Supply Chain ManagementManaging the Supply Chain

Key to matching demand with supplyCost and Benefits of inventory

Economies of ScaleInventory management of a retailer: EOQ + ROP Levers for improvement

Safety StockHedging against uncertaintyRole of lead time

Improving PerformanceCentralization & Pooling efficienciesPostponementAccurate Response

What is a Supply Chain?

What makes a “good” Supply Chain?

The Procurementor supply system

The OperatingSystem The Distribution System

Raw Materialsupply points Movement/

Transport

Raw MaterialStorage Movement/

TransportMovement/Transport

PLANT 1

PLANT 2

PLANT 3

WAREHOUSE

WAREHOUSE

WAREHOUSE

Movement/Transport

MARKETS

ManufacturingFinished GoodsStorage

A

B

C

Corporate FinanceCISCO SELECTRON

Current Assets BS/ 2000 BS/2000

Cash &

Equivalents

4,234 1,475.5

Short-term investments 1,291 958.6

AR 2,299 2,146.3

Inventories 1,232 %11 3,787.3 %44

Deferred Income 2,054 260.5

Total Current Assets 11,110 8,628.2

Inventories represent about %34 of current assets for a typical company in the US; %90 of working capital.

For each dollar of GNP in the trade and manufacturing sector, about 40cents worth of inventory was held.

Average logistics cost = 21c/dollar = %10.5 of GNP.

4

Another example of financial flows at the corporate level: Mobile Handsets

Data:– End of quarter inventory position from 10Q statements– Sales from income statement (smooth 9month avg.)

How can financial flows help explain the difference in performance during the downturn?

199912/31/99 3/31/00 6/30/00 9/30/00 12/31/00 3/31/01 6/30/01 9/30/01

1,786$ 1,925$ 2,290$ 2,062$ 2,014$ 1,985$ 1,622$ 1,774$ 1,437$ 1,437$ 1,437$ 1,437$ 1,437$ 1,692$ 1,692$ 1,692$ 1.24 1.34 1.59 1.43 1.40 1.17 0.96 1.05

Ericson ($M) Inventory 3,016$ 4,031$ 4,612$ 4,984$ 4,671$ 4,667$ 2,947$ 2,647$ 486$ 486$ 486$ 486$ 486$ 245$ 245$ 245$ 6.20 8.29 9.48 10.25 9.60 19.02 12.01 10.79

3,707$ 4,688$ 5,446$ 5,557$ 5,242$ 4,533$ 3,842$ 3,250$ 1,088$ 1,088$ 1,088$ 1,088$ 1,088$ 830$ 830$ 830$ 3.41 4.31 5.01 5.11 4.82 5.46 4.63 3.91

2000 2001

Time (months)Motorola ($M) Inventory

Sales per month (9 month avg)Time (months)

Nokia ($M) InventorySales per month (9 month avg)Time (months)

Sales per month (9 month avg)

5

Mobile Handsets: How explain the difference in performance?

$-

$1B

$2B

$3B

$4B

$5B

$6B

8/28/99 12/6/99 3/15/00 6/23/00 10/1/00 1/9/01 4/19/01 7/28/01 11/5/01

Nokia

Ericson

Motorola

Inventory

$-

$1B

$2B

$3B

$4B

$5B

$6B

8/28/99 12/6/99 3/15/00 6/23/00 10/1/00 1/9/01 4/19/01 7/28/01 11/5/01

Nokia

Ericson

Motorola

Inventory

0

2

4

6

8

10

12

14

16

18

20wks

8/28/99 12/6/99 3/15/00 6/23/00 10/1/00 1/9/01 4/19/01 7/28/01 11/5/01

Nokia

Ericson

Motorola

Flow Time

0

2

4

6

8

10

12

14

16

18

20wks

8/28/99 12/6/99 3/15/00 6/23/00 10/1/00 1/9/01 4/19/01 7/28/01 11/5/01

Nokia

Ericson

Motorola

Flow Time

Solectron’s executive officer compensation plan

• Base compensation• Bonuses

– “The Bonus Plan provides for incentive compensation ... based on certain worldwide, site and individual performance measures. Worldwide and site performance are measured based on targets w.r.t. profit before taxes, inventory turns, days sales outstanding and return on assets. The Compensation Committee believes that these factors are indicative of overall corporate performance and shareholder value.” [compensation committee report FY 96]

• Long Term Incentive Compensation

Supply Chain Metrics

Costs of not Matching Supply and Demand

• Cost of overstocking – liquidation– obsolescence– holding

• Cost of under-stocking – lost sales and customer goodwill– lost margin

Why hold Inventory?

