# News Vendor Model Explanation

Topics: Normal distribution, Standard deviation, Cumulative distribution function Pages: 12 (2150 words) Published: November 1, 2011
Newsvendor Model
Chapter 9

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Learning Goals
 Determine

the optimal level of product availability

– Demand forecasting – Profit maximization
 Other

measures such as a fill rate

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O‟Neill‟s Hammer 3/2 wetsuit

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Hammer 3/2 timeline and economics
Generate forecast of demand and submit an order to TEC

Economics:
• • • Each suit sells for p = \$180 TEC charges c = \$110/suit Discounted suits sell for v = \$90

Spring selling season

Nov Dec Jan

Feb Mar Apr May Jun

Jul Aug

Receive order from TEC at the end of the month

Left over units are discounted

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.
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Newsvendor model implementation steps
 Gather

economic inputs:

– selling price, – production/procurement cost, – salvage value of inventory

 Generate

a demand model to represent demand

– Use empirical demand distribution – Choose a standard distribution function » the normal distribution, » the Poisson distribution.

 Choose

an objective:

– maximize expected profit – satisfy a fill rate constraint. utdallas.edu/~metin

 Choose

a quantity to order.

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The Newsvendor Model: Develop a Forecast

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Historical forecast performance at O‟Neill
7000 6000 5000

Actual demand

.

4000 3000 2000 1000 0 0 1000 2000 3000 4000 5000 6000 7000

Forecast
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Forecasts and actual demand for surf wet-suits from the previous season

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How do we know the actual when the actual demand > forecast demand  If

we underestimate the demand, we stock less than necessary.  The stock is less than the demand, the stockout occurs.  Are the number of stockout units (= unmet demand) observable, i.e., known to the store manager? – Yes, if the store manager issues rain checks to customers. – No, if the stockout demand disappears silently.  No

implies demand filtering. That is, demand is known exactly only when it is below the stock.  Shall we order more than optimal to learn about demand when the demand is filtered? utdallas.edu/~metin

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Empirical distribution of forecast accuracy Order by A/F ratio Actual demand Product description Forecast JR ZEN FL 3/2 90 140 EPIC 5/3 W/HD 120 83 JR ZEN 3/2 140 143 WMS ZEN-ZIP 4/3 170 163 HEATWAVE 3/2 170 212 JR EPIC 3/2 180 175 WMS ZEN 3/2 180 195 ZEN-ZIP 5/4/3 W/HOOD 270 317 WMS EPIC 5/3 W/HD 320 369 EVO 3/2 380 587 JR EPIC 4/3 380 571 WMS EPIC 2MM FULL 390 311 HEATWAVE 4/3 430 274 ZEN 4/3 430 239 EVO 4/3 440 623 ZEN FL 3/2 450 365 HEAT 4/3 460 450 ZEN-ZIP 2MM FULL 470 116 HEAT 3/2 500 635 WMS EPIC 3/2 610 830 WMS ELITE 3/2 650 364 ZEN-ZIP 3/2 660 788 ZEN 2MM S/S FULL 680 453 EPIC 2MM S/S FULL 740 607 EPIC 4/3 1020 732 WMS EPIC 4/3 1060 1552 JR HAMMER 3/2 1220 721 HAMMER 3/2 1300 1696 HAMMER S/S FULL 1490 1832 EPIC 3/2 2190 3504 ZEN 3/2 3190 1195 ZEN-ZIP 4/3 3810 3289 WMS HAMMER 3/2 FULL 6490 3673 * Error = Forecast - Actual demand ** A/F Ratio = Actual demand divided by Forecast Error* A/F Ratio** -50 1.56 37 0.69 -3 1.02 7 0.96 -42 1.25 5 0.97 -15 1.08 -47 1.17 -49 1.15 -207 1.54 -191 1.50 79 0.80 156 0.64 191 0.56 -183 1.42 85 0.81 10 0.98 354 0.25 -135 1.27 -220 1.36 286 0.56 -128 1.19 227 0.67 133 0.82 288 0.72 -492 1.46 499 0.59 -396 1.30 -342 1.23 -1314 1.60 1995 0.37 521 0.86 2817 0.57

100% 90% 80% 70%
Probability

60% 50% 40% 30% 20% 10% 0% 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 A/F ratio Empirical distribution function for the historical A/F ratios.

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Normal distribution tutorial
 

All normal distributions are characterized by two parameters, mean = m and standard deviation = s All normal distributions are related to the standard normal that has mean = 0 and...