OPSM 501: Operations Management

Week 11:

The Newsvendor Problem-ways to avoid mismatch

Koç University Graduate School of BusinessMBA Program

Zeynep Aksinzaksin@ku.edu.tr

Hammer 3/2 timeline and economics

Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Generate forecast of demand and submit an order

to TEC

Receive order from TEC at the

end of the month

Spring selling season

Left overunits are

discounted

Economics:• Each suit sells for

p = $180• TEC charges

c = $110 per suit• Discounted suits

sell for v = $90

The “too much/too little problem”:

– Order too much and inventory is left over at the end of the season

– Order too little and sales are lost.

Marketing’s forecast for sales is 3200 units.

The demand-supply mismatch cost

Definition – the demand supply mismatch cost includes the cost of left over inventory (the “too much” cost) plus the opportunity cost of lost sales (the “too little” cost):

The maximum profit is the profit without any mismatch costs, i.e., every unit is sold and there are no lost sales:

The mismatch cost can also be evaluated with

saleslost ExpectedC

inventory over left ExpectedC cost Mismatch

u

o

cpprofit Maximum

Mismatch cost = Maximum profit – Expected profit

Revisit Example 3:

Manufacturing cost=60TL,

Selling price=80TL, Discounted price (at the end of the season)=50TL

Market research gave the following probability distribution for demand.

Find the optimal q, expected number of units sold for this orders size, and expected profit, for this order size.

Demand Probability500 0.10600 0.2700 0.2800 0.2900 0.101000 0.101100 0.10

P(D<=n-1)00.10.30.50.70.80.9

Cu=20 Co=10P(D<=n-1)<=20/30=0.66

<=0.66 q=800

For q=800:E(units sold)=710E(profit)=13,300Max profit=20*770=15400

When is the mismatch cost high? Hammer 3/2’s mismatch cost as a percentage of the maximum profit is

$31,680/$223,440 = 14.2%

Mismatch cost as a percent of the maximum profit increases as …

– (1) the coefficient of variability of demand increases

– (2) the critical ratio decreases

Coefficientof variation 0.4 0.5 0.6 0.7 0.8 0.9

0.10 10% 8% 6% 5% 3% 2%0.25 24% 20% 16% 12% 9% 5%0.40 39% 32% 26% 20% 14% 8%0.55 53% 44% 35% 27% 19% 11%0.70 68% 56% 45% 35% 24% 14%0.85 82% 68% 55% 42% 30% 17%1.00 97% 80% 64% 50% 35% 19%

Critical ratio

Options to reduce the mismatch cost

Make to order Reactive Capacity

– Unlimited– Limited

7

Make-to-Stock Model

ConfigurationAssemblySuppliers

8

Assemble-to-Order Model

ConfigurationAssemblySuppliers

Unlimited, but expensive reactive capacity

Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Generate forecast of demand and submit 1st order to TEC

Receive 1st order from TEC at the end of Jan Spring selling season

(Feb – Jul)

Left overunits are

discounted

Oct

Receive 2nd

order from TEC at the end of Apr

Observe Feb and Mar sales and

submit 2nd order to TEC

Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Generate forecast of demand and submit 1st order to TEC

Receive 1st order from TEC at the end of Jan Spring selling season

(Feb – Jul)

Left overunits are

discounted

Oct

Receive 2nd

order from TEC at the end of Apr

Observe Feb and Mar sales and

submit 2nd order to TEC

TEC charges a premium of 20% per unit ($132 vs. $110) in the second order.

There are no restrictions imposed on the 2nd order quantity. O’Neill forecast of total season sales is nearly perfect after observing

initial season sales. How many units should O’Neill order in October?

12-9

Revisit Example 2: Finding Cu and Co

A textile company in UK orders coats from China. They buy a coat from 250€ and sell for 325€. If they cannot sell a coat in winter, they sell it at a discount price of 225€. When the demand is more than what they have in stock, they have an option of having emergency delivery of coats from Ireland, at a price of 290.

