Planning Demand and Supply in a Supply Chain Capacity Planning and Assignment

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1 Planning Demand and Supply in a Supply Chain Capacity Planning and Assignment 1

2 Deterministic Capacity Expansion Issues Single vs. Multiple Facilities Dallas and Atlanta plants of Locheed Martin Single vs. Multiple Resources Machines and worforce; 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 maret? 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 ? Resource costs, economies of scale Penalty for demand-capacity mismatch Recallable capacity: Electricity bloc outs vs Electricity buy outs» Happens in Wisconsin and Texas Electricity maret for Industrial customers» What if American Airlines recalls my ticet Single vs. Multiple decision maers 2

3 A Simple Model Units x x Capacity Demand D(t)= t x/ Time (t) No stoc outs. x is the size of the capacity increments. δ is the increase rate of the demand. 3

4 Infinite Horizon Total Discounted Cost f(x) is expansion cost of capacity increment x; r is the interest rate Expansion index f(x) =0 x/δ exp(-rx/δ) f(x) =1 exp(-rx/δ) f(x) =2 f(x) exp(-r2x/δ) C(x) is the long run (infinite horizon) total discounted expansion cost x exp(-rx/δ)=(exp(-rx/δ)) f ( x) C( x) exp r( ) f ( x) f ( x) (exp( rx/ )) 1 exp( / rx )

5 Discounted Expansion Cost Solution of the Simple Model Expansion Size Solution can be: Each time expand capacity by an amount that is equal to 30-wee demand. 5

6 Shortages, Inventory Holding, Subcontracting Units Subcontracting Capacity Demand Surplus capacity Inventory build up Inventory depletion Use of Inventory and subcontracting to delay capacity expansions Time 6

7 Stochastic Capacity Planning: The case of flexible capacity 1 A y 1A =1, y 2A =1, y 3A =0 2 3 Plants B Products y 1B =0, y 2B =0, y 3B =1 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 D A + D B = Constant 7

8 Capacity allocation Say capacities are r 1 =r 2 = r 3 =100 Suppose that D A + D B = 300 and D A >100 and D B >100 With plant flexibility y 1A =1, y 2A =1, y 3A =0, y 1B =0, y 2B =0, y 3B =1. Scenario D A D B X 1A X 2A X 3A X 1B X 2B X 3B Shortage B B If the scenarios are equally liely, expected shortage is 50. 8

9 Capacity allocation with more flexibility Say capacities are r 1 =r 2 = r 3 =100 Suppose that D A + D B = 300 and D A >100 and D B >100 With plant flexibility y 1A =1, y 2A =1, y 3A =0, y 1B =0, y 2B =1, y 3B =1. Scenario D A D B X 1A X 2A X 3A X 1B X 2B X 3B Shortage Flexibility can decrease shortages. In this case, from 50 to 0. 9

10 A Formulation with Known Demands: D j =d j i denotes plants j denotes products, not necessarily substitutes c tooling cost to configure plant i to Max - cy i, j produce j m j contribution to margin of Subject to producing/selling a unit of j x ri for r i capacity at plant i j D j =d j product j demand x d j for i y =1 if plant i can produce product j, 0 o.w. x ri y for x =units of j produced at plant i x 0, y {0,1 } i, j m x each plant i j each product j each plant i and product j Solutions depend on scenarios: - If D A =200 and D B =100, then y 1A =y 2A =y 3B =1. - If D A =100 and D B =200, then y 1A =y 2B =y 3B =1. 10

11 Unnown Demands: D j =d j with probability p D j =d j product j demand under scenario x = units of j produced at plant i if scenario happens y =1 if plant i can produce product j, 0 o.w. Does y differ under different scenarios? Should my variable depend on scenarios? (Yes / No) Anticipatory variable and Nonanticapatory variable Max Subject to x x j i x x r - i 0, y i, j r d i y j c y for for {0,1} p i, j each plant i and scenario each product and scenario and scenario m x ; ; ; j for each plant i, product j j 11

