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Lin/Operations/Supply Chain Mgt 1
Supply Chain Management Module Managing the Supply Chain
» Key to matching demand with supply» Cost and Benefits of inventory
Economies of Scale» Palu Gear: Inventory management of a retailer: EOQ + ROP » Levers for improvement
Safety Stock» Hedging against uncertainty» Role of leadtime
Improving Performance» Centralization & Pooling efficiencies» Postponement» Optimal Service Level
Lin/Operations/Supply Chain Mgt 2
What is a Supply Chain?
What makes for a “good” SC?
Raw Materialsupply points
Movement/Transport
Raw MaterialStorage Movement/
TransportMovement/Transport
PLANT 1
PLANT 2
PLANT 3
WAREHOUSES(DCs)
Movement/Transport
MARKETS
Manufacturing
Finished GoodsStorage
A
B
C
1. Procurementor supply system
2. OperatingSystem 3. Distribution System
4. Salesor demand system
Lin/Operations/Supply Chain Mgt 4
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 = 21¢/sales dollar = 10.5% of GDP
Cisco SolectronCurrent Assets 7/30/95 8/25/95Cash & 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 75,297other 25,743 24,049 Total current assets 995,969 100% 726,358 100%
Investments 576,958PPE 136,653 203,609 other 47747 10,888 Total assets 1,757,327 940,855
Lin/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
Lin/Operations/Supply Chain Mgt 6
We never Talk anymore!
In Style
People
Vanity Fair
Vogue
The New Yorker
GQ
New York
Esquire
Rolling Stone
Us
Talk
64.7%
54.5%
45.6%
42.1%
39.9%
39.4%
35.1%
31.0%
28.0%
23.9%
18.0%
Data for Oct. 1999 – Oct. 2000
Magazine sales at newsstands as % of copies shipped to newsstands
Lin/Operations/Supply Chain Mgt 7
The Current Environment:The Grocery Industry 1985-1992
Number of products in average supermarket
1985 11,036
1990 16,486
1992 20,000
2004 ??
1975 1992 2002
2,000
20,000
Lin/Operations/Supply Chain Mgt 8
A Key to Matching Supply and Demand
When would you rather place your bet?
A B C D
A: A month before start of DerbyB: The Monday before start of DerbyC: The morning of start of DerbyD: The winner is an inch from the finish line
Lin/Operations/Supply Chain Mgt 10
Operational Flows
Throughput R
Inventory I
I = R T Flow time T = Inventory I / Throughput R
FLOW TIME T
Lin/Operations/Supply Chain Mgt 11
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
– Flooding, availability
Cycle/Batch stock
Safety stock
Seasonal stock
Strategic stock
Lin/Operations/Supply Chain Mgt 12
Annual jacket revenues at a Palü Gear retail store are roughly $1M. Palü jackets sell at an average retail price of $325, which represents a mark-up of 30% above what Palü Gear paid its manufacturer. Being a profit center, each store made its own inventory decisions and was supplied directly from the manufacturer by truck. A shipment up to a full truck load, which was about 3000 jackets, was charged a flat fee of $2,200. Typically, stores placed roughly two orders per year, each of about 1500 jackets. (Palü’s cost of capital is approximately 20%.)
What order size would you recommend for a Palü store in current supply network?
retailermanufacturer
Palü Gear: Retail Inventory Management & Economies of Scale
Lin/Operations/Supply Chain Mgt 13
Economies of Scale: Inventory Build-Up Diagram
R: Annual demand rate,
Q: Number of jackets per replenishment order
Number of orders per year = R/Q.
Average number of jackets in inventory = Q/2 .
Q
Time t
Inventory Profile:# of wind breakers in inventory over time.
R = Demand rate
Inventory
Lin/Operations/Supply Chain Mgt 14
Palü Gear: evaluation of current policy of ordering Q = 1500 units each time1. What is average inventory I?
