Transcript Document 7291453
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 1
What is a Supply Chain?
1. Procurement or supply system
Raw Material supply points Movement/ Transport
2. Operating System 3. Distribution System
Raw Material Storage Movement/ Transport Manufacturing PLANT 1 Movement/ Transport
4. Sales or demand system
Finished Goods Storage Movement/ Transport A PLANT 2 PLANT 3 What makes for a “good” SC?
Lin/Operations/Supply Chain Mgt B WAREHOUSES (DCs) C MARKETS 2
US Vehicle Inventory
Lin/Operations/Supply Chain Mgt 3
Corporate Finance
Current Assets
Cash & Equivalents Short-term Investments AR Inventories Deferred income taxes other Total current assets Investments PPE other
Total assets Cisco
7/30/95 204,846 234,681 384,242 71,160 75,297 25,743 995,969 576,958 136,653 47747 1,757,327 21% 7%
Solectron
8/25/95 89,959 58,643 254,898 298,809 100% 24,049 726,358 203,609 10,888 940,855 12% 41% 100% 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 Lin/Operations/Supply Chain Mgt 4
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 5
We never Talk anymore!
Magazine sales at newsstands as % of copies shipped to newsstands 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 Lin/Operations/Supply Chain Mgt 6
The Current Environment:
The Grocery Industry 1985-1992
Number of products in average supermarket 1985 1990 11,036 16,486 1992 2004 20,000 ??
20,000 2,000 1975 Lin/Operations/Supply Chain Mgt 1992 2002 7
A Key to Matching Supply and Demand
When would you rather place your bet?
A B A: B: C: D: Lin/Operations/Supply Chain Mgt A month before start of Derby The Monday before start of Derby The morning of start of Derby The winner is an inch from the finish line C D 8
Where is the Flow Time?
Buffer
Lin/Operations/Supply Chain Mgt
Waiting
Operation
Processing
9
Operational Flows
Lin/Operations/Supply Chain Mgt
Throughput R Inventory I FLOW TIME T
I = R T
Flow time
T
= Inventory
I
/ Throughput
R
10
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 Lin/Operations/Supply Chain Mgt
Cycle/Batch
stock
Safety
stock
Seasonal
stock
Strategic
stock 11
Palü Gear
: Retail Inventory Management & Economies of Scale 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
network?
store in current supply manufacturer retailer Lin/Operations/Supply Chain Mgt 12
Economies of Scale: Inventory Build-Up Diagram
R
: Annual demand
rate
,
Q
: Number of jackets per replenishment order Inventory
Inventory Profile
: # of wind breakers in inventory over time.
Number of orders per year =
R
/
Q.
Q R =
Demand rate Average number of jackets in inventory =
Q
/2 .
Time
t
Lin/Operations/Supply Chain Mgt 13
Palü Gear
: evaluation of current policy of ordering
Q
= 1500 units each time
1.
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 14
Find most economical order quantity: Spreadsheet for a Palü Gear retailer
Number of units Number of per order/batch Batches per
Q
Year:
R/Q
50 100 62 31 150 200 21 15 250 300 350 400 450 500 510 520 530 540 550 600 12 10 9 8 7 6 6 6 6 6 6 5 650 700 750 800 850 900 1000 5 4 4 4 4 3 3
Annual Annual Setup Cost Holding Cost
$ 135,385 $ 67,692 $ $ 1,250 2,500 $ 45,128 $ 33,846 $ 3,750 $ 5,000 $ 27,077 $ 22,564 $ 19,341 $ 16,923 $ 15,043 $ 13,538 $ $ $ $ $ $ 6,250 7,500 8,750 10,000 11,250 12,500 $ 13,273 $ 13,018 $ 12,772 $ 12,536 $ 12,308 $ 11,282 $ 10,414 $ 9,670 $ 9,026 $ 8,462 $ 7,964 $ 7,521 $ 6,769 $ 12,750 $ 13,000 $ 13,250 $ 13,500 $ $ 13,750 15,000 $ 16,250 $ 17,500 $ 18,750 $ 20,000 $ $ $ 21,250 22,500 25,000
Annual Total Cost
$ 136,635 $ 70,192 $ 48,878 $ 38,846 $ 33,327 $ 30,064 $ 28,091 $ 26,923 $ 26,293 $ 26,038 $ 26,023 $ 26,018 $ 26,022 $ 26,036 $ 26,058 $ 26,282 $ 26,664 $ 27,170 $ 27,776 $ 28,462 $ 29,214 $ 30,021 $ 31,769 $160,000 $140,000 $120,000 $100,000 $80,000 $60,000 $40,000 $20,000 $ 0 Setup Cost Holding Cost Total Cost 100 200 300 400 500 600 700 800 900 1000 Order (batch) size Q Lin/Operations/Supply Chain Mgt 15
Economies of Scale: Economic Order Quantity
EOQ
R S H Q
: : : : Demand per year, Setup or Order Cost ($/setup; $/order), Marginal annual holding cost ($ per unit per year), Order quantity.
