Lecture 9

James R. BurnsFall 2010

Rate Equations– EMPLOYEE SECTOR growth rate = growth norm * Junior

professionals Mature rate = Junior

professionals/mature time Grow rate = growth norm * Senior

professionals Retire rate = Senior professionals / work

time Death rate = retired / ret life

Rate Equations– APARTMENT SECTOR Apt const rate = (Apts desired –

Apartments)/const time Apt obs rate = Apartments /

lifetime

Rate Equations—HOMES SECTOR Home const rate = (Homes desired

– Homes) / const time Home obs rate = Homes / lifetime

Rate Equations—RETIREMENT SECTOR Ret const rate = (Retire units

desired – Retire units) / const time Ret obs rate = Retire units /

lifetime

Auxiliary equations Apts desired = Apts required *

Junior professionals Homes desired = Homes reqd *

Senior professionals Retire units desired = Ret reqd *

Retired

To do this right… You had to recognize sectors

Sector—all the structure associated with a single flow

Apartments cannot flow into homes Homes cannot flow into retirement units

You had to recognize the exponential smoothing structure A desired condition An actual condition

What about the stock equations?

Natural Gas problem

x1:population

x2: gasreserves

remaining

r1: Birth rate r2: Death rate

r3: gasconsumption rate

p1: Birth rate percapita per year

p2: Death rate percapita per year

v1: Fraction ofreserves remaining

p4: Initial gasreserves

p3: Gas consumptionper capita per year

Equations Birth rate = population * Birth rate

norm Death rate = population * Death

rate norm Gas usage rate = gas usage

normal * population * gas reserves remaining / initial gas reserves

Dimensionless ratios Doesn’t change the dimensionality

of the equation, but does allow for effects to be entered

Another dimensionless ratio

Rabbit populations grow rapidly with a reproduction fraction of .125 per month

When the population reaches the carrying capacity of 1000, the net growth rate falls back to zero, and the population stabilizes

Starting with two rabbits, run for 100 months with a time step of 1 month

(This model has two loops, an exponential growth loop (also called a reinforcing loop) and a balancing loop)

Shifting loop Dominance

Assumes the following relation for Effect of Resources

Effect of Resources = (carrying capacity - Rabbits)/carrying capacity

This is a multiplier Multipliers are always dimless

(dimensionless) When rabbits are near zero, this is near 1 When rabbits are near carrying capacity, this

is near zero This will shut down the net rabbit birth rate

RabbitsNet Rabbit Birth rate

Effect of resourcesCarrying capacity

Normal Rabbit Growth Rate

B

R

Rabbits

1,00040

00

0 20 40 60 80 100Time (Month)

Rabbits : rab1Net Rabbit Birth rate : rab1

Dimensionality Considerations VENSIM will check for dimensional

consistency if you enter dimensions Rigorously, all models must be

dimensionally consistent What ever units you use for stocks,

the associated rates must have those units divided by TIME

As we have seen before

VENSIM—the view MENU ITEM

VENSIM New Open Save Print Cut Copy Paste

Set {define dataset

name} Run Synthesim Run Reality check Build windows Build output windows Control Panel

Control Panel Variables Time axis Scaling Datasets Graphs

The new leadership involves… Managing the COMMONS DESIGN Purpose Story Articulate….

the goal, the standard, the vision The ground-truth reality Use the gap to produce CREATIVE

TENSION

What must leaders design?

Policies, strategies, “systems,” organizations, specifically

Selection policies Vision strategies Value systems Culture systems Measurement systems Rewards systems Criteria by which excellence will be

determined

Gives rise to a new discipline: Business Design

Must loose focus on the P&L statement Look at the long term, instead Have to get away from piecemeal

reactions to problems Have to integrate the five component

technologies Must integrate vision, values, purpose,

systems thinking, and mental models The synergy of the disciplines can propel

an organization to major breakthroughs

First tasks of Business Design

Design the governing ideas--purpose, vision, and core values

Building shared vision is important because it fosters a longer-term orientation and an imperative for learning

Get the systems thinking going early on Get the concept of mental models and

surfacing underlying assumptions going early as well

Subsequent tasks of Business Design Design the learning processes Get personal mastery going

The Leader as Steward Leaders have a purpose story

This is an overarching explanation of why they do what they do

how their organizations need to evolve how that evolution is part of

something larger Most gifted leaders have a “larger

story”

The Leader as Teacher First job of leader is to define

reality Leader must help people achieve

more accurate, more insightful and more empowering views of reality

Must view reality at four levels: events, patterns, structures and ultimately a “purpose story”

Junior professionals

Senior professionals Retiredgrowth rate mature rate retire rate

grow rategrowth norm

Apts desired Homes desired Retire units desired

Apartments Homes Retire units

Apt const rateHome const rate Ret const rate

Apt obs rate Home obs rate Ret obs rate

Apts required Homes reqd Ret reqd

lifetime

const time

death rate

ret life

mature time work time