Chapters 17 and 18
Business Dynamics by John D. Sterman
Supply Chains and the Origin of
Oscillations
4/13/2015
Chapters 17 and 18 in Sterman
1
Chapter outline



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What is a supply chain?
Supply Chains in Business and Beyond
The Stock Management Problem
The Stock Management Structure
Origin of Oscillations
Summary
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Homework:

Work the challenge questions on pages
674 and 675—questions 1 through 7
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3
§ What is a supply chain?

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
A supply chain (SC) is the set of structures
and processes an organization uses to deliver
an output to a customer
tangible or intangible product
Typically, supply chains consist of


Stock and flow structures for the acquisition of the
inputs to the processes, and
Management policies governing the various flows
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4
Why study SC Dynamics?


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SCs often exhibit persistent and costly
instability
Many business and social systems are
notorious for producing counter intuitive
behavior (Forrester, Sterman)
Understanding the behavior of SCs
under important contexts is imperative
for better management (Recall–Mental
Models’ limitations- first week’s lesson)
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The bane of Supply Chains—
Uncertainty

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Uncertainty in the forecast
Uncertainty in procurement details

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lead time
Procurement amount
Procurement product quality
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How to deal with the Uncertainty—
buffer it with INVENTORY or reduce
it with IT


What is IT?
But this totally changes the dynamics of
the SC System
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Without VISIBILITY…

Supply chains exhibit a behavior called
simply the hockey-stick phenomenon
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Approach-some premises

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
Stock management structure is used to
explain origin of oscillation
Preconditions for oscillation arenegative feedbacks and time delays
present in the system (recall-desired
inventory model)
Delays are simple enough to notice, yet
are often omitted in decision making
(experimental evidence supports)
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§ SCs in Business and Beyond



SCs extend beyond the boundaries of a firm
(organization) and include the suppliers,
distribution channels, and the customers (Recalldefinition of a SC)
SD models need to include these players as well,
to the extent the flows and rules within the firm
cause feedback from these players giving rise to
further dynamics in behavior of stocks
SCs are not limited to business--consider human
body- supply of glucose for energy-consumptionfood ingestion-digestion-storage-consumption
etc forms one big supply chain
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SC-what to expect?
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SC-to provide right output at right time
As requirements change, adjustments in flow
rates are initiated-and the negative feedback
loop is at work! Production and inventories
chronically overshoot and undershoot (17.1)
Due to time delays-SCs are prone to oscillate
Amplitude of fluctuations increases as they
propagate from customer to supplier- each
upstream stage lags behind its customer
Oscillation, amplification, and phase lag are
pervasive in SCs
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SC Dynamics Understanding
Process


Understand the internal dynamics and
structure within the firm
Understand the dynamics and structure
outside the firm
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§ Stock Management Problem

Consider a single firm structure

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Desired versus actual state-of stock
Typically, outflow rate is independent
Managers need to regulate inflow to keep
the stock level close to desired level
We all deal with such feedback loopsadjust temperature in shower, manage
checking account balance, credit card
account balance, etc
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The problem


Two parts: Structure and Rules
If there is no delay in acquisition (instantaneous
replenishments) current loss rate
customer orders
Stock
acquisition rate (AR)

loss rate (LR)
Stock to be controlled S is the accumulation of AR and LR
S=INTEGRAL(AR-LR, Sto)
(17-1 pp 668)
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We have studied this structure
before…
Stock Adjustment
Time
Stock S
Acquisition Rate
Desired Stock
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This is just a Balancing Loop…
Acquisition Rate
AR
-
Stock S
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Chapters 17 and 18 in Sterman
16
It gave us Balancing Loop
behavior that looked like this…
Stock S
1,000
750
500
250
0
0
10
20
30
40
50
60
Time (Month)
70
80
90
100
Stock S : stock 1

Called Exponential Goal-Seeking
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We can re-arrange this model ….

Without changing behavior…
Stock S
Acquisition Rate
AR
Adjustment for
Stock AS
Desired Stock S*
Stock Adjustment
Time SAT

Here, AS = (S* - S) / SAT and AR = AS
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18
We still get the same exact
behavior…
Stock S
1,000
750
500
250
0
0
10
Stock
S : stock2
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20
30
40
50
60
Time (Month)
70
Chapters 17 and 18 in Sterman
80
90
100
19
Now, we add a Loss Rate