• Economies of scale– Fixed costs of ordering/manufacturing

– Quantity discounts

– Trade Promotions

• Uncertainty– Information Uncertainty

– Supply/demand uncertainty

• Seasonal Variability• Strategic

– Flooding, availability

Cycle/Batch stock

Safety stock

Seasonal stock

Strategic stock

Cost of Inventory

• Physical holding cost

(out-of-pocket)

• Financial holding cost

(opportunity cost)

• Low responsiveness– to demand/market

changes– to supply/quality changes

Holding cost (H)

Costs Associated with Batches

• Ordering costs (S) – Changeover of production line (Set-up)– Transportation (Delivery)– Receiving

• Holding costs (H = r C)– Physical holding cost– Cost of capital (r)– Cost of obsolescence

Palü Gear: Retail Inventory Management

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. For each order up to 5000 jackets, the manufacturer charges a flat fee of $2,200 for delivery. To exploit economies of scale, stores typically orders 1500 jackets each time it places an order. (Palü’s cost of capital is approximately 20%.) What order size would you recommend for a Palü store in current supply network?

Palü Gear: Evaluation of current policy of ordering 1500 units each time

1. What is average inventory I? I = Annual cost to hold one unit H = Annual cost to hold I =

2. How often do we order? Annual throughput R = # of orders per year = Annual order cost =

3. What is total cost? TC =

Can we do better ?

Find the most economical order quantityMethod 1 : Enumerate

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

Economies of Scale: Inventory Build-Up Diagram

R: Annual demand rate (units/yr),

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

R = Demand rate

Inventory

Ttime between

ordersOrder placed, arrives immediatelyLead time=0

Order placed, arrives immediatelyLead time=0

T = Q/R

Economic Order Quantity EOQ

R : Demand per year,

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

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

Q : Order quantity.

C : Cost per unit ($/unit),

r : Cost of capital (% / yr),

H

SRQEOQ

2

Batch Size Q

Total annual costs

H Q/2: Annual holding cost

S R /Q:Annual setup cost

QEOQ

SRH2

What do we learn from the EOQ formula ? How does the ordering policy change if …

The product is a success and the demand picks up, now we are selling 4 times the original demand…

The interest rates double up, so does our unit inventory holding costs …

After investing in IT, we manage to reduce our fixed ordering cost by half …

Optimal Economies of Scale: For a Palü Gear retailer

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

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

Unit annual holding cost = H = $50/unit-yr

Optimal order quantity = EOQ = 520 units

Number of orders per year = R/Q = 3077/520 = 5.91

Time between orders = Q/R = 8.78 weeks

Annual order cost = (R/Q)S = $13,018/yr

Average inventory I = Q/2 = 260 units

Annual holding cost = (Q/2)H = $13,018/yr

Take-Aways I 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.

– To reduce batch size by a factor of 2, setup cost has to be reduced by a factor of 4.

Role of Supply 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:

Order placed

Order arrives

2wks

ROP

ROP =

1. How much to order ? Answer: EOQ

2. When to place an order ? Answer: ROP Reorder Point represents the amount of inventory on hand when we place a new order .

Delivery Lead Time = 0 (Instantaneous Delivery) then ROP = …….Delivery Lead Time > 0 then ROP = …….

ROP is driven by:Delivery Lead Time

Demand Uncertainty Customer Service Level

Two Key Decisions of Inventory Management

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

Demand uncertainty and forecasting

Year Demand Forecast Error

• 1 323

• 2 258

• 3 303

• 4 304

• 5 284

• 6 285

Demand uncertainty and forecasting• Forecasts depend on

– historical data– “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.

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 normally distributed. Recall that average weekly demand was about 60 jackets; the order lead time is 2 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

(ROP =120), 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%?

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. What is the probability that we run out of stock before a delivery arrives?

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

Consider the lead time between the placement of an order and the arrival of the order. L=2 weeks.Demand per week, R ~ (60, 30)

The mean demand during the lead time = 2*60 = 120

Standard deviation of demand during lead time

= (30)2 + (30)2

= 30 2

D lead time ~ N (120, 30 )2

Lead Time Demand

120Mean Demand

During Lead Time

IF ROP=120Probability of stock out (i.e., Probability that the demand duringlead time is greater than 120 ) = ?