I = Q/2 = Annual cost to hold one unit H = Annual cost to hold I = Holding cost × Inventory
2. How often do we order? Annual throughput R = # of orders per year = Throughput / Batch size Annual order cost = Order cost × # of orders
3. What is total cost? TC = Annual holding cost + Annual order cost =
4. What happens if order size changes?
Lin/Operations/Supply Chain Mgt 15
Find most economical order quantity: Spreadsheet for a Palü Gear retailer
Number of units Number ofper order/batch Batches per Annual Annual Annual
Q Year: R/Q Setup Cost Holding Cost Total Cost50 62 135,385$ 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
$160,000
0 100 200 300 400 500 600 700 800 900 1000
Order (batch) size Q
Setup Cost
Holding Cost
Total Cost
Lin/Operations/Supply Chain Mgt 16
Economies of Scale: Economic Order Quantity EOQ
R : Demand per year,
S : Setup or Order Cost ($/setup; $/order),
H : Marginal annual holding cost ($ per unit per year),
Q : Order quantity.
C : Cost per unit ($/unit),
r : Cost of capital (%/yr),
H = r C.
H
SRQEOQ
2
Batch Size Q
Total annual costs
H Q/2: Annual holding cost
S R /Q:Annual setup cost
EOQ
SRH2
Lin/Operations/Supply Chain Mgt 17
Optimal Economies of Scale: For a Palü Gear retailer
R = 3077 units/ year C = $ 250 / unitr = 0.20/year S = $ 2,200 / order
Unit annual holding cost = H =
Optimal order quantity = QEOQ =
Number of orders per year = R/Q =
Time between orders = Q/R =
Annual order cost = (R/Q)S = $13,008.87/yr
Average inventory I = Q/2 =
Annual holding cost = (Q/2)H =$13,008.87/yr
Average flow time T =
Lin/Operations/Supply Chain Mgt 18
Role of Leadtime L: Palü Gear cont.
The lead time from when a Palü Gear retailer places an order to when the order is received is two weeks. If demand is stable as before, when should the retailer place an order?
I-Diagram:
The two key decisions in inventory management are:– How much to order?– When to order?
Lin/Operations/Supply Chain Mgt 19
Learning Objectives: Batching & Economies of Scale
Increasing batch size of production (or purchase) increases average inventories (and thus cycle times).
Average inventory for a batch size of Q is Q/2. 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 Q and (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.
– If demand increases by a factor of 4, the flow time decreases by a factor of 2.
An inventory policy must specify when to order (the ROP) and how much to order (the batch size).
Lin/Operations/Supply Chain Mgt 20
Demand uncertainty and forecasting
Year Demand1992 194
1993 251
1994 320
1995 267
1995 233
1997 223
1998 266
1999 252
2000 251
2001 331
Lin/Operations/Supply Chain Mgt 21
Demand uncertainty and forecasting
Forecasts depend on (a) historical data and (b) “market intelligence.”
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.
Lin/Operations/Supply Chain Mgt 22
Palü Gear:Service levels & inventory management
In reality, a Palü Gear store’s demand fluctuates from week to week. In fact, weekly demand at each store had a standard deviation of about 30 jackets assume roughly normally distributed. 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 inventory during 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. The Palü retailer 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%?
Lin/Operations/Supply Chain Mgt 23
Applications: – Demand over the leadtime L has standard deviation = RL – Pooled demand over N regions or products has standard deviation = RN
R R R…
Sum of N independent random variables, each with identical standard deviation Rhas
standard deviation =
How find of lead time demand?
Lin/Operations/Supply Chain Mgt 24
Example: say we increase ROP to 140 (and keep order size at Q = 520)1. On average, what is the stock level when the replenishment arrives? 2. On average, what is the inventory profile?
3. What is the probability that we run out of stock?
4. How do we get that stock-out probability down to 5%?
0
100
200
300
400
500
Lin/Operations/Supply Chain Mgt 25
Safety Stocks
Q
Time t
ROP
L
R
L
order order order
mean demand during supply lead time:
= R L
safety stock Is
Inventory on hand
I(t)
Q
Is
0
L
Lin/Operations/Supply Chain Mgt 26
Safety Stocks & Service Levels: The relationship
Raise ROP until we reach appropriate SL
To do numbers, we need: Mean and stdev of demand during lead time Either Excel or tables with z - value such that CSL = F(z)
mean ROP
F(z)
demand during supply lead time
Stock-out probability
Cycle Service Level (CSL)
