Expert answer:paper more
Expert answer:a.Brown also considered whether it was possible to fit a normal probability distribution to the historical demand.i.What are the mean and standard deviation of the demand for the SKU? (The normal distribution is completely specified once the mean and standard deviation are known.)ii.Generate a histogram of the observed demand values for the Great White …iii.Compare the cumulative frequencies of your histogram with those of the histogram of a normal distribution with mean 40 and standard deviation 20 shown in Exhibit 1. (The histogram is also copied into columns Q – S in the Analysis #2 worksheet.) Comment on the fit of the normal distribution to the demand for great white.b.The inverse cumulative function of a demand distribution takes an in-stock rate and returns the order-up to-point that gives this in-stock rate.1 Create a table of order-up-to points for given in-stock ratesc.Construct a table of fill rates given inventory order points…d.Calculate the order-up-to point that has in-stock rate just greater than or equal to the critical fractile described in #1(b-iii) using the method described in Analysis #2(b).
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9-606-023
REV: JANUARY 7, 2009
NOEL WATSON
Paper and More (A)
January 10, 1998
Kevin Brown grudgingly lowered the volume on Miles Davis’ “Round About Midnight”1 and
resumed his work – reviewing his expansion plans for augmenting Paper and More’s sole store in
Jamaica, Vermont with at least eight more stores over the next two and a half years. In one month
Brown would be meeting with venture capitalist funding broker Mathew Abraham, who in
preliminary talks had emphasized the importance of establishing how store operations would scale
with the expansion. The rough plans under Brown’s pencil included ideas for siting stores,
marketing, working with suppliers, product assortment, and store inventory management.
Fresh out of business school and recently married, Brown had opened the first Paper and More
(P&M) store in 1995 using his personal finances. Operated as an office supply store that catered to
small businesses and home office users, P&M supplemented with printer supplies the many different
paper products it sold. These included paper for home and office printing and writing, text and
cover stocks (for external correspondence), and such other products as forms, envelopes, file folders,
index cards, tags, tickets, and pressure-sensitive and other special papers. Brands included
International Paper, Crane, Xerox, Georgia Pacific, Weyerhaeuser, and Fox River. Brown’s expansion
plans also included introducing P&M’s own store brand of paper.
Brown and Abraham, who, united by a love for Miles Davis, had been friends in business school,
had met at the end of October 1997 to discuss the expansion plans for P&M. Abraham advised
Brown that his proposals needed to address (i) up-front store costs, that is, the costs of opening each
new store, including siting, storefront development, and inventory; (ii) economies of scale associated
with opening each store; and (iii) the potential to successfully operate in different markets.
Explaining that the way in-store inventory was managed would have implications for up-front costs
and operating potential and the way the supply chain was managed for economies of scale, Abraham
suggested that were Brown successful in getting funding, a management team with a track record in
inventory management should be brought in. Brown insisted, though, that because inventory
management was core to his business model, he needed to better understand the dynamics of
matching inventory to demand.
1 Legacy Records, 1956.
________________________________________________________________________________________________________________
Professor Noel Watson prepared the original version of this case, “Paper and More,” HBS No. 604-093. This version was prepared by Professor
Noel Watson. Professor Ananth Raman and Professor Marshall Fisher (Wharton School) provided instrumental guidance. HBS cases are
developed solely as the basis for class discussion. Certain details are fictional. Cases are not intended to serve as endorsements, sources of
primary data, or illustrations of effective or ineffective management.
Copyright © 2005-2007, 2009 President and Fellows of Harvard College. To order copies or request permission to reproduce materials, call 1-800545-7685, write Harvard Business School Publishing, Boston, MA 02163, or go to http://www.hbsp.harvard.edu. No part of this publication
may be reproduced, stored in a retrieval system, used in a spreadsheet, or transmitted in any form or by any means—electronic, mechanical,
photocopying, recording, or otherwise—without the permission of Harvard Business School.
This document is authorized for use only by Abdulaziz Qumosani in Operations Management Fall 2016-1 taught by Askar, Dominican University – Illinois from August 2017 to February 2018.
For the exclusive use of A. Qumosani, 2017.