Q EOQ
2
SR H C r
: Cost per unit ($/unit), : Cost of capital (%/yr),
H
=
r C .
2
SRH
Total annual costs
H Q/2:
Annual holding cost Lin/Operations/Supply Chain Mgt EOQ
S R /Q:
Annual setup cost Batch Size
Q
16
Optimal Economies of Scale: For a Palü Gear retailer
R = 3077 units/ year r = 0.20/year Unit annual holding cost = H = C = $ 250 / unit S = $ 2,200 / order Optimal order quantity = Q EOQ = 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 17
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 18
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 19
Demand uncertainty and forecasting
Year
1992 1993 1994 1995 1995 1997 1998 1999 2000 2001
Demand
194 251 320 267 233 223 266 252 251 331 Lin/Operations/Supply Chain Mgt 20
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 21
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 22
How find
s
of lead time demand?
s
R
s
R
… s
R
Sum of
N independent
random variables, each with identical standard deviation s
R
, has standard deviation = Applications: – Demand over the leadtime
L
has standard deviation = s R
L
– Pooled demand over
N
regions or products has standard deviation = s R
N
Lin/Operations/Supply Chain Mgt 23
Example: say we increase ROP to 140 (and keep order size at Q = 520)
1.
2.
On average, what is the stock level when the replenishment arrives? On average, what is the
inventory profile
?
500 3.
400 300 200 100 0 What is the probability that we run out of stock?
4.
How do we get that stock-out probability down to 5%?
Lin/Operations/Supply Chain Mgt 24
Safety Stocks
Inventory on hand
I
(
t
)
ROP I s
0
order
Q
order
Q L
order
L R
mean demand during supply lead time: m
= R L
safety stock
I s L
Time
t
Lin/Operations/Supply Chain Mgt 25
Safety Stocks & Service Levels: The relationship
Cycle Service Level (CSL) Stock-out probability
F(z)
I s
= z
s mean ROP demand during supply lead time Raise ROP until we reach appropriate SL To do numbers, we need: Mean and stdev s of demand during lead time Either Excel or tables with z - value such that CSL =
F(z)
Lin/Operations/Supply Chain Mgt 26
1. How to find service level (given ROP)?
2. How to find re-order point (given SL)?
1.
2.
L
= Supply lead time,
D =N
(
R
, s
R
) = Demand per unit time is normally distributed with mean
R
and standard deviation s
R D L =N
( m
L
, s
L
) where m
L
=
RL
= Demand during the lead time and s
L
s R
L
, Given ROP, find SL = Cycle service level =
P
(no stock out) =
P
(demand during lead time <
ROP
) =
F
(
z*=
(
ROP-
m
L
)/ s
L
)
=
NORMDIST (
ROP
, m
L
, s
L
, True) Given SL, find ROP = m
L + I
s
=
m
L + z *
s
L
= NORMINV (SL, m
L
, s
L
) [use table] [or Excel] [use table to get [or Excel]
z *
] Safety stock
I s
=
z *
s
L
Reorder point
ROP =
m
L + I
s
Lin/Operations/Supply Chain Mgt 27
The standard normal distribution
F(z)
• Transform
X = N(
m,s
)
to
z = N(0,1) z =
(
X
m ) / s .
F
(
z
) = Prob(
N
(0,1) <
z
)
F(z)
0
z
• Transform back, knowing
z*
:
X*
= m
+ z*
s .
