d30 Supply Chain

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  • 8/12/2019 d30 Supply Chain

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    S. Chopra/Operations/Supply Chain Mgt 1

    Operations Management:

    Supply Chain Management Module

    Managing the Supply Chain Key to matching demand with supply

    Cost and Benefits of inventory

    Economies of Scale Factors affecting optimal batch size: EOQ

    Levers for improvement

    Safety Stock Factors affecting level of safety stock: ROP

    Levers for reducing safety stock Improving Performance

    Centralization & Pooling efficiencies

    Postponement

    Accurate Response

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    S. Chopra/Operations/Supply Chain Mgt 2

    Corporate Finance

    Inventories represent about 34% of current assets for a typical

    US company; 90% of working capital. For each dollar of GNP in the trade and manufacturing sector,

    about 40% worth of inventory was held.

    Average logistics cost = 21c/sales dollar = 10.5% of GDP

    Cisco Solectron

    Current Assets 7/30/95 8/25/95

    Cash & Equivalents 204,846 21% 89,959 12%

    Short-term Investments 234,681 58,643

    AR 384,242 254,898

    Inventories 71,160 7% 298,809 41%

    Deferred income taxes 75,297

    other 25,743 24,049

    Total current assets 995,969 100% 726,358 100%

    Investments 576,958

    PPE 136,653 203,609

    other 47747 10,888

    Total assets 1,757,327 940,855

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    S. Chopra/Operations/Supply Chain Mgt 3

    The Supply Chain

    The Procurement

    or supply system

    The Operating

    System The Distribution System

    Raw Material

    supply pointsMovement/

    Transport

    Raw Material

    Storage Movement/

    Transport

    Movement/

    TransportSTORAGE

    STORAGE

    STORAGE

    PLANT 1

    PLANT 2

    PLANT 3

    WAREHOUSE

    WAREHOUSE

    WAREHOUSE

    Movement/

    Transport

    MARKETS

    Manufacturing

    Finished Goods

    Storage

    A

    B

    C

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    S. Chopra/Operations/Supply Chain Mgt 4

    Key Financial Indicators of Supply

    Chain Performance

    Return on Assets

    Net Present Value

    These are LAGGINGindicators. What must the supply

    chain do to achieve this?

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    S. Chopra/Operations/Supply Chain Mgt 5

    Costs of not Matching Supply and

    Demand

    Cost of overstocking

    liquidation, obsolescence, holding

    Cost of under-stocking

    lost sales and resulting lost margin

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    S. Chopra/Operations/Supply Chain Mgt 6

    Accurately Matching Demand with

    Supply is the Key Challenge: Inventories

    ... by 1990 Wal-Martwas already winning an important

    technological war that other discounters did not seem to know

    was on. Wal-Mart has the most advanced inventory

    technology in the business and they have invested billions in

    it. (NYT, Nov. 95).

    WSJ, Aug. 93: Dell Computerstock plunges. The company

    was sharply off in forecast of demand resulting in inventory

    writedowns.

    BW 1997:

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  • 8/12/2019 d30 Supply Chain

    8/40S. Chopra/Operations/Supply Chain Mgt 8

    Where is the Flow Time?

    Buffer Operation

    Waiting Processing

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    Why do Buffers Build?

    Why hold Inventory?

    Economies of scale Fixed costs associated with batches

    Quantity discounts

    Trade Promotions

    Uncertainty

    Information Uncertainty

    Supply/demand uncertainty

    Seasonal Variability

    Strategic

    Prices, availability

    Cycle/Batch stock

    Safetystock

    Seasonalstock

    Strategicstock

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    Pal Gear: Retail Inventory

    Management & Economies of Scale

    Annual jacket revenues at aPal Gearretail store are roughly $1M.Pal

    jackets sell at an average retail price of $325, which represents a mark-up of30% above whatPal Gearpaid its manufacturer. Being a profit center,each store made its own inventory decisions and was supplied directly fromthe manufacturer by truck. A shipment up to a full truck load, which wasover 3000 jackets, was charged a flat fee of $2,200. Stores typically ordered1500 jackets at a time, twice a year. (Pals cost of capital isapproximately 20%.)