The demand for winter has a normal distribution with mean 32,500 and std dev 6750.

How much should they order from China??

Example 2: Finding Cu and Co

A textile company in UK orders coats from China. They buy a coat from 250€ and sell for 325€. If they cannot sell a coat in winter, they sell it at a discount price of 225€. When the demand is more than what they have in stock, they have an option of having emergency delivery of coats from Ireland, at a price of 290.

The demand for winter has a normal distribution with mean 32,500 and std dev 6750.

How much should they order from China??

Cu=75-35=40Co=25F(z)=40/(40+25)=40/65=0.61z=0.28 q=32500+0.28*6750=34390

Apply Newsvendor logic even with a 2nd order option

The “too much cost” remains the same:

– Co = c – v = 110 – 90 =20.

The “too little cost” changes:

– If the 1st order is too low, we cover the difference with the 2nd order.

– Hence, the 2nd order option prevents lost sales.

– So the cost of ordering too little per unit is no longer the gross margin, it is the premium we pay for units in the 2nd order.

• Cu = 132 – 110 = 22

Critical ratio:

Corresponding z-statistic (0.05)=0.5199, (0.06)=0.5239, so z = 0.06.

5238.02220

22

uo

u

CC

C

3263118106.03192 zQ

Profit improvement due to the 2nd order option

With a single ordering opportunity:– Optimal order quantity = 4101 units– Expected profit = $191,760– Mismatch cost as % of revenue = 4.9%

The maximum profit is unchanged = $223,440

With a second order option:– Optimal order quantity = 3263 units

– Reduction in mismatch cost = 38% (19,774 vs 31,680)– Mismatch cost as % of revenue = 3.1%

666,203$

43722$50820$440,223$

quantity entreplenishm secondExpectedC

inventory over left ExpectedC- profit Maximum profit Expected

u

o

Limited reactive capacity

Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Generate forecast of demand and submit 1st order to TEC

Receive both orders from TEC at the end of Jan Spring selling season

(Feb – Jul)

Left overunits are

discounted

Oct

Submit 2nd order to TEC

Observe pre-book orders

from retailers

Units in the 2nd order are no more expensive than in the 1st order

But there is limited capacity for a 2nd order

Sample of wetsuits

1st order must be at least 10,200 suits so that there is enough capacity for the 2nd order.

Also a minimum order quantity-order once What should we produce in the 1st order?

Sport Model Price Margin Discount

DIVE DIVE COMP 3/2 FULL 1100 660 0.60 120 38% 65%DIVE WMS 7000X 7MM FULL 600 360 0.60 275 38% 65%SURF EPIC 5/3 W/HD 800 296 0.37 225 38% 50%SURF HEAT 3/2 1200 444 0.37 110 38% 50%SURF HEATWAVE 4/3 700 259 0.37 140 38% 50%SURF ZEN-ZIP 4/3 3100 1147 0.37 165 38% 50%TRIATHLON TRIATHLON 4/3 FULL 2600 1690 0.65 210 45% 65%WAKE-BOARD REACTOR 3/2 1500 750 0.50 150 45% 65%WINDSURF CYCLONE 4/3 950 665 0.70 325 45% 65%WINDSURF WMS EVOLUTION 4/3 850 595 0.70 275 45% 65% = expected demand

= standard deviation of demand

Price = wholesale priceMargin = gross margin as a % of priceDiscount = anticipated end of season discount as % of price to sell left over inventory

Profit and mismatch with only 1 ordering opportunity

Use the Newsvendor model to evaluate the optimal order quantity, expected profit, maximum profit and mismatch cost

A suits produced in the 1st order earns the Newsvendor profit but a suit produced in the 2nd order earns the maximum profit.

