utdallas.edu/~metin planning demand and supply in a supply chain
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Planning Demand and Supply in a Supply Chain
Capacity Planning and Assignment
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Aside: Continuous Compounding If my $1investment earns an interest of r per year, what is my
interest+investment at the end of the year? Answer: (1+r) If I earn an interest of r/2 per six months, what is my interest+ investment at the
end of the year? Answer: (1+r/2)2
If I earn an interest of (r/m) per (12/m) months, what is my interest+investment? Answer: (1+r/m)m
Think of continuous compounding as the special case of discrete-time compounding when m approaches infinity.
What if I earn an interest of (r/infinity) per (12/infinity) months?
1201
241
61
21
11
111
where1lim :Answer
0
m
n
rm
n!e
emr
See the appendix of scaggregate.pdf for more on continuous compounding.
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Deterministic Capacity Expansion Issues Single vs. Multiple Facilities
– Dallas and Atlanta plants of Lockheed Martin Single vs. Multiple Resources
– Machines and workforce; or aggregated capacity Single vs. Multiple Product Demands
– Have you aggregated your demand when studying the capacity? Expansion only or with Contraction
– Is there a second-hand machine market? Discrete vs. Continuous Expansion Times
– Can you expand SOM building capacity during the spring term? Discrete vs. Continuous Capacity Increments
– Can you buy capacity in units of 2.313832? Resource costs, economies of scale Penalty for demand-capacity mismatch
– Recallable capacity: Electricity block outs vs Electricity buy outs» Happens in Wisconsin Electricity market» What if American Airlines recalls my ticket
Single vs. Multiple decision makers
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A Simple Model
No stock outs. x is the size of the capacity increments.δ is the increase rate of the demand.
D(t)= tx
Demand
Capacity
Units
Time (t)x/
x
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Infinite Horizon Total Discounted Cost
f(x) is expansion cost of capacity increment of size x
)/exp(1)())/(exp()()()(exp)(
00
rxxfrxxfxfxkrxC
k
k
k
.1 %;5 ;)( 5.0 rxxf
C(x) is the long run (infinite horizon) total discounted expansion cost
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Solution of the Simple Model
0
5
10
15
20
25
1 10 20 30 40 50 60 70 80 90 100
Expansion Size
Dis
coun
ted
Expa
nsio
n C
ost
Solution can be: Each time expand capacity by an amount that is equal to 30-week demand.
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Shortages, Inventory Holding, Subcontracting
Use of Inventory and subcontracting to delay capacity expansions
Demand
Units
Time
Capacity
Surpluscapacity
Inventorybuild up
Inventorydepletion
Subcontracting
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Stochastic Capacity Planning: The case of flexible capacity
Plant 1 and 2 are tooled to produce product A Plant 3 is tooled to produce product B A and B are substitute products
– with random demands DA + DB = Constant
1
2
3
A
B
Plants Products
y1A=1, y2A=1, y3A=0
y1B=0, y2B=0, y3B=1
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Capacity allocation
Say capacities are r1=r2= r3=100 Suppose that DA + DB = 300 and DA >100 and DB >100
Scenario DA DB X1A X2A X3A X1B X2B X3B Shortage
1 200 100 100 100 100 0
2 150 150 100 50 100 50 B
3 100 200 100 0 100 100 B
With plant flexibility y1A=1, y2A=1, y3A=0, y1B=0, y2B=0, y3B=1.
If the scenarios are equally likely, expected shortage is 50.
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Capacity allocation with more flexibility
Say capacities are r1=r2= r3=100 Suppose that DA + DB = 300 and DA >100 and DB >100
Scenario DA DB X1A X2A X3A X1B X2B X3B Shortage
1 200 100 100 100 0 100 0
2 150 150 100 50 50 100 0
3 100 200 100 0 100 100 0
With plant flexibility y1A=1, y2A=1, y3A=0, y1B=0, y2B=1, y3B=1.
Flexibility can decrease shortages. In this case, from 50 to 0.