    What order size would you recommend for aPalstore in current supplynetwork?

    retailer

    manufacturer

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    S. Chopra/Operations/Supply Chain Mgt 11

    Economies of Scale:

    Inventory Build-Up Diagram

    R: Annual demand rate,

    Q: Number of jackets per

    replenishment order

    Number of orders per year =

    R/Q.

    Average number of jacketsin inventory = Q/2 .

    Q

    Time t

    Inventory Profile:# of jackets in

    inventory over time.

    R = Demand rate

    Inventory

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    S. Chopra/Operations/Supply Chain Mgt 12

    Costs Associated with Batches

    Order costs (S)

    Changeover of

    production line

    Transportation Receiving

    Holding costs (H = rC)

    Physical holding cost

    Cost of capital

    Cost of obsolescence

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    S. Chopra/Operations/Supply Chain Mgt 13

    Pal Gear: evaluation of current policy of

    ordering Q= 1500 units each time

    1. What is average inventoryI? I = Q/2 =

    Annual cost to hold one unitH =

    Annual cost to holdI = Holding cost Inventory

    2. How often do we order? Annual throughputR =

    # of orders per year = Throughput / Batch size

    Annual order cost = Order cost # of orders

    3. What is total cost? TC =Annual holding cost + Annual order cost=

    4. What happens if order size changes?

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    S. Chopra/Operations/Supply Chain Mgt 14

    Find most economical order quantity:

    Spreadsheet for aPal Gearretailer

    Number of units Number of

    per order/batch Batches per Annual Annual Annual

    Q Year: R/Q Setup Cost Holding Cost Total Cost

    50 62 135,385$ 1,250$ 136,635$

    100 31 67,692$ 2,500$ 70,192$

    150 21 45,128$ 3,750$ 48,878$

    200 15 33,846$ 5,000$ 38,846$

    250 12 27,077$ 6,250$ 33,327$

    300 10 22,564$ 7,500$ 30,064$

    350 9 19,341$ 8,750$ 28,091$

    400 8 16,923$ 10,000$ 26,923$

    450 7 15,043$ 11,250$ 26,293$

    500 6 13,538$ 12,500$ 26,038$

    510 6 13,273$ 12,750$ 26,023$

    520 6 13,018$ 13,000$ 26,018$

    530 6 12,772$ 13,250$ 26,022$

    540 6 12,536$ 13,500$ 26,036$

    550 6 12,308$ 13,750$ 26,058$

    600 5 11,282$ 15,000$ 26,282$

    650 5 10,414$ 16,250$ 26,664$700 4 9,670$ 17,500$ 27,170$

    750 4 9,026$ 18,750$ 27,776$

    800 4 8,462$ 20,000$ 28,462$

    850 4 7,964$ 21,250$ 29,214$

    900 3 7,521$ 22,500$ 30,021$

    1000 3 6,769$ 25,000$ 31,769$

    $-

    $20,000

    $40,000

    $60,000

    $80,000

    $100,000

    $120,000

    $140,000

    $160,000

    0 100 200 300 400 500 600 700 800 900 1000

    Order (batch) size Q

    Setup Cost

    Holding Cost

    Total Cost

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    S. Chopra/Operations/Supply Chain Mgt 15

    Economies of Scale:

    Economic Order QuantityEOQ

    R : Demand per year,

    S : Setup or Order Cost ($/setup; $/order),

    H : Marginal annual holding cost ($/per unit per year),

    Q : Order quantity.

    C : Cost per unit ($/unit),r+h: Holding cost % (%/yr),

    H= (r+h) C.

    H

    SRQEOQ

    2

    Batch Size Q

    Total annual

    costs

    H Q/2: Annual

    holding cost

    S R /Q:Annual

    setup cost

    EOQ

    SRH2

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    S. Chopra/Operations/Supply Chain Mgt 16

    Optimal Economies of Scale:

    For aPal Gearretailer

    R= 3077 units/ year C= $ 250 / unit

    r = 0.20/year S= $ 2,200 / order

    Unit annual holding cost =H =

    Optimal order quantity = Q =

    Number of orders per year =R/Q=

    Time between orders = Q/R=

    Annual order cost = (R/Q)S= $13,008.87/yrAverage inventoryI = Q/2 =

    Annual holding cost = (Q/2)H=$13,008.87/yr

    Average flow time T =I/R =

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    S. Chopra/Operations/Supply Chain Mgt 17

    Learning Objectives:

    Batching & Economies of Scale

    Average inventory for a batch size of Qis Q/2.

