d30 supply chain
TRANSCRIPT
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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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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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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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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 $195. Marketing had forecasted a demand of 2000 Christmas-
jackets with a forecast error (standard deviation) of 500
How many jackets shouldPal Gear order?
1%
1%
3%
6%
10%
13%
16% 16%
13%
10%
6%
3%
1%
1%
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200
Demand forecast for Christmas jackets
Optimal Service Level in Responseto Demand
Uncertainty when you can order only once:Pal Gear
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In reality, you do not know demand for sureImpact of uncertainty if you order the expected Q = 2000
Stock: 2000
Demand
Probability
of Demand
units
sold
units
overstock
units
understock Profit
800 1% 800 1200 0 94000
1000 1% 1000 1000 0 145000
1200 3% 1200 800 0 1960001400 6% 1400 600 0 247000
1600 10% 1600 400 0 298000
1800 13% 1800 200 0 349000
2000 16% 2000 0 0 400000
2200 16% 2000 0 200 400000
2400 13% 2000 0 400 400000
2600 10% 2000 0 600 400000
2800 6% 2000 0 800 400000
3000 3% 2000 0 1000 400000
3200 1% 2000 0 1200 400000
Expected: 1825.6 141.6 240.0 357331
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S. Chopra/Operations/Supply Chain Mgt 35
What happens if you change your order level to hedge against
uncertainty? Performance for all possible Q using Excel
200
-55
= F(Q)
Order Probability Cumulative Expected Expected Expected Expected
size Q Demand = Q P(Demand < Q) units sold units overstock units understock Profit
1000 2% 2% 983.6 0.0 1082.0 196,721$
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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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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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)