumes a value of “1” The ratios are always dimensionless

24. We can now construct our Quality of Life Formula • Quality of Life = QLN * Pollution ratio * MSL ratio * Food ratio * Crowding ratio • Is this formula dimensionally consistent? • Under normal conditions, Quality of Life = ?? • If pollution gets higher than normal, what happens to quality of life, assuming everything else remains the same? • If food is higher than normal, what happens to quality of life, assuming everything else is the same?

25. The VENSIM Representation

26. What if we felt that Material Standard of Living affected birth and death rates? • BR = BRN * POPULATION *MSL ratio • MSL ratio = MSL / MSL Normal • Does this change the dimensionality of the BR formula? • Under “normal” conditions what effect does Material Standard of Living have on BR, birth rate? • Similarly for death rate

27. We could do something similar for food • BR = BRN * POPULATION * MSL ratio * Food ratio

28. Suppose that we believe that the effect of an increase in food is less than the ratio would suggest • We can amplify or attenuate the effect of a rise above normal conditions with the use of TABLE FUNCTIONS • We call these multipliers • They are also dimensionless

30. The new formula is: • Quality of Life = QLN * Pollution multiplier * MSL multiplier * Food multiplier * Crowding multiplier • It must be accompanied by the following equations • Pollution multiplier = TABLE(pollution ratio) • MSL multiplier = TABLE(MSL ratio) • Food multiplier = TABLE(Food ratio) • Crowding multiplier = TABLE(Crowding ratio)

31. In VENSIM these are written • Pollution multiplier = pollution multiplier tab(pollution ratio) • MSL multiplier = MSL multiplier tab(MSL ratio) • Food multiplier = food multiplier tab(Food ratio) • Crowding multiplier = crowding multiplier tab(Crowding ratio)

32. Here, the tables are defined as …. • pollution multiplier tab • MSL multiplier tab • food multiplier tab • crowding multiplier tab • Are treated as ‘constants’ and defined using the AS GRAPH capability

41. Some Forrester ‘tricks’ • Almost all of Forrester’s tables contain the point (1,1) on them. • What does this mean? • Under normal conditions, the ratio is 1 • Under normal conditions, the impact of the multiplier is ‘nil’ • That is to say, the multiplier neither enhances or attenuates the rate it affects. • So it has no effect.

42. Look at the Births (Birth Rate) Equation • Births = Population • * IF THEN ELSE ( Time • > switch time 1 , • birth rate normal 1 , • birth rate normal ) • * births material multiplier • * births crowding multiplier • * births food multiplier • * births pollution multiplier

43. Look at the Births (Birth Rate) Equation • Births = Population • * birth rate normal • * births material multiplier • * births crowding multiplier • * births food multiplier • * births pollution multiplier

45. Let’s look at the World Model and try this!!