Delays

James R. Burns

Fall 2010

04/21/23 2

Today

• Recitation

• Lecture

• Hands-on

04/21/23 3

Recitation

• What does it take to create a table lookup function in VENSIM

• The HW problem

04/21/23 4

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

04/21/23 15

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

04/21/23 22

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

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

04/21/23 30

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

04/21/23 32