Lead time demand distribution

ROP

Increase reorder pointabove average demand during lead time, lower the probability of stockout! BETTER SERVICE LEVEL!

SAFETY STOCK

Safety stock increase with the service level.

e.g., % 95

Less demand variabilitySmall variance / SD

120

%95

ROP

120

Higher VariabilityLarger SD/ variance

%95

ROP

Safety stock increaseswith the variance (SD) of lead time demand

Safety Stock

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 *

Palü Gear: Determining the required Reorder Point for 95% service

DATA:

R = 60 jackets/ week R = 30 jackets/ week

H = $50 / jacket, year standard deviation of weekly demand

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 lead time demand = 42.42

2. Required # of standard deviations z* = 1.64

3. Reorder Point = 120+1.64*42.42= 190 jackets

4. Safety stock Is = 1.64*42.42=70 jackets

Review of ProbabilityThe standard normal distribution F(z)

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.0 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*.

Safety Stocks

EOQ

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)

EOQ

Is

0

L

Comprehensive Financial Evaluation:Inventory Costs of Palü Gear

1. Cycle Stock (Economies of Scale)

1.1 Optimal order quantity =

1.2 # of orders/year =

1.3 Annual ordering cost per store = $13,009

1.4 Annual cycle stock holding cost. = $13,0092. Safety Stock (Uncertainty hedge)

2.1 Safety stock per store = 70

2.2 Annual safety stock holding cost = $3,5003. Total Costs for 5 stores = 5 (13,009 + 13,009 + 3,500)

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

How to find service level (given ROP)?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() = Demand during the lead time is normally distributed

with mean = RL and standard deviations RL

1. Given ROP, find SL = Cycle service level = P(stock out)

= P(demand during lead time >ROP)

= 1-F(z*= (ROP- )/) [use table]

= 1- NORMDIST(ROP, , , True) [or Excel]

2. Given SL, find ROP = + Is

= + z* [use table to get z* ]

= NORMINV(1-SL, , ) [or Excel]

Safety stock Is = z* Reorder point ROP = + Is

Take-Aways IIDemand Uncertainty & Inventory Management

Cycle Cost : EOQ: How much to order?Balance the fixed costs of ordering with the average

inventory holding cost.Total Cycle Cost are quiet robust to misestimating the

parameters Growth brings scale economies, adjust operating policies as markets conditions change.

Safety Stock Cost: Reorder Point : When to place an order? Uncertainty is nothing but forecasting error.Determined by the Service Level P(D(lead time)>ROP)ROP=RxL+Safety Stock

Distribution Centralization

Product Postponement (HP)

Process Postponement (Benetton)

Capacity Analysis (Benetton)

Improving The Supply Chain

How can we reduce supply chain costs without sacrificing customer service?

How can we improve customer service without increasing supply chain costs?

Is=400

Centralization Distribution

Improving Supply Chain Performance:1. The Effect of Pooling/Centralization

Is=100Is=100

Is=100Is=100

Decentralized Distribution

Is= 400

Centralized vs. Decentralized Distribution

Pros Cons

Palü Gear’s Internet restructuring:Centralized inventory management

Weekly demand per store= 60 jackets/ week with standard deviation = 30 / week

H = $ 50 / jacket, year S = $ 2,200 / order Supply lead time L = 2 weeksService level : 95% availability.

Palü Gear now is considering restructuring to an Internet store. So 5 local stores will be closed and a National DC will be opened to distribute direct to customers.

Demand R per week for each storess

Demand during Supplier lead time (L=2)

ltdltd

Safety Stock for each store (%95 availability)

Total Safety Stock

Compare the safety stock in the decentralized and centralized systems

Demand R per weekfor the centralized warehouse cc

Demand During Supplier Lead Time(L=2)

ltdltd

Safety Stock for the centralized warehouse(%95 availability)

Decentralized Centralized – 5 stores

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 = $29,0891.4 Annual cycle stock holding cost = $29,089

2. Safety Stock (Uncertainty hedge)2.1 Safety stock for e-store =

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

3. Total Costs for consolidated e-store = 29,089 + 29,089 + 7,800 = $65,980

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).