606-023
Paper and More (A)
Store Operations
For the past two years Brown had sought to create and preserve goodwill by maintaining high
inventory levels for printing supplies and paper. P&M assessed inventory levels and placed orders
for paper products every other Saturday. The P&M store was conveniently located within three
hours of its product distributors in Vermont and New Hampshire, enabling orders dispatched by the
end of the business day (3 p.m. on Saturday) to be received by the 10 a.m. store opening on Monday
(the store was closed on Sundays).
Considering how inventory might be managed more systematically in anticipation of expansion,
Brown realized that there were advantages to the current store location that might not carry over to
other locations. He nevertheless wondered whether his experience to date might help him gain a
better appreciation for inventory-demand dynamics. For example, two years’ worth of historical
sales information for paper products might be used to simulate store performance under different
assumptions about inventory policies. Brown subsequently undertook a series of analyses.
Note: For the following analyses, please use the Paper and More Excel workbook distributed
with the case. Each worksheet tab identifies the analysis to which the worksheet corresponds. The
Data Tables and Solver routines have been preset in the worksheets to minimize the effort
required to run the Excel analysis tools. Saving often is highly advised when performing these
analyses.
Note: Instructions for both Microsoft Excel 2003 and 2007 (where instructions for Excel 2007 are
different they are placed in parentheses) are included in this case.
Analysis #1
Brown decided to analyze sales for a staple brand for office and home printing: Great White
Multi-Use 20-lb. 8½” x 11” 90 Bright from International Paper. Brown did not make much money on
this stock-keeping unit (SKU), but he thought the product was important because it helped drive
overall store traffic. The product’s wholesale price was $20.00 per ream (500 sheets), which P&M
retailed for $21. Brown estimated his annual inventory-carrying costs for paper products at 25% of
the product’s wholesale price.
For the past two years the P&M store held an average inventory level of about 80 reams of Great
White, although the actual inventory level varied considerably due to product sales, demand
uncertainty, and inconsistent ordering policies. Saturday’s biweekly stocktaking confirmed that the
product had always been in stock and thus had a 100% in-stock rate (i.e., the ratio of weeks during
which the item did not stock out to the total number of weeks was 100%). An example of one type of
service level measure retailers used, in-stock rate was often referred to as a “Type 1” service level.
Fill rate, the percentage of demand satisfied from in-stock inventory, sometimes referred to as a
“Type 2” service level, was also 100% for Great White over the two-year period. Although a 100% fill
rate was ideal from a customer service perspective, Brown knew that he was paying a premium to
hold inventory to meet that service level. Brown believed that a 98% fill rate (Type 2) was acceptable
customer service, and sought to devise a simple, but consistent inventory policy to meet that goal.
Brown considered establishing a consistent order-up-to point policy, so that each time he checked
his inventory levels, he would order enough to bring his inventory up to a target order-up-to level.
Since customer loyalty for Great White was high, he further assumed that there was no substitution
to another product in the event of a stock-out, so if customers found this product out of stock, they
failed to purchase and their sales were lost to P&M.
2
This document is authorized for use only by Abdulaziz Qumosani in Operations Management Fall 2016-1 taught by Askar, Dominican University – Illinois from August 2017 to February 2018.
For the exclusive use of A. Qumosani, 2017.
Paper and More (A)
606-023
To estimate inventory-carrying costs he assumed a uniform daily demand rate over a two-week
period and used that assumption as follows. If the product did not stock out, the average inventory
for the two-week period was half the sum of the starting and ending inventories. Otherwise, the
average inventory over the entire two-week period was the product of the fraction of the two-week
period that the product was not stocked out and the average inventory over this period. The
assumption of a uniform daily demand rate implied that the fraction of time that the product was not
stocked out was equal to the ratio of actual sales (starting inventory) to demand and the average
inventory over this period was simply half of the starting inventory (since the ending inventory was
zero). For example, if starting inventory was 20 and the product stocked out at the end of the first
week, then average inventory over a two-week period was five (since the product was not stocked
out for half the period and had an average of 20/2 = 10 units of inventory in the first week). Having
calculated these two-week average inventory totals for each two-week period in the two year history,
the inventory holding cost over the entire two year period was equal to the sum of all the two-week
average inventories * 12 days/300 days * 25% * cost of the product. Here 12 days was the number of
business days in a two-week period and 300 days the number of business days in the year (the store
was closed on Sundays and closed for two weeks in January.)
Brown wondered how much he could reduce inventory if his goal was to achieve a 98% fill rate.