12 Reality Chec: How do car manufacturers assign products to plants? The last formulation treats the problem of assigning products to plants. This type of assignment is called for tooling/preparation of each plant 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 wor with the current assignments to meet the demand. When maret conditions change, the product-to-plant assignment is revisited. Almost all car manufacturers in North America are retooling their previously truc manufacturing plants to manufacture compact cars as consumer demand basically disappeared for trucs with high gas prices. Also note that the profit margin made from a truc sale is 2-5 times more than the margin made from a car sale. No wonder why manufacturers prefer to sell trucs! In the following pages, you will find the product to plant assignment of all major car manufacturers in the North America. These assignments were updated in the summer of 2008 just about the time when manufacturers started taling about retooling plants to produce compact cars. 12

13 All of Toyota Plants in the North America Toyota. Cambridge Corolla, Matrix, Lexus, Rav4 Toyota-Subaru. LaFayette Camry Nummi: Toyota-GM. Freemont. Corolla, Tacoma, Pontiac Vibe Toyota. Princeton Tundra, Suquoia, Sienna Toyota. Georgetown Avalon, Camry, Solara Toyota. Long Beach Hino Toyota. Blue Springs Highlander Toyota. Tuana, Mexico Tacoma Toyota. San Antonio Tundra 13

14 All of Honda Plants in the North America Honda. Alliston, Ca. Civic, Acura, Odyssey, Pilot, Ridgeline Honda. Decatur TBO in 2008 Honda. Marysville Accord, Acura Honda. Lincoln Odyssey, Pilot Honda. El Salto, Me Accord 14

15 All of Nissan Plants in the North America Nissan. Smyrna Frontier, Xterra, Altima, Maxima, Pathfinder Nissan. Canton Quest, Armada, Titan, Infiniti, Altima 15

16 All of Hyundai-Kia Plants in the North America Kia. LaGrange TBO in 2009 Hyundai. Montgomery Sonata, Santa Fe 16

17 All of Mercedes and BMW Plants in the North America BMW. Spartanburg Z4, X5, X6 M roadster, coupes Mercedes. Tuscaloosa M, R classes 17

18 All of Ford Plants in the North America Ford. Dearborn F-150, Lincoln Mar LT Ford. Flat Roc Mustang, Mazda 6 Ford. Oaville, Ca. Edge, Lincoln MKX Ford. Saint Thomas, Ca. Crown Victoria, Grand Marquis Ford. Saint Paul Ranger, Mazda B series Ford. Chicago Taurus, Mercury Sable Ford. Wayne Focus, Expedition, Lincoln Navigator Ford. Avon Lae E Series Ford. Kansas City Escape, Escape Hybrid, Mazda Tribute, Mercury Mariner, F-150 Ford. Louisville F-250, F-550, Explorer, Mercury Mountaineer Ontario, Michigan, Illinois, Indiana, Ohio in Focus Ford. Hermosillo, Mex. Ford Fusion, Lincoln MKZ, Mercury Milan 18 Ford. Cuatitlan, Mex. F-150, 250, 350, 450, 550,Ion

19 All of Chrysler Plants in the North America Chrysler. Sterling Heights Dodge Avenger, Chrysler Sebring Chrysler. Warren Dodge Ram, Daota, Mitsubishi Raider Chrysler. Detroit-Jefferson North Jeep Grand Cheroee and Commander Chrysler. Brampton, Ca Chrysler 300, Dodge Challenger, Dodge Charger Chrysler. Detroit-Conner Ave. Dodge Viper, SRT 10 Roadster Chrysler. Windsor, Ca Dodge Grand Caravan, Chrysler Town Chrysler. Toledo Jeep Liberty, Dodge Nitro Chrysler. Belvidere Dodge Caliber, Jeep Compass, Jeep Patriot Chrysler. Newar Dodge Durango, Chrysler Aspen Will close in 2009 Chrysler. Fenton-North Dodge Ram Chrysler. Fenton-South Grand Voyager, Grand Caravan, Cargo Van Ontario, Michigan, Illinois, Indiana, Ohio in Focus Chrysler. Saltillo, Mex. Dodge Ram 19 Chrysler. Toluca, Mex. Chrysler PT Cruise, Dodge Journey

All of GM Plants in the North America GM. Lansing-Grand River Cadillac E-SRX GM. Lansing-Delta Township Buic Enclave, Saturn Outloo, GMC Acadia GM. Orion Pontiac G6, Chevrolet Malibu GM.