    Increasing batch size of production (or purchase) increases average

    inventories (and thus cycle times).

    The optimal batch size trades off setup cost and holding cost.

    To reduce batch size, one has to reduce setup cost (time).

    Square-root relationship between Qand (R, S):

    If demand increases by a factor of 4, it is optimal to increase batch size

    by a factor of 2 and produce (order) twice as often.

    To reduce batch size by a factor of 2, setup cost has to be reduced by a

    factor of 4.

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    S. Chopra/Operations/Supply Chain Mgt 18

    Role of LeadtimeL:

    Pal Gearcont.

    The lead time from when aPal Gearretailer places an orderto when the order is received is two weeks. If demand is stableas before, when should the retailer place an order?

    I-Diagram:

    The two key decisions in inventory managementare:

    How much to order?

    When to order?

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    S. Chopra/Operations/Supply Chain Mgt 19

    Demand uncertainty and forecasting

    Forecasts are usually (always?) wrong.

    A good forecast has at least 2 numbers (includes a

    measure of forecast error, e.g., standard deviation). The forecast horizon must at least be as large as the

    lead time. The longer the forecast horizon, the less

    accurate the forecast.

    Aggregate forecasts tend to be more accurate.

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    J.A. Van Mieghem/Operations/Supply Chain Mgt 20

    Pal Gear:

    Service levels & inventory management

    In reality, aPal Gearstores demand fluctuates from week toweek. In fact, weekly demand at each store had a standarddeviation of about 30 jackets assume roughly normallydistributed. Recall that average weekly demand was about 59

    jackets; the order lead time is two weeks; fixed order costs are

    $2,200/order and it costs $50 to hold one jacket in inventoryduring one year.

    Questions:1. If the retailer uses the ordering policy discussed before, what will the

    probability of running out of stock in a given cycle be?

    2. ThePalretailer would like the stock-out probability to be smaller.How can she accomplish this?

    3. Specifically, how does it get the service level up to 95%?

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    S. Chopra/Operations/Supply Chain Mgt 21

    Example: say we increase ROP to 140

    (and keep order size at Q = 520)

    1. On average, what is the stock level when the replenishmentarrives?

    2. What is the probability that we run out of stock?

    3. How do we get that stock-out probability down to 5%?

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    S. Chopra/Operations/Supply Chain Mgt 23

    1. How to find service level (given ROP)?

    2. How to find re-order point (given SL)?

    L = Supply lead time, D =N(R, sR) = Demandper unit timeis normally distributed

    with meanRand standard deviation sR,

    DL=N(m, s) = Demand during the lead time

    where m=RL and s sRL1. Given ROP, find SL = Cycle service level =P(no stock out)

    =P(demand during lead time

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    S. Chopra/Operations/Supply Chain Mgt 24

    The standard normal distributionF(z)z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

    0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359

    0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753

    0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141

    0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517

    0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879

    0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224

    0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549

    0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852

    0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133

    0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389

    1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621

    1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830

    1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015

    1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177

    1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319

    1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441

    1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545

    1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633

    1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706

    1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767

    2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817

    2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857

    2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.98902.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916

    2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936

    2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952

    2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964

    2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974

    2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981

    2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986

    3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990

    3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993

    3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995

    3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997

    F(z)

    z0

    TransformX = N(m,s)toz =N(0,1)

    z = (X - m) / s.

    F(z) = Prob(N(0,1)

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    S. Chopra/Operations/Supply Chain Mgt 25

    Pal Gear: Determining the required

    Safety Stock for 95% service

    DATA:

    R= 59 jackets/ week sR= 30 jackets/ week

    H= $50 / jacket, year

    S= $ 2,200 / order L= 2 weeks

    QUESTION: What should safety stock be to insure a desired cycle service level of

    95%?

    ANSWER:

    1. Determine slead time demand =

    2. Required # of standard deviations z* =

    3. Answer: Safety stock Is=

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    S. Chopra/Operations/Supply Chain Mgt 26

    Comprehensive Financial Evaluation:

    Inventory Costs ofPal Gear

    1. Cycle Stock (Economies of Scale)

    1.1 Optimal order quantity =

    1.2 # of orders/year =

    1.3 Annual ordering cost per store = $13,0091.4 Annual cycle stock holding cost. = $13,009

    2. Safety Stock (Uncertainty hedge)

    2.1Safety stock per store = 702.2Annual safety stock holding cost = $3,500.

