forecasting and aggregate planning - the university of ...metin/or6366/folios/scaggregate.ppt ·...
TRANSCRIPT
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Planning Demand and Supply in a Supply Chain
Forecasting and Aggregate PlanningChapters 8 and 9
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Learning Objectives
Overview of forecasting Forecast errors
Aggregate planning in the supply chain Managing demand Managing capacity
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Phases of Supply Chain Decisions
Strategy or design: Forecast Planning: Forecast Operation/Execution Actual demand
Since actual demands differ from the forecasts, … so does the execution from the plans. – E.g. Supply Chain degree plans for 40 students per year
whereas the actual is ??
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Characteristics of forecasts Forecasts are always wrong. Include expected value and measure of error. Long-term forecasts are less accurate than short-term forecasts.
Too long term forecasts are useless: Forecast horizon– Forecasting to determine
» Raw material purchases for the next week; Ericsson» Annual electricity generation capacity in TX for the next 30 years; Texas Utilities » Boat traffic intensity in the upper Mississippi until year 2100; Army Corps of Engineers
Aggregate forecasts are more accurate than disaggregate forecasts– Variance of aggregate is smaller because extremes cancel out
» Two samples: {3,5} and {2,6}. Averages: 4 and 4.
Totals : 8 and 8.» Variance of sample averages/totals=0» Variance of {3,5,2,6}=5/2
– Several ways to aggregate» Products into product groups; Telecom switch boxes» Demand by location; Texas region » Demand by time; April demand
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Forecasting Methods Qualitative
– Expert opinion» E.g. Why do you listen to Wall Street stock analysts?
– What if we all listen to the same analyst? S/He becomes right! Time Series
– Static – Adaptive
Causal: Linear regression Forecast Simulation for planning purposes
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Master Production Schedule (MPS)
MPS is a schedule of future deliveries. A combination of forecasts and firm orders.
Volume
Time
Firm Orders Forecasts
Frozen Zone Flexible Zone
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Aggregate PlanningChapter 8
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Aggregate Planning (Ag-gregate: Past part. of Ad-gregare: Totaled)
If the actual is different than the plan, why bother sweating over detailed plans
Aggregate planning: General plan for our frequency decomposition– Combined products = aggregate product
» Short and long sleeve shirts = shirt Single product
» AC and Heating unit pipes = pipes at Lennox Iowa plant – Pooled capacities = aggregated capacity
» Dedicated machine and general machine = machine Single capacity
– E.g. SOM has 100 instructors
– Time periods = time buckets» Consider all the demand and production of a given month together
When does the demand or production take place in a time bucket? Increase the number of time buckets; decrease the bucket length.
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Fundamental tradeoffs in Aggregate Planning
Capacity: Regular time, Over time, Subcontract?Inventory: Backlog / lost sales, combination: Customer patience?
Basic Strategies Chase (the demand) strategy; produce at the instantaneous demand rate
– fast food restaurants
Level strategy; produce at the rate of long run average demand
– swim wear
Time flexibility; high levels of workforce or capacity – machining shops, army
Deliver late strategy– spare parts for your Jaguar
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Matching the Demand
Use
inve
ntor
y
Use delivery time
Use cap
acity
Demand
Demand
Demand
Adjust the capacity to match the demand
Demand
- Which is which? Level Deliver late Chase Time flexibility
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Capacity Demand Matching Inventory/Capacity tradeoff
Level strategy: Leveling capacity forces inventory to build up in anticipation of seasonal variation in demand
Chase strategy: Carrying low levels of inventory requires capacity to vary with seasonal variation in demand or enough capacity to cover peak demand during season
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Case Study: Aggregate planning at Red Tomato
Farm tools:
Shovels
Spades
Forks
Aggregate by similar characteristics
Generic tool, call it Shovel
Same characteristics?
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Aggregate Planning at Red Tomato Tools
Month Demand Forecast
January 1,600 February 3,000 March 3,200 April 3,800 May 2,200 June 2,200 Total 16,000
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Aggregate Planning
Item Cost Materials $10/unit Inventory holding cost $2/unit/month Marginal cost of a backorder $5/unit/month Hiring and training costs $300/worker Layoff cost $500/worker Labor hours required 4hours/unit Regular time cost $4/hour Over time cost $6/hour Max overtime hrs per employee per month 10hours Cost of subcontracting $30/unit Revenue $40/unit
What is the cost of production per tool? That is materials plus labor. Overtime production is more expensive than subcontracting.