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A Formulation with Known Demands: Dj=dj
i denotes plants j denotes products, not necessarily substitutes
cij tooling cost to configure plant i to produce j
mj contribution to margin of producing/selling a unit of j
ri capacity at plant i Dj=dj product j demand yij=1 if plant i can produce product
j, 0 o.w. xij=units of j produced at plant i }1,0{y , 0x
dx
rx
rxSubject to
xm c-Max
ijij
ji
ij
ijiij
jiij
ji,ijjij
ji,ij
jproduct each for
jproduct and iplant each for
iplant each for
y
y
- If DA=200 and DB=100, then y1A=y2A=y3B=1.- If DA=100 and DB=200, then y1A=y2B=y3B=1.
Solutions depend on scenarios:
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Unknown Demands: Dj=djk with probability pk
Dj=djk product j demand
under scenario k xij
k= units of j produced at plant i if scenario k happens
yij=1 if plant i can produce product j, 0 o.w. Does yij differ under different scenarios?
Should my variable depend on scenarios? (Yes / No)Anticipatory variable and Nonanticapatory variable }1,0{y , 0x
dx
rx
rx
Subject to
xmp c-Max
ijkij
kj
i
kij
ijikij
ji
kij
k ji,
kijj
kij
ji,ij
k scenario and
iproduct each for
k scenario and
jproduct i,plant each for
k scenario and
iplant each for
y
y
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Reality Check: How do car manufacturers assign products to plants? With the last formulation, we treated the problem of assigning products to
plants. This type of assignment called for tooling/preparation of each plant
appropriately so that it can produce the car type it is assigned to. These tooling (nonanticipatory) decisions are made at most once a year and
manufacturers work with the current assignments to meet the demand. When market conditions change, the product-to-plant assignment is revisited.
– Almost all car manufacturers in North America are retooling their previously truck manufacturing plants to manufacture compact cars as consumer demand basically disappeared for trucks with high gas prices.
– Also note that the profit margin made from a truck sale is 2-5 times more than the margin made from a car sale. No wonder why manufacturers prefer to sell trucks!
In the following pages, you will find the product to plant assignment of major car manufacturers in the North America. These assignments were updated in the summer of 2008 just about the time when manufacturers started talking about retooling plants to produce compact cars.
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All of Toyota Plants in the North America
Toyota. Tijuana, MexicoTacoma
Toyota. Long BeachHino
Nummi: Toyota-GM. Freemont.Corolla, Tacoma, Pontiac Vibe
Toyota. San AntonioTundra
Toyota. Blue SpringsHighlander
Toyota. GeorgetownAvalon, Camry, Solara
Toyota. PrincetonTundra, Suquoia, Sienna
Toyota-Subaru. LaFayetteCamry
Toyota. CambridgeCorolla, Matrix, Lexus, Rav4
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All of Honda Plants in the North America
Honda. El Salto, MeAccord
Honda. LincolnOdyssey, Pilot
Honda. MarysvilleAccord, Acura
Honda. DecaturTBO in 2008
Honda. Alliston, Ca.Civic, Acura, Odyssey,
Pilot, Ridgeline
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All of Nissan Plants in the North America
Nissan. CantonQuest, Armada,
Titan, Infiniti, Altima
Nissan. SmyrnaFrontier, Xterra, Altima,
Maxima, Pathfinder
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All of Hyundai-Kia Plants in the North America