    3. Total Costs for 5 stores = 5 (13,009 + 13,009 + 3,500)

    = 5 x $29,500 = $147.5K.

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    S. Chopra/Operations/Supply Chain Mgt 27

    Learning Objectives

    safety stocks

    Levers to decrease safety stock without hurting level of

    service:

    Decrease demand variability or forecast error,

    Decrease delivery lead time,

    Decrease delivery lead time variability.

    LzI Rs s*

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    S. Chopra/Operations/Supply Chain Mgt 28

    Improving Supply Chain Performance:

    1. The Effect of Pooling/Centralization

    System A (Decentralized) System B (Centralized)

    Which of the two systems provides a higher level of service for a given level

    of safety stock?

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    S. Chopra/Operations/Supply Chain Mgt 29

    Pal Gears Internet restructuring:

    Centralized inventory management

    Weekly demand per store = 59 jackets/ week

    with standard deviation = 30 / week

    H= $ 50 / jacket, year

    S= $ 2,200 / order

    Supply lead timeL= 2 weeksDesired cycle service level F(z*) = 95%.

    Pal Gearnow is considering restructuring to an Internet store.

    m=

    s=

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    S. Chopra/Operations/Supply Chain Mgt 30

    Pal Gears Internet restructuring:

    comprehensive financial inventory evaluation

    1. Cycle Stock (Economies of Scale)

    1.1 Optimal order quantity =

    1.2 # of orders/year =

    1.3 Annual ordering cost of e-store = $29,089

    1.4 Annual cycle stock holding cost = $29,089

    2. Safety Stock (Uncertainty hedge)

    2.1Safety stock for e-store =

    2.2Annual safety stock holding cost = $7,800.

    3. Total Costs for consolidated e-store = 29,089 + 29,089 + 7,800

    = $65,980.

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    S. Chopra/Operations/Supply Chain Mgt 31

    Improving Supply Chain Performance:

    2. Postponement & Commonality (HP Laserjet)

    Generic Power

    Production

    Unique Power

    Production

    Process I: Unique

    Power Supply

    Europe

    N. America

    Europe

    N. America

    Transportation

    Process II: Universal

    Power Supply

    Make-to-Stock Push-Pull Boundary Make-to-Order

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    S. Chopra/Operations/Supply Chain Mgt 32

    Learning Objectives:

    Supply Chain Performance

    Pooling of stock reduces the amount of inventoryphysical

    information

    specialization

    substitution

    commonality/postponement

    Benetton: Tailored response (e.g., partial postponement) can be

    used to better match supply and demand

    Single product

    Multi product

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    S. Chopra/Operations/Supply Chain Mgt 33

    Pal Gears is planning to offer a special line of winter jackets, especially designed

    as gifts for the Christmas season. Each Christmas-jacket costs the company $250

    and sells for $450. Any stock left over after Christmas would be disposed of at a

    deep discount of $195. Marketing had forecasted a demand of 2000 Christmas-

    jackets with a forecast error (standard deviation) of 500

    How many jackets shouldPal Gear order?

    1%

    1%

    3%

    6%

    10%

    13%

    16% 16%

    13%

    10%

    6%

    3%

    1%

    1%

    0%

    2%

    4%

    6%

    8%

    10%

    12%

    14%

    16%

    18%

    800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200

    Demand forecast for Christmas jackets

    Optimal Service Level in Responseto Demand

    Uncertainty when you can order only once:Pal Gear

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    S. Chopra/Operations/Supply Chain Mgt 34

    In reality, you do not know demand for sureImpact of uncertainty if you order the expected Q = 2000

    Stock: 2000

    Demand

    Probability

    of Demand

    units

    sold

    units

    overstock

    units

    understock Profit

    800 1% 800 1200 0 94000

    1000 1% 1000 1000 0 145000

    1200 3% 1200 800 0 1960001400 6% 1400 600 0 247000

    1600 10% 1600 400 0 298000

    1800 13% 1800 200 0 349000

    2000 16% 2000 0 0 400000

    2200 16% 2000 0 200 400000

    2400 13% 2000 0 400 400000

    2600 10% 2000 0 600 400000

    2800 6% 2000 0 800 400000

    3000 3% 2000 0 1000 400000

    3200 1% 2000 0 1200 400000

    Expected: 1825.6 141.6 240.0 357331

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    S. Chopra/Operations/Supply Chain Mgt 35