z
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
0.9772
0.9821
0.9861
0.9893
0.9918
0.9938
0.9953
0.9965
0.9974
0.9981
0.9987
0.9990
0.9993
0.9995
0.00
0.5000
0.5398
0.5793
0.6179
0.6554
0.6915
0.7257
0.7580
0.7881
0.8159
0.8413
0.8643
0.8849
0.9032
0.9192
0.9332
0.9452
0.9554
0.9641
0.9713
0.9778
0.9826
0.9864
0.9896
0.9920
0.9940
0.9955
0.9966
0.9975
0.9982
0.9987
0.9991
0.9993
0.9995
0.01
0.5040
0.5438
0.5832
0.6217
0.6591
0.6950
0.7291
0.7611
0.7910
0.8186
0.8438
0.8665
0.8869
0.9049
0.9207
0.9345
0.9463
0.9564
0.9649
0.9719
0.9783
0.9830
0.9868
0.9898
0.9922
0.9941
0.9956
0.9967
0.9976
0.9982
0.9987
0.9991
0.9994
0.9995
0.02
0.5080
0.5478
0.5871
0.6255
0.6628
0.6985
0.7324
0.7642
0.7939
0.8212
0.8461
0.8686
0.8888
0.9066
0.9222
0.9357
0.9474
0.9573
0.9656
0.9726
0.9788
0.9834
0.9871
0.9901
0.9925
0.9943
0.9957
0.9968
0.9977
0.9983
0.9988
0.9991
0.9994
0.9996
0.03
0.5120
0.5517
0.5910
0.6293
0.6664
0.7019
0.7357
0.7673
0.7967
0.8238
0.8485
0.8708
0.8907
0.9082
0.9236
0.9370
0.9484
0.9582
0.9664
0.9732
0.9793
0.9838
0.9875
0.9904
0.9927
0.9945
0.9959
0.9969
0.9977
0.9984
0.9988
0.9992
0.9994
0.9996
0.04
0.5160
0.5557
0.5948
0.6331
0.6700
0.7054
0.7389
0.7704
0.7995
0.8264
0.8508
0.8729
0.8925
0.9099
0.9251
0.9382
0.9495
0.9591
0.9671
0.9738
0.9798
0.9842
0.9878
0.9906
0.9929
0.9946
0.9960
0.9970
0.9978
0.9984
0.9989
0.9992
0.9994
0.9996
0.05
0.5199
0.5596
0.5987
0.6368
0.6736
0.7088
0.7422
0.7734
0.8023
0.8289
0.8531
0.8749
0.8944
0.9115
0.9265
0.9394
0.9505
0.9599
0.9678
0.9744
0.9803
0.9846
0.9881
0.9909
0.9931
0.9948
0.9961
0.9971
0.9979
0.9985
0.9989
0.9992
0.9994
0.9996
0.06
0.5239
0.5636
0.6026
0.6406
0.6772
0.7123
0.7454
0.7764
0.8051
0.8315
0.8554
0.8770
0.8962
0.9131
0.9279
0.9406
0.9515
0.9608
0.9686
0.9750
0.9808
0.9850
0.9884
0.9911
0.9932
0.9949
0.9962
0.9972
0.9979
0.9985
0.9989
0.9992
0.9995
0.9996
0.07
0.5279
0.5675
0.6064
0.6443
0.6808
0.7157
0.7486
0.7794
0.8078
0.8340
0.8577
0.8790
0.8980
0.9147
0.9292
0.9418
0.9525
0.9616
0.9693
0.9756
0.9812
0.9854
0.9887
0.9913
0.9934
0.9951
0.9963
0.9973
0.9980
0.9986
0.9990
0.9993
0.9995
0.9996
0.08
0.5319
0.5714
0.6103
0.6480
0.6844
0.7190
0.7517
0.7823
0.8106
0.8365
0.8599
0.8810
0.8997
0.9162
0.9306
0.9429
0.9535
0.9625
0.9699
0.9761
0.9817
0.9857
0.9890
0.9916
0.9936
0.9952
0.9964
0.9974
0.9981
0.9986
0.9990
0.9993
0.9995
0.9997
0.09
0.5359
0.5753
0.6141
0.6517
0.6879
0.7224
0.7549
0.7852
0.8133
0.8389
0.8621
0.8830
0.9015
0.9177
0.9319
0.9441
0.9545
0.9633
0.9706
0.9767
Lin/Operations/Supply Chain Mgt 28
Palü Gear
: Determining the required Safety Stock for 95% service
DATA:
R
= 59 jackets/ week
H
= $50 / jacket, year
S
= $ 2,200 / order s
R
= 30 jackets/ week
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 s lead time demand =
3.
Answer: Safety stock
I s
= Lin/Operations/Supply Chain Mgt 29
Comprehensive Financial Evaluation: Inventory Costs of
Palü Gear
Cycle Stock (Economies of Scale) 1.1
Optimal order quantity
1.2
# of orders/year
1.3
Annual ordering cost per store
1.4
Annual cycle stock holding cost.