Fort Wayne Chevy Silverado, GMC Sierra GM. Detroit Buic Lucerne, Cadillac DTS GM. Janisville Chevy Tahoe, Suburban, GMC Yuon Will stop in 2010 GM. Wilmington Saturn L series, Pontiac Solstice GM.

20 All of GM Plants in the North America GM. Lansing-Grand River Cadillac E-SRX GM. Lansing-Delta Township Buic Enclave, Saturn Outloo, GMC Acadia GM. Orion Pontiac G6, Chevrolet Malibu GM. Flint GMC Sierra, Chevy Silverado, Chevy - GMC medium trucs. GM. Oshawa, Ca Chevy Impala, Buic Allure, Chevy Silverado, GMC Sierra. Trucs will stop in GM. Pontiac Chevy Silverado, GMC Sierra GM. Fort Wayne Chevy Silverado, GMC Sierra GM. Detroit Buic Lucerne, Cadillac DTS GM. Janisville Chevy Tahoe, Suburban, GMC Yuon Will stop in 2010 GM. Wilmington Saturn L series, Pontiac Solstice GM. Moraine Chevy Trailblazer, GMC Envoy, Oldsmobile Bravada, Isuzu Ascender, Saab 9-7X Will stop in 2010 GM. Lordstown Chevy Cobalt, Pontiac Pursuit, G4, G5 GM. Fairfax Chevy Malibu, Malibu Maxx, Saturn Aura GM. Wentzville Chevy Express, GMC Savana GM. Bowling Green Cadillac XLR, Chevy Corvette GM. Spring Hill Saturn Ion and Vue Currently down GM. Doraville Chevy Uplander, Pontiac Montana Ontario, Michigan, Illinois, Indiana, Ohio in Focus GM. Arlington Chevy Tahoe, Suburban, GMC Yuon, Cadillac Escalade GM. Shreveport Chevy Colorado, GMC Canyon, Isuzu brands, Hummer H3 GM. Ramos Arizpe, Mex. Pontiac Azte, Chevy Cavalier, Chevrolet Checy, Pontiac Sunfire, Buic Rendezvous GM. Silao, Mex. Chevrolet Suburban, Chevrolet Avalanche, GMC Yuon, Cadillac Escalade GM. Toluca, Mex. Chevrolet Kodia Truc Stopping in

21 GM s Restructuring Plan from 2009 GM s Plan details a return to sustainable profitability in 24 months Demonstrates GM s viability under conservative economic assumptions Expands and accelerates the Plan submitted on December 2 Lowers the Company s breaeven to a U.S. maret of M units annually GM is comprehensively transforming its business, globally Brands, nameplates and dealer networs streamlined and focused Productivity and flexibility gains enabling more facility consolidations Shared global vehicle architectures creating substantial cost savings Unprofitable foreign operations addressed GM s Plan emphasizes the Company s continued focus on great products Fewer, better vehicles in U.S. : supporting Chevrolet, Cadillac, Buic and GMC Renewed commitment to lead in fuel efficiency, hybrids, advanced propulsion All major U.S. introductions in are high-mileage cars and crossovers GM s Plan calls for considerable sacrifice from all staeholders Bondholders and other debtors Hourly and salaried employees, executives and retirees Dealers and suppliers Shareholders 21

22 Summary Capacity Planning Product-to-plant Assignment 22

23 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 Thin 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? Answer: e n0 1 n! lim 1 m m r m e r 1 24 where See the appendix of scaggregate.pdf for more on continuous compounding. 23

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