    What happens if you change your order level to hedge against

    uncertainty? Performance for all possible Q using Excel

    200

    -55

    = F(Q)

    Order Probability Cumulative Expected Expected Expected Expected

    size Q Demand = Q P(Demand < Q) units sold units overstock units understock Profit

    1000 2% 2% 983.6 0.0 1082.0 196,721$

    1001 984.6 0.0 1081.0 196,914$

    1200 3% 5% 1177.4 2.9 888.2 235,323$

    1400 6% 12% 1364.8 12.2 700.8 272,291$

    1600 10% 21% 1540.2 33.6 525.4 306,184$1800 13% 34% 1696.2 74.3 369.4 335,142$

    2000 16% 50% 1825.6 141.6 240.0 357,331$

    2200 16% 66% 1924.0 240.0 141.6 371,593$

    2400 13% 79% 1991.2 369.4 74.3 377,929$

    2600 10% 88% 2032.0 525.4 33.6 377,496$

    2800 6% 95% 2053.3 700.8 12.2 372,126$

    2999 2062.6 887.2 3.0 363,726$3000 3% 98% 2062.7 888.2 2.9 363,683$

    Towards the newsboy model Suppose you placed an

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    S. Chopra/Operations/Supply Chain Mgt 36

    What happens if I order one more unit (on top of Q = 2000)?

    Sell the extra unit withprobability

    P= ..

    Do not sell the extra unitwith probability

    P= ..

    Expected profit from additional unit

    E(P) = So? ... Order more?

    Towards the newsboy model Suppose you placed anorder of 2000 units but you are not sure if you should

    order more.

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    S. Chopra/Operations/Supply Chain Mgt 37

    Accurate response:

    Find optimal Q from newsboy model

    Cost of overstocking by one unit = Co the out-of-pocket cost per unit stocked but not demanded

    Say demand is one unit below my stock level. How much did the one unit

    overstocking cost me? E.g.: purchase price - salvage price.

    Cost of understocking by one unit = Cu The opportunity cost per unit demanded in excess of the stock level provided

    Say demand is one unit above my stock level. How much could I have saved

    (or gained) if I had stocked one unit more? E.g.: retail price - purchase price.

    Given an order quantity Q, increase it by one unit if and only if theexpected benefit of being able to sell it exceeds the expected cost of having

    that unit left over.

    Marginal Analysis: Order more as long asF(Q) < Cu/ (Co+ Cu)

    = smallest Q such that service levelF(Q) > critical fractile Cu/ (Co+ Cu)

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    S. Chopra/Operations/Supply Chain Mgt 38

    Where else do you find newsboys?

    Deciding on economic service level

    Benefits: Flexible Spending Account decision

    ATM

    Capacity Mgt

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    S. Chopra/Operations/Supply Chain Mgt 39

    Goal of a Supply Chain

    Match Demand with Supply

    It is hard Why?

    Hard to Anticipate DemandForecasts are wrong why?

    There is lead time why there

    is lead time?

    Lead time (flow time) = Activity

    time+ Waiting Time

    Because there is waiting time..Why there is waiting time?

    There is inventory in the SC

    (Littles Law)

    Why there is Inventory?

    Economies of Scale

    There are fixed costs

    of ordering/production

    Q*=

    Uncertainty

    Forecast Error

    Safety Stock Is= zsR

    Seasonality

    H

    SR2

    Implications:

    How fast cycle inventory grows

    if demand grows.

    How much to invest in fixed cost

    reduction to reduce batch size.

    L

    Implications:

    Is z (service level

    appropriate)

    Reduce Lead time

    Reduce sR

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    Implications:

    Is z (service level

    appropriate)

    Reduce Lead time

    Reduce sR

    Where does sRcome from?

    Customer Demand Uncertainty

    Normal Variations

    How do we deal with it?

    Aggregation

    Physical

    Information

    Specialization

    Component CommonalityPostponement

    Information Uncertainty

    Balance overstocking and understocking

    Newsboy Problem

    Critical Fractile = 1- P(stockout)