Is = z
Lin/Operations/Supply Chain Mgt 27
1. How to find service level (given ROP)?2. How to find re-order point (given SL)?
L = Supply lead time, D =N(RR) = Demand per unit time is normally distributed
with mean R and standard deviation R ,
DL =N(LL) = Demand during the lead time
where L = RL and LRL
1. Given ROP, find SL = Cycle service level = P(no stock out)
= P(demand during lead time < ROP)
= F(z*= (ROP- L)/L) [use table]
= NORMDIST(ROP, L, L, True) [or Excel]
2. Given SL, find ROP = L + Is
= L + z*L[use table to get z* ]
= NORMINV(SL, L, L) [or Excel]
Safety stock Is = z*L Reorder point ROP = L + Is
Lin/Operations/Supply Chain Mgt 28
The standard normal distribution F(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 0.53590.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.57530.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.61410.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.65170.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.68790.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.72240.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.75490.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.78520.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.81330.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.83891.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.86211.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.88301.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.90151.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.91771.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.93191.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.94411.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.95451.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.96331.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.97061.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.97672.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.98172.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.98572.2 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 0.99162.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.99362.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.99522.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.99642.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.99742.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.99812.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.99863.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.99903.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.99933.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.99953.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997
F(z)
z0
• Transform X = N() to z = N(0,1)
z = (X - ) / .
F(z) = Prob( N(0,1) < z)
• Transform back, knowing z*:
X* = + z*.
Lin/Operations/Supply Chain Mgt 29
Palü Gear: Determining the required Safety Stock for 95% serviceDATA:
R = 59 jackets/ week R = 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. Required # of standard deviations z* for SL of 95% =
2. Determine lead time demand =
3. Answer: Safety stock Is =
Lin/Operations/Supply Chain Mgt 30
Comprehensive Financial Evaluation:Inventory Costs of Palü Gear
Cycle Stock (Economies of Scale)
1.1 Optimal order quantity = 520
1.2 # of orders/year = 5.9
1.3 Annual ordering cost per store = $13,009
1.4 Annual cycle stock holding cost. = $13,009
2. Safety Stock (Uncertainty hedge)
2.1 Safety stock per store = 70
2.2 Annual 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.
Lin/Operations/Supply Chain Mgt 31
Learning Objectives safety stocks
Safety stock increases (decreases) with an increase (decrease) in:
demand variability or forecast error,
delivery lead time for the same level of service,
delivery lead time variability for the same level of service.
LzI Rs *
Lin/Operations/Supply Chain Mgt 32
Is=400
Centralization Distribution
Improving Supply Chain Performance:1. The Effect of Pooling/Centralization
Is=100Is=100
Is=100Is=100
Decentralized Distribution
Is= 400
Lin/Operations/Supply Chain Mgt 33
Palü Gear’s Internet restructuring:Centralized inventory management
Weekly demand per store = 59 jackets/ week with standard deviation = 30 / week
H = $ 50 / jacket, yearS = $ 2,200 / orderSupply lead time L = 2 weeksDesired cycle service level F(z*) = 95%.
Palü Gear now is considering restructuring to an Internet store. – Assuming Internet store is sum of the five stores and demands are
independent.R = 5 59 = 295 jackets/week average total demand over lead time
L = 2 295 = 590.R = 5 30 = 67.1 STD of total demand over lead time
L = 2 67.1 = 94.9.
Lin/Operations/Supply Chain Mgt 34
Palü Gear’s Internet restructuring: comprehensive financial inventory evaluation
1. Cycle Stock (Economies of Scale)1.1 Optimal order quantity = x 520 = 11631.2 # of orders/year = 5 x 5.9 = 13
1.3 Annual ordering cost of e-store = $29,0891.4 Annual cycle stock holding cost= $29,089
2. Safety Stock (Uncertainty hedge)
2.1 Safety stock for e-store = 1562.2 Annual safety stock holding cost = $7,800
3. Total Costs for consolidated e-store = 29,089 + 29,089 + 7,800
= $65,980 = 147.5/ 5
Note: This is 5 3500 -- cost of safety inventory at one store.