Sport ModelOrder

quantityExpected

profitMaximum

profitMismatch

costDIVE DIVE COMP 3/2 FULL 1241 $30,086 $50,160 $20,074DIVE WMS 7000X 7MM FULL 677 $37,608 $62,700 $25,092SURF EPIC 5/3 W/HD 1009 $58,048 $68,400 $10,352SURF HEAT 3/2 1514 $42,568 $50,160 $7,592SURF HEATWAVE 4/3 883 $31,604 $37,240 $5,636SURF ZEN-ZIP 4/3 3910 $164,953 $194,370 $29,417TRIATHLON TRIATHLON 4/3 FULL 3449 $164,582 $245,700 $81,118WAKE BOARD REACTOR 3/2 1877 $75,536 $101,250 $25,714WINDSURF CYCLONE 4/3 1284 $89,538 $138,938 $49,399WINDSURF WMS EVOLUTION 4/3 1149 $67,788 $105,188 $37,399Total 16993 $762,311 $1,054,105 $291,794

12-16

Produce “safer” products early, produce “risky” products with reactive capacity

Sort items by their mismatch cost to order quantity ratio. Fill the 1st order up to the minimum quantity (10,200) with the items that have the lowest mismatch – quantity ratio

The mismatch cost is reduced by 66%!

ModelOrder

quantity

Newsvendorexpected

profitMismatch

cost

Mismatch cost-order quantity

ratioFirst order

quantity ProfitHEAT 3/2 1514 $42,568 $7,592 5.0 1514 $42,568HEATWAVE 4/3 883 $31,604 $5,636 6.4 883 $31,604ZEN-ZIP 4/3 3910 $164,953 $29,417 7.5 3910 $164,953EPIC 5/3 W/HD 1009 $58,048 $10,352 10.3 1009 $58,048REACTOR 3/2 1877 $75,536 $25,714 13.7 1877 $75,536DIVE COMP 3/2 FULL 1241 $30,086 $20,074 16.2 1241 $30,086TRIATHLON 4/3 FULL 3449 $164,582 $81,118 23.5 0 $245,700WMS EVOLUTION 4/3 1149 $67,788 $37,399 32.6 0 $105,188WMS 7000X 7MM FULL 677 $37,608 $25,092 37.1 0 $62,700CYCLONE 4/3 1284 $89,538 $49,399 38.5 0 $138,938Total 16993 $762,311 $291,794 10434 $955,320

12-17

18

Push-Pull Supply Chains

Push-Pull Boundary

PUSH STRATEGY PULL STRATEGY

Low Uncertainty High Uncertainty

The Supply Chain Time Line

CustomersSuppliers

19

A new Supply Chain Paradigm

A shift from a Push System...– Production decisions are based on forecast

…to a Push-Pull System– Parts inventory is replenished based on forecasts– Assembly is based on accurate customer demand

20

Demand Forecast

The three principles of all forecasting techniques:

– Forecasts are always wrong– The longer the forecast horizon the worst is the

forecast – Aggregate forecasts are more accurate

• The Risk Pooling Concept

21

Business models in the Book Industry

From Push Systems...– Barnes and Noble

...To Pull Systems– Amazon.com, 1996-1999

And, finally to Push-Pull Systems– Amazon.com, 1999-present

• Around 40 warehouses

22

Business models in the Grocery Industry

From Push Systems...– Supermarket supply chain

...To Pull Systems– Peapod, 1989-1999

• Stock outs 8% to 10%

And, finally to Push-Pull Systems– Peapod, 1999-present

• Dedicated warehouses• Stock outs less than 2%

23

Locating the Push-Pull Boundary

24

Organizational Skills Needed

RawMaterial Customers

PullPush

Low Uncertainty

Long Lead Times

Cost Minimization

Resource Allocation

High Uncertainty

Short Cycle Times

Service Level

Responsiveness

25

Speculative Production capacity

ReactiveProduction capacity

Initial forecast Later orders

Low Risk: Push High Risk: Push-Pull

O’Neill: quick response (reactive capacity)

Announcement

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