The inventory carrying cost data would give him a sense of the savings he might realize from lower
inventory levels. Finally, Brown wondered how he might explicitly optimize the product’s net profit.
Performing Analysis #1
The worksheet “Analysis #1” shows the historical demand data for the Great White and simulates
performance metrics (including costs, profits, and service levels) for the order-up-to point entered by
the user.
In the worksheet, a table with column heading has already been started for you in columns N
through R. Also, formula references to the in-stock rate, fill rate, total inventory cost, and net profits
have been inserted in row 2 of columns O through R so that Excel’s Data Table command can be
used.
a) Construct in the worksheet “Analysis #1” a table giving in-stock rate, fill rate, total inventory costs,
and net profit for various order-up-to points using the following instructions.
Instructions for creating Data Table:
•
Enter the numbers 0 through 85 in cells N3–N88. This is the range of values for the order-upto points.
•
Highlight cells N2–R88.
•
From the drop-down menu, select “Data,” then “Table.” (For Excel 2007 – From the dropdown menu, select “Data,” then “What-If Analysis,” then “Data Table…”)
•
Enter K3 in “Column input cell,” leave “Row input cell” blank, and hit OK.
•
Hit the F9 key to calculate the different metrics for each order-up-to level2.
2 This step may be unnecessary depending on your computer’s configuration. If the F9 key does not recalculate the measures,
try locking the F-Lock button on your keyboard and hit F9 again.
3
This document is authorized for use only by Abdulaziz Qumosani in Operations Management Fall 2016-1 taught by Askar, Dominican University – Illinois from August 2017 to February 2018.
For the exclusive use of A. Qumosani, 2017.
606-023
Paper and More (A)
Questions:
i)
What order-up-to point gives a 98% in-stock rate (Type 1 service)?
ii) A 98% fill rate (Type 2 service)?
iii) Why are they not the same?
iv) Why is there a tendency for one to be higher than the other?
v)
What order-up-to point maximizes the net profit on Great White?
b) The order-up-to point that maximizes the profit for Great White can also be determined by
considering the logic of the newsvendor problem, in which a newsvendor faces uncertain daily
demand and must decide upon an order quantity before the beginning of the day and is unable to
replenish supplies during the day. The cost of overage (underage) is the cost to the newsvendor of
one extra unit (one lost sale) at the end of the day. (See Appendix A.) The optimal order-up-to point
is based on the ratio of the cost of underage to the sum of the costs of overage and underage. This
ratio is referred to as the critical fractile and is the optimal in-stock rate that maximizes profits. The
smallest inventory order-up-to point that gives this in-stock rate (or higher) is the optimal inventory
order-up-to point.
Questions:
i)
Evaluate Brown’s proposal that he should use the holding cost for one unit for the two-week
period as the cost of overage in the newsvendor model. Calculate this overage cost for the
Great White SKU.
ii)
Evaluate Brown’s proposal that he should use the margin on one unit (= retail price –
wholesale price) as the cost of underage.
iii) Calculate the critical fractile based on the underage and overage costs given (i) and (ii)
above. This gives the optimal in-stock rate for those costs. The corresponding optimal
order-up-to point is the smallest order-up-to point that has an in-stock rate equal to or
higher than the critical fractile. Use your table of order-up-to points and in-stock rates to
find the optimal order-up-to point based on your calculated critical fractile.
Optional: 1b iv) and v)
iv) The number calculated from (iii) does not match the order-up-to point determined in #1(av). Brown wonders if his cost of underage depends on his order-up-to point. Evaluate
Brown’s thought that if his order-up-to point is high enough, the cost of underage is close to
his margin minus the holding cost, but as his order-up-to point gets lower and lower the cost
of underage should get closer to just the margin.
v)
Based on (iv), the margin calculated in (ii) is the maximum value of the cost of underage.
Calculate the minimum value of the cost of underage and the corresponding order-up-to
point. What is the maximum difference in net profits over the range of order-up-to points
from the order point calculated in (iii) to the order-up-to point calculated here?
c) What type of inventory policy, fill-rate service level, in-stock rate service level, or profit
maximization criteria should Brown choose? What strategic product characteristics or overall
retailing strategy could influence his decision?
4
This document is authorized for use only by Abdulaziz Qumosani in Operations Management Fall 2016-1 taught by Askar, Dominican University – Illinois from August 2017 to February 2018.