Akin to a Sales Rate, a Depreciation
Rate or whatever…
Variables XU
Stock S
Acquisition Rate
AR
Loss Rate
Adjustment for
Stock AS
Stock Adjustment
Time SAT
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Desired Stock S*
Chapters 17 and 18 in Sterman
20
Now we see the problem….
Stock S
1,000
750
500
250
0
0
10
Stock S : stock3
Stock S : stock2
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20
30
40
50
60
Time (Month)
70
80
Chapters 17 and 18 in Sterman
90
100
21
Let examine the Acquisition
Rate…
Acquisition Rate AR
200
150
100
50
0
0
10
20
30
Acquisition Rate AR : stock3
Acquisition Rate AR : stock2
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40
50
60
Time (Month)
70
Chapters 17 and 18 in Sterman
80
90
100
22
How does the Acquisition Rate
look in relation to the Loss Rate?
200
150
100
50
0
0
10
20
30
Acquisition Rate AR : stock3
Loss
Rate : stock3
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40
50
60
Time (Month)
70
Chapters 17 and 18 in Sterman
80
90
100
23
The problem is Stock S….


Will never reach the Desired Stock S*,
but will always differ from it by a
significant amount—600 units in this
case
Notice that, in steady state, the
Acquisition Rate settles down to the
Loss Rate
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Loss Rate - LR

Loss Rate -outflow rate- may arise from
usage (material or wip) or decay
(depreciation) and must depend on
stock itself (also to prevent negative
draining)


LR may depend on exogenous variables X
LR may depend on endogenous variables U
LR = ƒ (S, X, U)
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…
(17-2 pp 668)
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The Loss Rate…

LR = IF THEN ELSE( Stock S > 0 ,
Variables XU , 0 )
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How can we fix the problem
we just observed….


Namely, that the Stock S will always
differ from the Desired Stock S* by the
amount of the Loss Rate LR????
This will make inventory managers very
unhappy because they cannot achieve
their targeted service levels—many
customers will arrive to buy but no
stock will be available
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A way to fix the problem



Create a new variable called the DAR—
Desired Acquisition Rate…
DAR = Adjustment for Stock + Loss
Rate
DAR = AS + LR
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Here DAR = AS + LR
Variables XU
Acquisition Rate
AR
Stock S
Loss Rate
Desired Acquisition
Rate DAR
Adjustment for
Stock AS
Desired Stock S*
Stock Adjustment
Time SAT
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A better way…
Variables XU
Stock S
Acquisition Rate
AR
Loss Rate
Desired Acquisition
Rate DAR
Adjustment for
Stock AS
Stock Adjustment
Time SAT
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Desired Stock S*
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We can always…

Reconstruct the information created in
a rate elsewhere without having to take
information directly from a rate, as
Sterman does here
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Now let’s look at Behavior…
Stock S
1,000
750
500
250
0
0
10
Stock S : stock4
Stock S : stock3
Stock S : stock2
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20
30
40
50
60
Time (Month)
70
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80
90
100
32
Acquisition Rate - AR

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
Typically production requires use of
resources, hiring requires efforts-or time
delays
If no such delays- refer to model (pp 669)
AR=MAX(0, DAR)
(17-3 pp 668)


Max function coupled with 0 ensures positive or
zero AR-prevents negative AR
If excess units are returnable, that needs to be
modeled separately and not by negative AR
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If Desired stock changes




Adjustment for stock AS needs to change
Consider example STOCKMGT.MDL from chapter
17 or 17-4 on pp 669
Desired acquisition rate formulation can depend
on several factors- this needs to be modeled
based on information available to managerstypically managers use heuristic rules (falls
under ‘Bounded Rationality’ domain)
DAR=EL+AS
(17-4 pp 670)


EL=expected loss (= LR here)
AS=Desired-actual/time delay (=0 here)
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EL and AS formulations

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

Actual Loss is difficult to measure-prone to
change-hence EL-avg
In certain situations LR may not be directly
observable or measurable-must be estimatedintroducing measurement, reporting and
perception delays- think about trend in sales
Creates a negative Stock control feedback loopsimplest form-linear
AS = (S* - S)/SAT
(17-5 pp 671)


SAT= Stock adjustment time
S* =desired stock level-(could be a CONSTANT or
variable)
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§ Steady State Error

Omission of EL in DAR leads to Steady
State error- stock differs with desired
value even in equilibrium
Production=(DI-I)/IAT …(17-6 pp671)
 Equilibrium condition: Production=shipments
 Production=(DI-I)/IAT=shipments… (17-7)
 I=DI-Shipments*IAT
… (17-8)
When in equilibrium the Inventory will be lower
than Desired Inventory

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Fix for Steady State Error

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Including the EL in the production decision will
fix this steady state error
Production=AvgOR+(DI-I)/IAT…(17-6a)
Equilibrium: Avg Orders= Actual Orders, I=DI,
and Orders=Shipments
Avg OR- to smooth out sharp spikes- and avoid
costly changes in production
Evidence suggests that managers do include EL
in production decisions
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Managing a Stock: Behavior

