Development of System Dynamics Models using Hierarchical Decomposition

Karim Chichakly

Background • Functional decomposition of models (1993) • Hierarchical modules (2005) – – – – –

Many systems naturally hierarchical Easier to understand, build, debug Multiple modelers Re-use Version control

• Khalid Saeed (2005): Extend modeling process hierarchically 2

Modeling process • • • • • •

Draw reference mode Develop dynamic hypothesis Build model Verify model, especially against reference mode Analyze model Perform policy experiments

3

Hierarchy with Modules Housing Demand Demand f or Houses

Housing Supply

Module Module output

Demand

Module input (placeholder) Module input (assigned)

Housing Demand.Demand for Houses

4

Simple Limits to Growth births Population.being born 1: Population 1: 2:

2: Natural Resources

100 100

2

+

2

+

2

1: 2:

(R)

(R)

1

Population

Population

60 65 1

+

+ 1

1 1: 2:

6.25

12.50 Y ears Ref erence Mode

18.75

-

-

2

20 30 0.00

Page 1

(B)

(B) 25.00

Natural Resources

Natural Resources

5

Underlying Models Population

being born

dying death rate

birth rate

resources\ person

resources consumed per person Natural Resources.Natural Resources

Natural Resources regenerating

consuming

regeneration rate Population.Population

6

Hierarchical modeling process • Draw high-level aggregated reference mode (RM) • Develop high-level aggregated dynamic hypothesis • For each module in this dynamic hypothesis (DH): – Draw reference mode – Develop dynamic hypothesis – Repeat this step for this DH if going down another level Or for each module in this DH: • Build and test stock-flow submodel • Combine submodels (at this level) and verify the reference mode • Analyze module behavior

• Combine modules and verify aggregate RM • Analyze model; Perform policy experiments 7

Dynamic hypotheses at many levels

8

Sahel High level: 1: Populations 1: 2:

2: Natural Resources

100 100

2

2

-

1 2

1: 2:

Natural Resources

(B)

Populations 60 65 1

+

1

1 1: 2:

2

20 30 0.00

6.25

12.50 Y ears

Page 1

18.75

25.00

Top-lev el Ref erence Mode

Populations: 1: Humans 1: 2:

2: Cattle

100

+ 2 1: 2:

(R)

Humans

60 1 2

Cattle

+

1 2 1: 2:

20

1 0.00

Page 1

2

1 6.25

12.50 Y ears

18.75

25.00

Populations Ref erence Mode

9

Explore Sahel Model

10

US Health Care System 1: Population 1: 2: 3:

2: Health Care Utilization

3: Technology

324 132 82

3 1: 2: 3:

312 116 66

2 1 3 1

1: 2: 3: Page 1

300 100 50

1 0.00

2

3

1 12.50

2

2

3 25.00 Y ears

37.50

50.00

Ref erence Mode

11

Health Care Dynamic Hypothesis Population

(R1)

IP

OP

ER

Physicians

(R2)

Technology

12

Physicians 1: Phy sician Visits 1: 2: 3:

2: Phy sician Capacity

70 56 50

3: Phy sician Pricing 3

3

(utilization)

3

2

2

2 1 1 1: 2: 3:

50 50 48

3

-

+ Physician Pricing

1 0.00

Page 1

Physician Visits

(B)

60 53 49

2

1: 2: 3:

+

Physician Capacity

1

12.50

25.00 Y ears

37.50

50.00

Phy sicians Ref erence Mode

13

Inpatient Care

(LOS-related complications)

(B3) + +

(B1)

LOS

IP Capacity

-

+

(B2)

IP Visits

-

(utilization)

14

Technology technology growth effect

Pharma.cumulative drug market growth

Pharma

OMT.cumulative tech market growth

OMT

15

Explore Health Care Model

16

Urban Dynamics without Modules Cannot be represented on one page

17

Urban Dynamics with Modules – One Level A very naïve approach… workf orce

jobs

businesses

premium housing condition

labor mobility

new enterprise growth

attractiv eness f or underemploy ed

perceptions

housing

underemploy ed mobility

attractiv eness f or managers

attractiv eness f or labor

f inance

policies

worker housing condition

18

Urban Dynamics with Modules – Multiple Levels Finally getting somewhere… workforce

(R1)

(R2) (R4) (R3)

jobs

housing

-

(B5) (B1)

(B4)

(B3)

(B2)

business

land used

19

Workforce underemployed mobility

labor mobility population

manager attractiveness

underemployed attractiveness labor attractiveness

20

Housing

houses

premium housing condition

worker housing condition

21

Business

businesses

new enterprise growth

22

Explore Urban Dynamics

23

Summary • Hierarchical modeling process effectively decomposes large problems – Natural extension to standard process – Reference modes and dynamic hypotheses at each level increase confidence in model – Shifts focus to details important at each level

• Caveats: – First-order loops do not appear at module level – Behavior at higher levels may not correspond exactly to their reference modes (variable correspondence) – Decomposition may assist structural disaggregration, rather than behavioral 24

Hierarchical Decomposition.pdf

Page 2 of 24. 2. Background. • Functional decomposition of models (1993). • Hierarchical modules (2005). – Many systems naturally hierarchical. – Easier to ...

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