= 520 = 5.9
= $13,009 = $13,009
2. Safety Stock (Uncertainty hedge)
2.1 Safety stock per store
2.2
Annual safety stock holding cost = 70 = $3,500 .
3. Total Costs for 5 stores
Lin/Operations/Supply Chain Mgt
= 5 (13
,009 + 13,009 + 3,500) = 5 x $29,500 = $147.5K
.
30
Learning Objectives safety stocks
I s
z
* s
R L 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. Lin/Operations/Supply Chain Mgt 31
Improving Supply Chain Performance: 1. The Effect of Pooling/Centralization
Decentralized Distribution Centralization Distribution I s =100 I s =100 I s =100 I s =100
Lin/Operations/Supply Chain Mgt 32
Palü Gear’s
Internet restructuring: Centralized inventory management
Weekly demand per store with standard deviation
H
= $ 50 / jacket, year
S
= $ 2,200 / order = 59 jackets/ week = 30 / week Supply lead time
L
= 2 weeks Desired cycle service level F(z*) = 95%.
Palü Gear
now is considering restructuring to an Internet store.
R
s
R
– =
5
Assuming Internet store is sum of the five stores and demands are independent.
59 = 295 jackets/week
average total demand over lead time
m =
5
s
L L
= 2
295 = 590.
30 = 67.1
STD of total demand over lead time =
2
67.1 = 94.9.
Lin/Operations/Supply Chain Mgt 33
Palü Gear’s
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
1.4
Annual cycle stock holding cost = 5 =
5
x 520 = 1163 x 5.9 = 13 = $29,089 = $29,089
2. Safety Stock (Uncertainty hedge)
2.1 Safety stock for e-store
2.2
Annual safety stock holding cost
3. Total Costs for consolidated e-store
Lin/Operations/Supply Chain Mgt = = 156 $7,800
Note: This is
5
3500 - cost of safety inventory at one store.
=
29,089 + 29,089 + 7,800 =
$65,980 = 147.5/
5
34
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 35
Improving Supply Chain Performance:
2. Postponement & Commonality (HP Laserjet) Generic Power Production Process I: Unique Power Supply Unique Power Production Transportation Europe N. America Process II: Universal Power Supply Europe N. America Make-to-Stock Lin/Operations/Supply Chain Mgt Push-Pull Boundary Make-to-Order 36
Variety and Marketing/Operations: Be smart with product differentiation
High Low
Consumer Hierarchy Score
Low High • 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 Source: Mohan Sawhney Lin/Operations/Supply Chain Mgt 37
Learning Objectives: Supply Chain Performance
Pooling of stock reduces the amount of inventory – physical – information – specialization – substitution – commonality/postponement Single product Multi product Tailored response (e.g., partial postponement) can be used to better match supply and demand The entire supply chain must plan to customer demand Lin/Operations/Supply Chain Mgt 38
Finding the optimal service level: The newsvendor problem
Optimal Service Level
when you can order only once:
Palü Gear
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?
Demand Forecast for Christmas jackets
18% 16% 15.9% 14.6% 14.6% 14% 12% 10% 11.6% 11.6% 7.8% 7.8% 8% 6% 4.5% 4% 2.2% 2% 0.5% 0% 600 Lin/Operations/Supply Chain Mgt 0.9% 800 1000 1200 1400 1600 1800 2000 2200 4.5% 2.2% 0.9% 0.5% 2400 2600 2800 3000 3200 3400 40
In reality, you do not know demand for sure…
Impact of uncertainty if you order the expected
Q =
2000 IF: THEN:
Demand Order/Stock Q = Probability of Demand
600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400 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% Expected values: 2000
units sold
units overstock
600 800 1000 1200 1400 1600 1800 2000 2000 2000 2000 2000 2000 2000 2000 1802 1400 1200 1000 800 600 400 200 0 0 0 0 0 0 0 0 198
units understock
0 0 0 0 0 0 0 0 200 400 600 800 1000 1200 1400 198
Profit ($000)
$ 43 $ 94 $ 145 $ 196 $ 247 $ 298 $ 349 $ 400 $ 400 $ 400 $ 400 $ 400 $ 400 $ 400 $ 400 $ 350 Lin/Operations/Supply Chain Mgt 41
What happens if you change your order level to hedge against uncertainty?