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
Consider example-Plant & Equipment
Avg life time = 8 yrs
Delays in reporting negligible EL=AL
Adjustment time = 3 yrs (Senge, 1978)
Desired Capital stock=exogenous; it depends on
demand for firm’s products
Net Change in Capital Stock= (S*-S)/SAT (17-9)the first order linear negative feedback system
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System response to a change

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Step (1, .20) produces changes in AR
Amplification in AR-for a mere 20% increase in
desired stock 19.2/12.5%= 53% at peak
Amplification - temporary- disequilibrium stage
If stock is to increase then AR>LR
Since AR=receipts from suppliers- a 20%
increase in the operations impacts supplier
more than the firm (although temporarily)
Try at least 3 tests suggested on page 674 (#4
in particular)
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BOT Chart of Stock
140
2
120
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1 2
1
1
100
12
1 2
1
80
0
1
2
3
4
5
6
Time (Year)
7
8
1
1
Stock S : bdscm2
"Desired Stock S*" : bdscm2
1
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2
1
2
1
2
1
2
1
2
1
2
9
1
2
10
1
2
2
Units
Units
40
BOT Chart of rates
20
1
1
1
1
16.66
13.33
2
2
12
2
1
1
1
2
2
2
2
1
1
2
1
1
2
1
2
2
2
1
2
12
10
0
1
2
3
Acquisition Rate AR : bdscm2
2
Loss Rate LR : bdscm2
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4
1
5
6
Time (Year)
1
2
1
2
1
2
7
1
2
8
1
2
1
2
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1
2
2
10
Units/Year
Units/Year
41
§ The Stock Mgmt Structure

Delay between order and acquisition

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
Capital stock—construction starts/delivery time
Workforce--hiring /training time
Supply Line introduced-refer model (pp 676)


SL=INTEGRAL(OR-AR, SLt )…(17-10 pp 675)
AR=L(SL, AL)
…(17-11 pp 675)
o


AL =ƒ(SL, X, U)


Most likely AR=SL/AL
…(17-12 pp 675)
L() denotes the material delay
Typically average acquisition lag is relatively constant
until requisition rate exceeds capacity
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The Stock Mgmt Structure…






Typically, OR=Max(0,IO)
…(17-13)
Cancellations of orders need to be modeled as
distinct outflows from SL
IO=DAR+ASL
… (17-14)
ASL=(SL*-SL)/SLAT similar to AS ..(17-15)
SL*=EAL * DAR
…(17-16)
Managers use SL*=EAL*EL
…(17-16a)


not sophisticated- instead use avg loss rate
Revised DAR=MAX(0,EL+AS)

To ensure a non negative DAR
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Chapters 17 and 18 in Sterman
…(174a)
43
Oscillations—how do we get
them??



Oscillations require delays, which
involve additional stocks (states)
Negative Feedback systems without
delays will not oscillate
Delays between corrective actions and
their effects create a supply line of
corrections that have been initiated but
not yet had their impact
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More on oscillations


To oscillate the time delay must be at
least partially ignored
Managers must continue to initiate
corrective actions in response to the
perceived gap between the desired and
actual state of the system, even after
sufficient corrections to close the gap
are in the pipeline
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The Beer Distribution Game


Originally developed by Forrester in the
1950’s
Consists of a supply chain of four entities





Retailer
Wholesaler
Distributor
Factory
Each entity has the same exact structure
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The Beer Distribution Game





One person assumes the role of each entity
At each stage there are order processing and
shipping delays
Each player’s objective is to minimize holding
costs and stockout costs
Holding costs run $.50 per case per week
Stockout costs run $1.00 per case per week
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The Beer Distribution Game



Incoming orders deplete inventory
Players must try to maintain a ‘desired’
inventory
Pattern for customer demand is:

Starting from equuilibrium, there is a small
unannounced one-time increase in
customer orders from 4 to 8 cases per
week.
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Beer Distribution Game
Behavior




Most players develop a backlog—
meaning negative actual inventory
Eventually inventories throughout the
supply chain start to rise
But then all entities inventories
overshoot
See page 687
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49
Beer Distribution Game
Behavior


Most players ignore the delays and
order the difference between their
desired inventory and their actual
inventory
This creates a huge overshoot in actual
inventory when it all arrives
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Why Do We Ignore the Supply
line—the Delays??