What is the saving achieved by producing a tool in house rather than subcontracting?
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1. Aggregate Planning (Decision Variables)
Wt = Number of employees in month t, t = 1, ..., 6
Ht = Number of employees hired at the beginning of month t, t = 1, ..., 6
Lt = Number of employees laid off at the beginning of month t, t = 1, ..., 6
Pt = Production in units of shovels in month t, t = 1, ..., 6
It = Inventory at the end of month t, t = 1, ..., 6
St = Number of units backordered at the end of month t, t = 1, ..., 6
Ct = Number of units subcontracted for month t, t = 1, ..., 6
Ot = Number of overtime hours worked in month t, t = 1, ..., 6
Did we aggregate production capacity?
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2. Objective Function:
.80 0 ,6,...,1 01
,1
WwheretforLtH tW tW t
orLtH tW tW t
6
130
6
110
6
15
6
12
6
16
6
1500
6
1300
6
12084
tCt
tPt
tS t
tI t
tOt
tLt
tH t
tW tMin
3. ConstraintsWorkforce size for each month is based on hiring and layoffs
Production (in hours) for each month cannot exceed capacity (in hours)
.6,...,1 ,0440or 2084
tforPtOtW t
OtW tPt
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3. Constraints Inventory balance for each month
tP
.500 and 01,000, where1,...,6,for t
0,
,
IS I SISDCPIISDSCPI
600
tt1tttt1t
t1ttttt1t
Periodt
Periodt+1
Periodt-1
1tI tI
tD1tS
tC
tS
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3. Constraints
Overtime for each month
1,...,6.for t 010
or 10
OWWO
tt
tt
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Execution Solve the formulation, see Table 8.3
– Total cost=$422.275K, total revenue=$640K
Apply the first month of the plan Delay applying the remaining part of the plan until the next
month Rerun the model with new data next month
This is called rolling horizon execution
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Aggregate Planning at Red Tomato Tools
Month Demand Forecast January 1,600 February 3,000 March 3,200 April 3,800 May 2,200 June 2,200 Total 16,000
This solution was for the following demand numbers:
What if demand fluctuates more?
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Increased Demand Fluctuation
Month Demand Forecast January 1,000
February 3,000 March 3,800 April 4,800 May 2,000 June 1,400 Total 16,000
Total costs=$432.858K.16000 units of total production as before why extra cost?
With respect to $422.275K of before.
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Manipulating the DemandChapter 9
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Matching Demand and Supply
Supply = Demand Supply < Demand => Lost revenue opportunity Supply > Demand => Inventory Manage Supply – Productions Management Manage Demand – Marketing
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Managing Predictable Variability with SupplyManage capacity
» Time flexibility from workforce (OT and otherwise)» Seasonal workforce, agriculture workers
» Subcontracting» Counter cyclical products: complementary products
Similar products with negatively correlated demands– Snow blowers and Lawn Mowers– AC pumps and Heater pumps
» Flexible capacities/processes: Dedicated vs. flexible
a,b,c,d
Similar capabilities One super facility
a
bc
d a
bc
d
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Managing Predictable Variability with Inventory Component commonality
– Remember fast food restaurant menus– Component commonality increase the benefit of postponement.
» More on this later Build seasonal inventory of predictable products in preseason
– Nothing can be learnt by procrastinating Keep inventory of predictable products in the downstream supply
chain
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Managing Predictable Variability with PricingRevisit Red Tomato Tools
Manage demand with pricing– Original pricing:
» Cost = $422,275, Revenue = $640,000, Profit=$217,725 Demand increases from discounting
– Market growth– Stealing market share from competitors– Forward buying
» stealing your own market share from the future
Discount of $1 in a period increases that period’s demand by 10% (market and market share growth) and moves 20% of next two months demand forward
Can you gather this information –price sensitivity of the demand- easily? Does your company have this information?
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Off-Peak (January) Discount from $40 to $39
Month Demand Forecast January 3,000=1600(1.1)+0.2(3000+3200) February 2,400=3000(0.8) March 2,560=3200(0.8) April 3,800 May 2,200 June 2,200
Cost = $421,915, Revenue = $643,400, Profit = $221,485
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Peak (April) Discount from $40 to $39
Month Demand Forecast January 1,600 February 3,000 March 3,200 April 5,060=3800(1.1)+0.2(2200+2200) May 1,760=2200(0.8) June 1,760=2200(0.8)
Cost = $438,857, Revenue = $650,140, Profit = $211,283Discounting during peak increases the revenue but decreases the profit!
