delays james r. burns fall 2010. 11/16/20152 today recitation lecture hands-on
TRANSCRIPT
Delays
James R. Burns
Fall 2010
04/21/23 2
Today
• Recitation
• Lecture
• Hands-on
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Recitation
• What does it take to create a table lookup function in VENSIM
• The HW problem
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White-collarpopulation
Blue-collarpopulation
White In-migration
WhiteOut-migration
Blue In-migration
Blue Out-migration
White to Blue rate
Blue-to-white rate
In-migrationnormal
Out-migrationnormal
WTB Norm
BTW Norm
White hsng req Blue hsng req
White hsng desired Blue hsng desired
White collarhousing
Blue collarhousing
Construction rate WTB Transfer rate Obsolescence rate
White hsng lifetime Blue hsng lifetimeConstruction time
White housingratio
Blue housing ratio
<White housingratio>
<Blue housingratio>
Obsoletehousing
White Jobs req
Blue Jobs req
White jobs desired
Blue jobs desires
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Delays
• Delays always breed danger – Miguel de Cervantes (Don Quixote)
• Never do today what you can put off till tomorrow. Delay may give clearer light as to what is best to be done.
– Arron Burr
• What does Peter Senge tell us about Delays in the book THE FIFTH DISCILPLINE?
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Where can delays occur?
• In information channels• (In the transmission of information)
• In flows• (of people, resources, goods, money etc.)
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Specific instances in which Delays can occur…
• aging populations, mail delays, perception delays, shipping delays, appearance delays, adjustment delays, scheduling delays and queue delays.
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Flow Delays
• Pipeline (Boxcar)
• Exponential• Third order
• First order
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Some Flow Delays that
we’ve already
looked at
Pop 0-15
Pop 16-45
Pop 46-60
Pop 61-75
Unprovenreserves
Provenreserves
Crude oil
Refined oilproducts
birth rate
r 15to16
r46to46
r60to61
death rate
discovery rate
extraction rate
refinery rate
consumptioin rate
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Cascaded Coflow -- "Hines"
Hines 1996characteristicof new stuff
Avgcharacteristicnew material
Change incharacteristic
of new material
dilution time ofnew Material
New materialMaterialmaturing
Time tomature
Materialflowing in
Maturematerial
Old material
Materialaging
Materialflowing out
Time to age Time to flowout
Avgcharacteristic ofMature material
Change incharacteristic ofmature material
Maturematerial
dilution time
Avg Characteristicof Old Material
Change incharacteristicof old material
Old MaterialDilution Time
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MaterialMaterialflowing
out
Time to flowout
Material Delay
Materialflowing in
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Information Delays
• First order
• Smoothing
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Recall the balancing loop structure
inventory
Orders
Adjustment TimeDesired Inventory
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Boxcar Delay
actualinventory
day 4pipeline
inventory
day 3pipeline
inventory
day 2pipeline
inventory
day 1pipeline
inventory
order ratedesired inventory adjustment time
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Problems with Boxcar Delay
• Pipeline or boxcar delays are considered “pure” in the sense that no output is produced until the delay is over, or until the elapsed time is greater than the delay. Moreover, the output tends to be somewhat discontinuous, causing the model state (or, stock) trajectories to lack smoothness.
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Exponential Delay
actualinventory
day 4inventory
day 3inventory
day 2inventory
day 1inventory
order rate
r1to2
r2to3
r3to4
r4to5
desired inventory adjustment time
delay length
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• As previously mentioned, the boxcar approach tends to introduce discontinuities into the simulation model. To overcome this problem Forrester replaced the boxcars with levels or states separated by rates whose associated equations were determined to be
• ri = n * xi / D,• where n is the order of the delay in terms of states
and D is the length (in the time units of the simulation) of the delay.
