Newsvendors Tackle the Newsvendor Problem

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• Newsvendors Tackle the Newsvendor Problem
• Martin A.
  Koschat
• AOL Time Warner
• Syracuse University, SOM
• Faculty Seminar
• March 26, 2001

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Time Inc., Retail Sales and Marketing

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The Business According to AA
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The Business According to MAK

• The ratio of advertising revenue vs. circulation
  revenue varies over time.
• Newsstand revenue accounts for 25 of Time Inc.s
  circulation revenue.
• Newsstand profits account for 33 of Time Inc.s
  circulation profits.

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The (classical) Newsboy Problem

• Optimal draw allocation depends on
• Marginal cost (m)
• Revenue per copy sold (r)
• Distribution of demand (f)

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The Principle of Marginal Efficiency

• Consider a representative sales pattern for one
  store for 12 issues.
• Assume that for all 12 issues draw was equal to
  10 copies.
• In summary, there is a total draw of 120 copies
  and total sales of 54 copies for an overall
  efficiency of 45.

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The Principle of Marginal Efficiency

• Rank order issues by sales.
• Shipping 10 copies per issue instead of 9 copies
  resulted in an overall draw increase of 12
  copies, but resulted in an overall sales increase
  of only 1 copy.
• The marginal efficiency at a draw of 9 is
  therefore ?S/?D
  1/12 8.
• The marginal efficiency also equals the sell-out
  probability.

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Store-level Allocation

• Assume that a wholesaler has received D copies
  that need to be distributed across N stores with
  respective demand distributions Fi.
• The profit maximizing draw allocation for store i
  is
• di Fi-1(?)
• where ? has to be chosen such that ?di
  D.
• In practice, the allocation is made via a formula
  file.
• If the formula file is chosen properly, this
  procedure provides an allocation that is close to
  optimal.

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Store-level Allocation cont.
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Wholesaler Allocation

• Assume that the national print order for an issue
  has been determined to be D.
• D is optimally allocated across N wholesalers, if
  each wholesaler has the same marginal efficiency.
• Since the marginal efficiency is not easily
  determined, the gross efficiency is used as a
  proxy.

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Wholesaler Allocation Estimating Marginal
Efficiency

• One can conduct a market experiment.
• If store level draw and sales data are available,
  one can conduct a pseudo market experiment.

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Wholesaler Allocation Marginal vs. Gross
Efficiency

• For 40 wholesalers store level data were
  available.
• The marginal efficiencies were estimated by a
  pseudo-market experiment.

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National Print Order

• The national print order is determined with
  consideration of the marginal efficiency.
• In addition, there are other business
  considerations that affect the size of the
  national print order.

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Distribution of demand - Parameters

• Search within parametric classes of distribution
• Frequently used parameters -location and
  dispersion
• Explore relation between location and dispersion

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Distribution of demand - Parameters

• B-FM B-SV SD-FM SD-SV
• Sports Ill. .11 .06 .96
  1.10
• People -.03
  -.03 .68 .71
• Time .01 -.14 1.22
  1.42
• EW .26 .23
  1.06 1.15
• Estimated bias and standard deviation for the
  median based estimator (FM) and the sample
  variance (SV).
• Comparison is on a log-scale for a
  pr-period covering the first half of 1997 and a
  post-period covering the
• second half of 1998. Comparison involves
  raw data for 18,000 stores.

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Distribution of demand - Shape

• Shape of the distribution
• Theoretical and practical research suggests the
  use of power transformations
• Fourth root transformation transforms data to
  near Normality

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Distribution of demand - Censoring
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Distribution of demand - Summary

• If the fraction of censored observations is not
  too large, the median and the inter-quartile
  range of the distribution of sale is also the
  median and inter-quartile range of the
  distribution of demand.

• Thus, in most instances the median of sale
  provides a comprehensive summary of the
  distribution of demand.

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Distribution of demand - Implications

• The optimal draw allocation at the store level is
  therefore a function of the median of sale - in
  practice, a function of the historical median of
  sale for a particular time period.
• If the store-level distributions of demand are
  known, expected sales under different draw
  allocation procedures can be calculated.
• Different procedures can be compared.
• In particular, approximate procedures can be
  compared with the optimal procedure.

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Results Sales Lift

•  
•  
•  

Percent Sales Due to Improved Due to
Improved Lift Formula File
Wholesaler Alloc. People 1.38
0.58 0.80 Sports Illustrated
1.26 0.56 0.70 Entertainment
Weekly 1.22 0.62
0.60 Time 1.10 0.41
0.40 Money 1.05 0.79
0.26 Fortune 0.94 0.30
0.64 Parenting 0.82 0.26
0.56 InStyle 0.73 0.44
0.29 Life 0.69 0.39
0.30 Sunset 0.49 0.26
0.23 Teen People 0.47 0.30
0.17
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The Channel Problem

• A producer and a distributor share the revenue r
  of one unit sold that is rp rp r.
• For the producer and distributor the respective
  marginal cost per unit are cp and cp. The cost
  of producing and distributing one unit is cp cp
  c.

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The Channel Problem

• The optimal production level Dp for the producer
  is
• Dp H-1 (cp /rp)

• The optimal distribution level Dd for the
  distributor is
• Dd H-1 (cd /rd)

• The actual production/distribution level D
  satisfies
• min( Dp, Dd ) ? D ? max( Dp, Dd )

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The Channel Problem

• The channels profits are maximized if
• Dp Dd
• cp /rp cd /rd
• The channels profits are maximized if the
  revenues are split in proportion to the marginal
  costs.
• The channel member with the smaller marginal cost
  receives a smaller share of the revenue.

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The Channel Problem

• An alternative way of maximizing the channels
  profits is through a per unit transfer payment t
  either to or from the producer to the distributor
• - cp lt t lt cd
• The effective net cost for the producer and the
  distributor are, respectively,
• cp cp t
• cd cd - t

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The Channel Problem

• The magnitude of the transfer payment determines
  the revenue split between producer and
  distributor.
• The channel member that carries the larger share
  of cost reaps corresponding rewards.