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Demand Management
Pricing and Aggregate Planning must be done jointly Factors affecting discount timing and their new values
– Consumption: 100% increase in consumption instead of 10% increase
– Forward buy, still 20% of the next two months– Product Margin: Impact of higher margin. What if discount
from $31 to $30 instead of from $40 to $39.)
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January Discount: 100% increase in consumption, sale price = $40 ($39)
Month Demand Forecast January 4,440=1600(2)+0.2(3000+3200)
February 2,400=0.8(3000) March 2,560=0.8(3200) April 3,800 May 2,200 June 2,200
Off peak discount: Cost = $456,750, Revenue = $699,560Profit=$242,810
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Peak (April) Discount: 100% increase in consumption, sale price = $40 ($39)
Month Demand Forecast January 1,600 February 3,000 March 3,200 April 8,480=3800(2)+(0.2)(2200+2200) May 1,760=(0.8)2200 June 1,760=(0.8)2200
Peak discount: Cost = $536,200, Revenue = $783,520Profit=$247,320
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Performance Under Different ScenariosRegular Price
Promotion Price
Promotion Period
% increase in demand
% forward buy
Profit Average Inventory
$40 $40 NA NA NA $217,725 895 $40 $39 January 10% 20% $221,485 523 $40 $39 April 10% 20% $211,283 938 $40 $39 January 100% 20% $242,810 208 $40 $39 April 100% 20% $247,320 1,492 $31 $31 NA NA NA $73,725 895 $31 $30 January 100% 20% $84,410 208 $31 $30 April 100% 20% $69,120 1,492 Use rows in bold to explain Xmas discounts. The product, with less (forward buying/market growth) ratio, is discounted more.What gift should you buy on the special days (peak demand) when retailers supposedly give discounts?
E.g. Think of flowers on valentine’s day. How about diamonds?For flowers, what is (forward buying/market growth) due to discounting?How about for diamonds?
Need empirical data. What is available?
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Empirical Data: Who spends / How much on Valentine’s day The average consumer spends $122.98 on 2008 Valentine’s Day, similar to
$119.67 of 2007. Total US spending on Valentine’s Day is $17.02 B by 18+. Spending
– by gender » Men again dishes out the most in 2008, spending an average of $163.37 on gifts and cards,
compared to an average of $84.72 spent by women. – by age
» Adults: 25-34 spend $160.37.» Young adults: 18-24 spend $145.59.» Upper Middle age: 45-54 spend $117.91. » Lower Middle age: 35-44 spend $116.35.» Elderly: 55-64 spend $110.97.
Gifts» 56.8% of all consumers give a greeting card. » 48.2% plan a special night out. » 48.0% buy candy.» 35.9% buy flowers.» 12.3% give a gift card.» 11.8% buy clothing. » ??.?% buy diamonds
– Source: National Retail Federation www.nrf.com
Where is
forward buy or m
arket g
rowth
due to disc
ounting?
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Factors Affecting Promotion Timing
Factor Favored timing High forward buying Low demand period High stealing share High demand period High growth of market High demand period High margin High demand period Low margin Low demand period High holding cost Low demand period Low capacity volume flexibility
Low demand period
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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 of Learning Objectives
Forecasting Aggregate planning Supply and demand management during
aggregate planning with predictable demand variation– Supply management levers– Demand management levers
Capacity Planning
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Material Requirements Planning Master Production Schedule (MPS) Bill of Materials (BOM) MRP explosion Advantages
– Disciplined database– Component commonality
Shortcomings– Rigid lead times– No capacity consideration
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Optimized Production Technology
Focus on bottleneck resources to simplify planning
Product mix defines the bottleneck(s) ? Provide plenty of non-bottleneck resources. Shifting bottlenecks
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Just in Time production Focus on timing Advocates pull system, use Kanban Design improvements encouraged Lower inventories / set up time / cycle time Quality improvements Supplier relations, fewer closer suppliers, Toyota city
JIT philosophically different than OPT or MRP, it is not only a planning tool but a continuous improvement scheme