Lin/Operations/Supply Chain Mgt 35
Learning Objectives: centralization/pooling
Different methods to achieve pooling efficiencies:– Physical centralization
– Information centralization
– Specialization
– Raw material commonality (postponement/late customization)
Cost savings are sqrt(# of locations pooled).
Lin/Operations/Supply Chain Mgt 36
Improving Supply Chain Performance: 2. Postponement & Commonality (HP Laserjet)
Generic PowerProduction
Unique PowerProduction
Process I: UniquePower Supply
Europe
N. America
Europe
N. America
Transportation
Process II: UniversalPower Supply
Make-to-Stock Push-Pull Boundary Make-to-Order
Lin/Operations/Supply Chain Mgt 37
Variety and Marketing/Operations:Be smart with product differentiation
• Braking system
• Transmission
• Electrical design
• Chassis design
• Exterior body panels
• Engine block
• Front & rear seats
• Floor mats
• Airbags & antilock system
• Rear-view mirrors
• Dashboard layout
• Headlights
• Cup holders
• Remote keyless entry
Consumer Hierarchy Score
Tec
hn
ical
Hie
rarc
hy
Sco
re
Low
High
High
Low
Source: Mohan Sawhney
Lin/Operations/Supply Chain Mgt 38
Learning Objectives:Supply Chain Performance
Pooling of stock reduces the amount of inventory
– physical
– information
– specialization
– substitution
– commonality/postponement
Tailored response (e.g., partial postponement) can be used to better match supply and demand
The entire supply chain must plan to customer demand
Single product
Multi product
Lin/Operations/Supply Chain Mgt 40
Palü Gear’s 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 should Palü Gear’s order?
Optimal Service Level when you can order only once: Palü Gear
0.5%0.9%
2.2%
4.5%
7.8%
11.6%
14.6%
15.9%
14.6%
11.6%
7.8%
4.5%
2.2%
0.9%0.5%
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400
Demand Forecast for Christmas jackets
Lin/Operations/Supply Chain Mgt 41
In reality, you do not know demand for sure…Impact of uncertainty if you order the expected Q = 2000
IF:
THEN:
Order/Stock Q = 2000
DemandProbability of Demand
units sold
units overstock
units understock
Profit ($000)
600 0.5% 600 1400 0 43$ 800 0.9% 800 1200 0 94$ 1000 2.2% 1000 1000 0 145$ 1200 4.5% 1200 800 0 196$ 1400 7.8% 1400 600 0 247$ 1600 11.6% 1600 400 0 298$ 1800 14.6% 1800 200 0 349$ 2000 15.9% 2000 0 0 400$ 2200 14.6% 2000 0 200 400$ 2400 11.6% 2000 0 400 400$ 2600 7.8% 2000 0 600 400$ 2800 4.5% 2000 0 800 400$ 3000 2.2% 2000 0 1000 400$ 3200 0.9% 2000 0 1200 400$ 3400 0.5% 2000 0 1400 400$
Expected values: 1802 198 198 350$
What happens if you change your order level to hedge against uncertainty? Performance for all possible Q using Excel:
Order Probability Expected Expected Expected Expected
size Q Demand = Q units sold units overstock units understock Profit
600 0.5% 600 0 1400 120$ 800 0.9% 799 1 1201 160$
1000 2.2% 996 4 1004 199$ 1200 4.5% 1189 11 811 237$ 1400 7.8% 1373 27 627 273$ 1600 11.6% 1541 59 459 305$ 1800 14.6% 1686 114 314 331$ 2000 15.9% 1802 198 198 350$ 2200 14.6% 1886 314 114 360$ 2400 11.6% 1941 459 59 363$ 2600 7.8% 1973 627 27 360$ 2800 4.5% 1989 811 11 353$ 3000 2.2% 1996 1004 4 344$ 3200 0.9% 1999 1201 1 334$ 3400 0.5% 2000 1400 0 323$
Expected Profit
$120
$160
$200
$240
$280
$320
$360
$400
600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400
Order/Stock Quantity Q
- Co = - 55
+ 200 = Cu
Lin/Operations/Supply Chain Mgt 43
What happens if I order one more unit (on top of Q = 2000)?
Sell the extra unit withprobability …
= …..
Do not sell the extra unit with probability …
= …..
Expected profit from additional unit E() = So? ... Order more?