Examples of situations where we ignore
delays appear on page 695
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Boom and Bust in real Estate
Markets



Real Estate markets exhibit large amplitude
cycles of 10 to 20 years
Booms are often accompanied by periods of
intense speculation involving expansion of
credit and banking activity
When the bubble bursts, the resulting bad
loans, defaults, and unemployment can throw
an entire region into recession or even
depression
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Recent Real Estate Boom/Bust
Cycles


North American and European Property
markets boomed in the 1980’s, but then
crashed in the early 1990’s
Similar behavior was observed in Japan
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How does the cycle begin?







See Figure 17-15—another adaptation of the stock
management structure
Interest and mortgage rates go down to stimulate
the economy
Employment goes up
Vacancy rates go down as employment goes up
Rents go up as do market values
Developers see an opportunity and initiate
construction
This causes construction starts to increase and go
higher
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What happens next?




High profits attract new developers and
investors
Many new projects are started, swelling the
supply line of buildings under development
After a long delay—2 to 5 years—the supply
of buildings rises, rents start to fall, as
vacancy rates go up, dragging down market
values
Meanwhile there is still a huge supply of new
construction starts underway
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What should developers do?


They should assess the profitability of a
potential new development and forecast
the future vacancy rate by projecting
the growth of demand and supply
In other words they should develop a
structure like that in figure 17-15 and
take the feedback structure of the
market into account
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What else?



Developers and bankers should consider the
supply line of buildings under development
taken in relation to the growth of demand
Banks, in particular, should assume a leading
role
This means using SD models to assess
demand taken in relation to supply. And
giving specific attention to the pipeline and
construction delays
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What else?


Regulatory agencies should establish a
regulatory environment that forces
banks to behave in a more fiscally
responsible way.
The HERD instinct is wrong and should
be avoided at all costs
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Average
Life
-
Stock S
+
Acquisition
Rate AR
Loss Rate
LR
+
B
Stock Control
Adjustment
for Stock
AS
Desired
Acquisition
Rate DAR
+
+
-
+
Desired
Stock S*
Stock
Adjustment
Time SAT
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Expected
Loss Rate
+
EL
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Basic Stock Management
Structure
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Variables U
Endogenous
Variables X
Acquisition
Lag AL
-
+
Supply Line
SL
Order Rate
OR
Stock S
Acquisition
Rate AR
Loss Rate
LR
+
+
+
B
B
Supply Line
Control
Stock Control
Expected
Acquisition
Lag EAL
<Initial
Desired
Stock>
-
Indicated
Orders IO
+
+
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Adjustment
for Supply
Line ASL
+
-
Supply Line
Adjustment
Time SLAT
Desired
Stock S*
+
Desired
Supply Line
SL*
Adjustment
for Stock
AS
+
-
<Input>
+
Stock
Adjustment
Time SAT
+
Desired
Acquisition
Rate DAR
+
+
Chapters 17 and 18 in Sterman
Expected
Loss Rate
EL
61
Stock Management Structure
Applied to Capital Investment
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Acquisition Lag
AL
Supply Line SL
Order Rate OR
Average
Lifetime L
Stock S
Loss Rate
Acquisition Rate
AR
Expected Acquisition
Lag EAL
Adjustment for
Supply Line ASL
Indicated
Orders IO
Desired Supply
Line SL*
Desired Stock S*
Adjustment for
Stock AS
Supply Line Adjustment
time SLAT
Stock Adjustment
Time SAT
Desired Acquisition
Rate DAR
Expected Loss
Rate EL
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+
+
Productivity
Inventory
Shipment +
Rate
Production
Rate
-
+
Manufacturing
Cycle Time
+
Adjustment +
for WIP
-
Workweek
B
+
Over/Under
Time
Effect of
Schedule
Pressure on
Workweek
<Labor>
Table for Effect of
Schedule
Pressure on
Workweek
Standard
Workweek
+
Desired WIP
WIP
Adjustment
Time
+
-
+
B
B
Inventory
Control
Order
Fulfillment
Inventory
Adjustment
Time
-
+
Maximum
Shipment
Rate
Production
Adjustment +
from Inventory
Order
Fulfillment
Ratio
+
Desired
Shipment
Rate
+
-
+
Table for
Order
Fulfillment
Minimum
Order
Processing
Time
+
Desired
+
Inventory
+
+
Customer
Order Rate
Safety
Stock
Coverage
Desired
Inventory
Coverage
+
Desired +
Production
Expected
Order Rate
+
Change in
Exp Orders
+
-
Time to Average
Order Rate
Standard
Production
+ Start Rate
+
+
<Expected
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Productivity>
+
+
Desired
Production
Start Rate
Schedule
Pressure
-
+
Work in
Process
Inventory
Production
Start Rate
Inventory
Coverage
Chapters 17 and 18 in Sterman
67