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Third-Order Exponential Delay
First orderstock
Secondorder stock
Third orderstock
ActualInventory
Order rateDesired inventory
Adjustment time
r1
r2
r3
delay length/3Inventory on hand
and in pipeline
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Information Delay
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Delay functions in VENSIM
• DELAY3(input, delay time) – a third-order exponential delay• Input should be a rate
• Output is returned through the name—DELAY3
• Output will also be a rate—a delayed one
• Delay time must have consistent units with the VENSIM time variable
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The structure of the DELAY3() function
• DL = delay time/3
• LV1 = INTEGRAL(input-RT1, DL)
• RT1 = LV1/DL
• LV2 = INTEGRAL(RT1 – RT2, DL)
• RT2 = LV2/DL
• LV3 = INTEGRAL(RT2 – DELAY3, DL)
• DELAY3 = LV3/DL
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Delay functions in VENSIM
• DELAY3I(input, delay time, initial value)• Same as DELAY3() except each stock is
loaded with an initial value of initial value/3• DELAY1(input, delay time) – a first-order
exponential delay• DELAY1I(input, delay time, initial value) –
a first-order exponential delay with initial value)
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More delay functions
• DELAY INFORMATION (input, delay time, initial value) – discrete information delay
• DELAY MATERIAL (input, delay time, initial value, missval) – discrete material or flow delay
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Supply Chain 1
actualinventory
desired inventory adjustment time
order/ship rate
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Supply Chain 2
actualinventory
desired inventory adjustment time
order/ship rate
informationdelay
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Supply Chain 3actual
inventory
desired inventory adjustment time
order/ship rate
informationdelay
actualinventory 0
desired inventory0 adjustment time0
order/ship rate0
informationdelay 0
actualinventory 1
desired inventory1 adjustment time1
order/ship rate1
informationdelay 1
demand rate
demand rate 0
demand rate 1
Customer orders
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Supply Chain 4
Actualcondition
desired condition
distributiondelay
adjustment rate
adjustment time
delayed flow
delay time
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Supply Chain 5
Actualcondition
desired condition
distributiondelay
adjustment rate
adjustment time
delayed flow
delay time
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Supply Chain 6actual
inventory
sales
integratedinventory
orders intransit
prod-trans rate
order rate
production time
monthly carryingcost
OIT carry costper mo
AI carry cost permo
OIT unit cost
AI unit cost
actualinventory 0
sales0
integratedinventory 0
customerpurchases
0
orders intransit 0
prod-trans rate 0
order rate0
productiontime 0
monthly carryingcost 0
OIT carry costper mo 0
AI carry cost permo 0
OIT unitcost 0
AI unit cost0
total inventory cost
Supplier
Firm
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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Supply Chain 7
actualinventory
sales
orders intransit
prod-trans rate
order rate
production timeOIT unit cost
AI unit cost
actualinventory 0
sales0
customerpurchases
0orders intransit 0
prod-trans rate 0
order rate0
productiontime 0
OIT unitcost 0
AI unit cost0
Supplier
Firm
SupplierHolding Cost
OIT Holding Costper mo
AI Holding Costper mo
monthly HoldingCost
TOTAL HOLDINGCOST
Firm's HoldingCost
Firm's OIT HoldingCost per mo
Firm's AI HoldingCost per mo
Firm's monthlyholding cost
TOTALINVENTORY
ACCUMINVENTORY
Invent rate
ACCUM SALES
sales rate
-------------------------------------------------------------------------------------------------------
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actualinventory
sales
orders intransit
prod-trans rate
order rate
production timeOIT unit cost
AI unit cost
actualinventory 0
sales0
customerpurchases
0orders intransit 0
prod-trans rate 0
order rate0
productiontime 0
OIT unitcost 0
AI unit cost0
Supplier
Firm
SupplierHolding Cost
OIT Holding Costper mo
AI Holding Costper mo
monthly HoldingCost
TOTAL HOLDINGCOST
Firm's HoldingCost
Firm's OIT HoldingCost per mo
Firm's AI HoldingCost per mo
Firm's monthlyholding cost
TOTALINVENTORY
ACCUMINVENTORY
Invent rate
ACCUM SALES
sales rate
-------------------------------------------------------------------------------------------------------
Supply Chain 8
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