lecture 9 james r. burns fall 2010. rate equations– employee sector growth rate = growth norm *...
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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