Towards the newsboy model Suppose you placed an order of 2000 units but you are not sure if you should order more.
Lin/Operations/Supply Chain Mgt 44
• In general: raise service level (i.e., order an additional unit) if and only if
E() = (1-SL)Cu – SLCo > 0 Sell Do not sell
Thus, optimal service level SL* (= Newsvendor formula)
• Example: use formula for Palu-Gear Christmas order
1. SL* = 2. So how much should Palu order then?
How does this compare to forecasted demand of 2000?
The Value-maximizing Service Level The newsvendor formula
Demand Prob. Cum. Prob.800 1% 1%
1,000 1% 2%1,200 3% 5%1,400 6% 12%1,600 10% 21%1,800 13% 34%2,000 16% 50%2,200 16% 66%2,400 13% 79%2,600 10% 88%2,800 6% 95%3,000 3% 98%3,200 1% 99%
21
1
pp
cp
CC
C
ou
u
Lin/Operations/Supply Chain Mgt 45
= smallest Q such that service level F(Q) > critical fractile Cu / (Co + Cu)
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 the expected benefit of being able to sell it exceeds the expected cost of having that unit left over.
Marginal Analysis: Order more as long as F(Q) < Cu / (Co + Cu)
Lin/Operations/Supply Chain Mgt 46
Where else do you find newsvendors?
Deciding on economic service level Benefits: Flexible Spending Account decision
Capacity Mgt
Lin/Operations/Supply Chain Mgt 47
Whistler Blackcomb Ski & Snowboard School
Has over 1,200 instructors (including part timers).– Organized into 36 pods.
Manager of a pod must determine today the number of instructors to call in for tomorrow’s lessons.– A master schedule is generated on a monthly basis but
adjusted daily. Skiers can pre-book (i.e., reserve) a lesson or can
walk in.– Total demand depends on a number of factors: Day of the
week, point in the season, US/Canadian exchange rate etc.
Lin/Operations/Supply Chain Mgt 48
Whistler Blackcomb Economics of Individual Lessons
If unable to staff a lesson, lose $320 in revenue. Instructors are paid $40 per hour for lessons.
– An instructor who gives a lesson is paid for three hours.
– An instructor on stand by who does not give lesson is paid for two hours.
Tomorrow Today
Pre-bookings made for today
3:00pm
Finish lessons for day
5:00pm
Determine forecast demand and instructor requirements for tomorrow
Begin morning lessons (demand realized)
9:00pm
Call instructors to fill in or to call off
12:00pm
Afternoon lessons begin
8:00am 8:00am
Lin/Operations/Supply Chain Mgt 49
Whistler Blackcomb Staffing Decision
A forecasting model predicts that demand for individual lessons tomorrow is 56.– Error in forecast (i.e., standard deviation) is 3.12.
If demand is normally distributed, how many instructors should be called in?– Assume each instructors teaches just one individual lesson.
Lin/Operations/Supply Chain Mgt 50
Whistler Blackcomb Analysis
If one too many instructors, must pay for two hours.– Co = 2 × 40 = $80.
If one too few instructors, lose margin on a lesson.– Cu = 320 – (3 × 40 ) = 320 – 120 = $200.
Critical fractile = Cu/(Co+Cu)=200/(200+80) = 71.4%.
z71.4 = Normsinv(0.714) = 0.5659.
Optimal decision for normal distribution:
Q = μ + z71.4 × σ = 56 + 0.5659 × 3.12 = 57.7 ≈ 58
Goal of a Supply ChainMatch 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
(Little’s Law)
Why there is Inventory?
Economies of ScaleThere are fixed costs
of ordering/production
Q*=
UncertaintyForecast Error
Safety Stock Is= zR
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 R
Implications:
Is z (service level appropriate)
Reduce Lead time
Reduce R
Where does R come from?
Customer Demand UncertaintyNormal Variations…
How do we deal with it?
Aggregation•Physical•Information•Specialization•Component Commonality•Postponement
How do we deal with it?
•Make the SC more visible•Align Incentives
Balance overstocking and understockingNewsboy Problem … Critical Fractile = 1- P(stockout)
Bullwhip EffectCauses•Demand Signaling•Rationing•Batching•Promotions