Performance for all possible
Q
using Excel:
Order size Q
600 800 1000 1200 1400 1600 1800 2000 2200
2400
2600 2800 3000 3200 3400
Probability Demand = Q
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% Expected
units sold
600 799 996 1189 1373 1541 1686 1802 1886
1941
1973 1989 1996 1999 2000 Expected
units overstock
0 1 4 11 27 59 114 198 314
459
627 811 1004 1201 1400 Expected Profit Expected
units understock
1400 1201 1004 811 627 459 314 198 114
59
27 11 4 1 0
Expected
Profit
$ 120 $ 160 $ 199 $ 237 $ 273 $ 305 $ 331 $ 350 $ 360
$ 363
$ 360 $ 353 $ 344 $ 334 $ 323 $400 $360 $320 $280 $240
- C
o
= - 55
$200 $160 $120 600
+ 200 = C
u
800 1000 1200 1400 1600 1800 2000 2200 2400 2600
Order/Stock Quantity Q
2800 3000 3200 3400
Towards the newsboy model S
uppose you placed an order of 2000 units but you are not sure if you should order more.
What happens if I order one more unit (on top of
Q =
2000)?
Sell the extra unit with probability … Do not sell the extra unit with probability … Lin/Operations/Supply Chain Mgt DP = …..
DP = Expected profit from additional unit E( DP ) = …..
So? ... Order more?
43
•
The Value-maximizing Service Level
The newsvendor formula
In general: raise service level (i.e., order an additional unit)
if and only if
E(
DP
) =
(1-
SL
)
C u
–
SL
C o
> 0 Sell Do not sell Thus, optimal service level
SL
*
C u C
u C o p p
1 1
c p
2 (= Newsvendor formula) • Example: use formula for Palu-Gear Christmas order 1.
2.
SL * = So how much should Palu order then?
How does this compare to forecasted demand of 2000?
Lin/Operations/Supply Chain Mgt
Demand
1,000 1,200 1,400 1,600 1,800 2,000 2,200 2,400 2,600 2,800 3,000 3,200
Prob. Cum. Prob.
1% 1% 3% 6% 10% 13% 16% 16% 13% 10% 6% 3% 1% 1% 2% 5% 12% 21% 34% 50% 66% 79% 88% 95% 98% 99% 44
Accurate response: Find optimal
Q
from newsboy model
Cost of overstocking by one unit =
C
o – 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 =
C u
– 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
) <
C u
/ (
C
o +
C
u ) = smallest
Q
such that service level
F
(
Q
) > critical fractile
C u
/ (
C
o +
C
u ) Lin/Operations/Supply Chain Mgt 45
Where else do you find newsvendors?
Deciding on economic service level Benefits: Flexible Spending Account decision Capacity Mgt Lin/Operations/Supply Chain Mgt 46
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 47
Whistler Blackcomb Economics of Individual Lessons
Today 8:00am 12:00pm 3:00pm 5:00pm 9:00pm Tomorrow 8:00am Begin morning lessons (demand realized) Afternoon lessons begin Finish lessons for day Determine forecast demand and instructor requirements for tomorrow Call instructors to fill in or to call off Pre-bookings made for today 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.
Lin/Operations/Supply Chain Mgt 48
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 49
Whistler Blackcomb Analysis
If one too many instructors, must pay for two hours.
– C o = 2 × 40 = $80.
If one too few instructors, lose margin on a lesson.
– C u = 320 – (3 × 40 ) = 320 – 120 = $200.
Critical fractile = C u /(C o +C u )=200/(200+80) = 71.4%.
z 71.4
= Normsinv(0.714) = 0.5659.
Optimal decision for normal distribution:
Q = μ + z 71.4
× σ = 56 + 0.5659 × 3.12 = 57.7 ≈ 58
Lin/Operations/Supply Chain Mgt 50
Goal of a Supply Chain
Match Demand with Supply It is hard … Why?
Hard to Anticipate Demand Forecasts 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 Scale
There are fixed costs of ordering/production Q*= 2
SR H
Implications:
How fast cycle inventory grows if demand grows.
How much to invest in fixed cost reduction to reduce batch size.
Uncertainty
Forecast Error
Safety Stock Is
= z s R
L
Implications:
Is z (service level appropriate) Reduce Lead time Reduce s R
Seasonality
Implications:
Is z (service level appropriate) Reduce Lead time Reduce s R Where does s R come from?
Balance overstocking and understocking Newsboy Problem …
Critical Fractile = 1- P(stockout)
Customer Demand Uncertainty
Normal Variations… How do we deal with it?
Aggregation
•Physical •Information •Specialization •Component Commonality •Postponement
Bullwhip Effect
Causes
•Demand Signaling •Rationing •Batching •Promotions
How do we deal with it?
•Make the SC more visible •Align Incentives