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

Benetton’s Production and Distribution Network

Tailored Inventories: Postponement

• Simple solution– Produce all garments as Greige goods

(Production cost is 10% higher)

• Tailored solution– Base load manufactured from colored thread

(cheaper but long lead time sourcing)– Safety stock held as Greige goods and

manufactured on demand (10% more expensive but short lead times)

Process Postponement

Dyeing2 wks

Knitting2 wks

Make to Stock Dye to Order

Dyeing2 wks

Postponement and Re-assortment:The Advantage to Forecasting

0

500

1000

1500

2000

2500

3000

3500

4000

0 500 1000 1500 2000 2500 3000 3500 4000

0

500

1000

1500

2000

2500

3000

3500

4000

0 500 1000 1500 2000 2500 3000 3500 4000

0

500

1000

1500

2000

2500

3000

3500

4000

0 500 1000 1500 2000 2500 3000 3500 4000

Initial Forecast Updated Forecast after observing 20% of sales after 80%

Actual total sales

Each data point represents the forecast and the actual season sales for a particular item (at the style-color level).

Reactive CapacityShort Lead Time - expensive

Speculative CapacityLong Lead Time cheap

How do we decide on the size of the speculative capacity?

Commit before observing the demand

Gamble!

Commit after observing the early sales data

Benetton: Two types of Production Capacities

• Palü Gear’s is planning to offer a special line of winter jackets, especially designed as gifts for the Christmas season. Each Christma-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?

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 and Accurate Response to Demand Uncertainty when you can order only once:

Optimal Service Level and Accurate Response: with Excel(1) Performance for a given order Q, say Q = 2000

Stock: 2000

DemandProbability of Demand

units sold

units overstock

units understock Profit

800 1% 800 1200 0 940001000 1% 1000 1000 0 1450001200 3% 1200 800 0 1960001400 6% 1400 600 0 2470001600 10% 1600 400 0 2980001800 13% 1800 200 0 3490002000 16% 2000 0 0 4000002200 16% 2000 0 200 4000002400 13% 2000 0 400 4000002600 10% 2000 0 600 4000002800 6% 2000 0 800 4000003000 3% 2000 0 1000 4000003200 1% 2000 0 1200 400000

Expected: 1825.6 141.6 240.0 357331

Optimal Service Level and Accurate Response : with Excel(2) Performance for all possible Q

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 modelSuppose you placed an order of 2000 units but you are not sure about whether you should have ordered one more unit.

What is the contribution of ordering an additional unit?

Expected contribution of an additional unit E() = ………………..

Earn a margin (p-c) = B with propability (1-p)=

P(D>2000)

= ..

Incur an overage cost of (c-s) = C with probability p = P(D<=2000)

= …..

So? ... Order more?

Marginal CostMarginal Benefit

Accurate Response: The newsboy model

In general: at the optimal Q E() <= 0 – no incentives to order more

(1-p)B = pC

Sell Do not sell

Equivalently, choose the smallest Q such that

p = P(D<Q) = F(Q) >= B / (B+C)

Example:• Critical fractile

B / (B+C) =

• Find Q by rounding up!Q =

Expected Profit ($k)

120130140150160170180190200210220230

10001200140016001800200022002400260028003000

Order/Stock Quantity Q

+ 200 = Cu

- Co = - 55

Accurate response:Find optimal Q from newsboy model

Cost of overstocking by one unit = C– 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 = B – 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) < B / (B + C)

= smallest Q such that service level F(Q) > critical fractile B / (B + C)

Where else do you find newsboys?

Benefits: Flexible Spending Account decision ATM Perishable Products (Newspaper, Medical Supplies,

Fashion Goods) Weddings, Conferences…

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 do we hold inventory?

Economies of Scale

Manage the trade-off between Ordering cost and Inventory Holding Cost

Q*=

UncertaintyForecast Error

Safety Stock Is= zR

H

SR2

Implications:

• As long as you are in the flat region you are doing fine.

•Growth brings economies of scale, hence should reflect that into ordering decisions.

•To reduce the order size n times,One has to cut the fixed cost per order by n2 times (the square root formula!)

L

SUPPLY CHAIN MANGEMENT

ROP & Rules of Forecasting

Uncertainty~ Probability Distribution (Mean, SD)Demand Uncertainty During Lead Time (L)

Shorter Horizon less UncertaintyAggregate Forecasts, less uncertain

How do we deal with uncertainty?

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

Customer Demand UncertaintyNormal Variations…

How do we deal with it?

Aggregation•Physical•Information•Specialization•Component Commonality•Postponement

Bullwhip EffectCauses•Demand Signaling•Rationing•Batching•Promotions

How do we deal with it?

•Make the SC more visible•Align Incentives

Balance overstocking and understockingNewsboy Problem … Critical Fractile = 1- P(stockout)