Hyundai. MontgomerySonata, Santa Fe
Kia. LaGrangeTBO in 2009
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All of Mercedes and BMW Plants in the North America
Mercedes. TuscaloosaM, R classes
BMW. SpartanburgZ4, X5, X6
M roadster, coupes
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All of Ford Plants in the North America
Ford. Hermosillo, Mex. Ford Fusion, Lincoln MKZ, Mercury Milan
Ford. Kansas CityEscape, Escape Hybrid,
Mazda Tribute, Mercury Mariner, F-150
Ford. Cuatitlan, Mex. F-150, 250, 350, 450, 550,Ikon
Ford. Saint PaulRanger, Mazda B series
Ford. LouisvilleF-250, F-550, Explorer,Mercury Mountaineer
Ford. ChicagoTaurus, Mercury Sable
Ford. Avon LakeE Series
Ford. Saint Thomas, Ca.Crown Victoria, Grand Marquis
Ford. Oakville, Ca.Edge, Lincoln MKX
Ford. WayneFocus, Expedition, Lincoln Navigator
Ford. Flat RockMustang, Mazda 6
Ford. DearbornF-150, Lincoln Mark LT
Ontario, Michigan, Illinois, Indiana, Ohio in Focus
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All of Chrysler Plants in the North America
Chrysler. Toluca, Mex.Chrysler PT Cruise, Dodge Journey
Ontario, Michigan, Illinois, Indiana, Ohio in Focus
Chrysler. Saltillo, Mex.Dodge Ram
Chrysler. NewarkDodge Durango, Chrysler Aspen
Will close in 2009
Chrysler. Fenton-SouthGrand Voyager, Grand Caravan, Cargo Van
Chrysler. Fenton-NorthDodge Ram
Chrysler. BelvidereDodge Caliber, Jeep
Compass, Jeep PatriotChrysler. ToledoJeep Liberty, Dodge Nitro
Chrysler. Brampton, CaChrysler 300,
Dodge Challenger, Dodge Charger
Chrysler. Windsor, CaDodge Grand Caravan, Chrysler Town
Chrysler. Detroit-Jefferson NorthJeep Grand Cherokee and Commander
Chrysler. Detroit-Conner Ave.Dodge Viper, SRT 10 Roadster
Chrysler. WarrenDodge Ram, Dakota, Mitsubishi Raider
Chrysler. Sterling HeightsDodge Avenger, Chrysler Sebring
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All of GM Plants in the North America
GM. Ramos Arizpe, Mex.Pontiac Aztek, Chevy Cavalier, Chevrolet
Checy, Pontiac Sunfire, Buick Rendezvous
Ontario, Michigan, Illinois, Indiana, Ohio in Focus
GM. Silao, Mex.Chevrolet Suburban, Chevrolet Avalanche,
GMC Yukon, Cadillac Escalade
GM. Toluca, Mex.Chevrolet Kodiak Truck
Stopping in 2008
GM. ArlingtonChevy Tahoe,
Suburban, GMC Yukon,
Cadillac Escalade
GM. ShreveportChevy Colorado,
GMC Canyon, Isuzu brands, Hummer H3
GM. FairfaxChevy Malibu, Malibu Maxx, Saturn Aura
GM. WentzvilleChevy Express, GMC Savana
GM. DoravilleChevy Uplander, Pontiac Montana
GM. Spring HillSaturn Ion and Vue
Currently down
GM. Bowling GreenCadillac XLR, Chevy Corvette
GM. WilmingtonSaturn L series, Pontiac Solstice
GM. LordstownChevy Cobalt, Pontiac
Pursuit, G4, G5
GM. MoraineChevy Trailblazer, GMC
Envoy, Oldsmobile Bravada, Isuzu Ascender, Saab 9-7X
Will stop in 2010
GM. Fort WayneChevy Silverado,
GMC Sierra
GM. JanisvilleChevy Tahoe,
Suburban, GMC YukonWill stop in 2010
GM. Oshawa, CaChevy Impala, Buick Allure,
Chevy Silverado, GMC Sierra.Trucks will stop in 2009. GM. Lansing-Grand River
Cadillac E-SRX
GM. Lansing-Delta TownshipBuick Enclave, Saturn Outlook, GMC Acadia
GM. FlintGMC Sierra, Chevy Silverado, Chevy - GMC medium trucks.
GM. PontiacChevy Silverado, GMC Sierra
GM. DetroitBuick Lucerne, Cadillac DTS
GM. OrionPontiac G6,
Chevrolet Malibu
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Summary
Capacity Planning Product-to-plant Assignment