For the exclusive use of A. Qumosani, 2017.
Paper and More (A)
606-023
d) The foregoing analysis suggests a process for managing individual product inventory: Periodically
determine the inventory order-up-to point that meets the required inventory policy for that product on
historical data and use this order-up-to point for the future. What concerns about the efficacy of the
process might Brown still have, and how might he try to address them using his data?
Analysis #2
Brown considered if it would be useful to try to fit a normal probability distribution to his
historical demand.
Performing Analysis #2
a) The worksheet “Analysis #2” is the same as “Analysis #1,” showing the historical demand data for
the Great White SKU.
i) What are the mean and standard deviation of the demand for the SKU? (The normal
distribution is completely specified once the mean and standard deviation are known.)
ii) Generate a histogram of the observed demand values for the Great White using the following
instructions.
Instructions for creating Histogram:
•
Enter the numbers 10, 20, 30, . . . , 80 in cells K26–K33.
•
From the drop-down menu select “Tools” then “Data Analysis.”3 (For Excel 2007 – From
the drop-down menu select “Data” then “Data Analysis.”)4
•
From the menu in the “Data Analysis” dialog box that appears choose “Histogram” and
hit OK.
•
Put cells B2–B51 in the “Input Range” and cells K26–K33 in the “Bin Range.”
•
Check the “Cumulative Percentage” and the “Chart Output” checkboxes. Then hit OK.
•
The histogram, both a table and a chart, will be generated in a new worksheet. (A general
note on creating histograms in Excel is located at the end of the case.)
iii) Compare the cumulative frequencies of your histogram with those of the histogram of a
normal distribution with mean 40 and standard deviation 20 shown in Exhibit 1. (The histogram
is also copied into columns Q – S in the Analysis #2 worksheet.) Comment on the fit of the normal
distribution to the demand for Great White.
b) The inverse cumulative function of a demand distribution takes an in-stock rate and returns the
3 If “Data Analysis” is not available from the Tools menu, first select “Tools” then “Add-ins” from the drop-down menu and
add the “Analysis Toolpak.”
4 For Excel 2007 – If “Data Analysis” is not available from the Data menu, first select the Windows button in the top left corner
and then “Excel Options” (to the left of “Exit Excel”). Then select “Add-ins” from the left column of options, then select to
manage “Excel Addins” and hit Go. Then add the “Analysis Toolpak.”
5
This document is authorized for use only by Abdulaziz Qumosani in Operations Management Fall 2016-1 taught by Askar, Dominican University – Illinois from August 2017 to February 2018.
For the exclusive use of A. Qumosani, 2017.
606-023
Paper and More (A)
order-up-to point that gives this in-stock rate.5 Create a table of order-up-to points for given in-stock
rates using the NORMINV() function and the mean and standard deviation calculated in a) (above)
along with the following instructions.
Instructions for creating table of in-stock rates:
•
The table should be placed in columns N and O. In column N, list the in-stock rates being
considered, which range from 1% to 99%, in cells N2 to N100.
•
In column O, calculate the smallest order-up-to point that has the considered in-stock rate or
greater. For example, =NORMINV(0.2,10,5) returns the order-up-to point that has in-stock
rate 0.2 (20%) for a normal demand distribution with mean 10 and standard deviation 5. If
the order-up-to point returned is a fraction, then round up to the nearest integer to get the
smallest order-up-to point. The Excel command =ROUNDUP(x,0) rounds up x to the nearest
integer. (It is not necessary to use the Data Table command here.)
c) The order-up-to point that generates a particular fill rate can be calculated using a simulation,
although some look-up tables exist for normal and other common distributions. The worksheet
“Analysis #2(c)” generates random numbers drawn from a normal distribution based on the mean
and standard deviation the user inputs in cells H6 and H7.6 Given an order-up-to point entered by
the user in cell H2, the worksheet calculates and reports in cell H3 the corresponding fill rate, that is,
the percentage of total demand that is met from in-stock inventory.
Construct a table of fill rates given inventory order points using the following instructions.
Instructions for creating table of order-up-to points
•
In worksheet “Analysis #2(c),” enter in cells H6 and H7 the mean and standard deviation
calculated in Analysis #2(a).
•
In the worksheet, a table with column heading has already been started for you in columns J
and K. Also, a formula reference to the fill rate has been inserted in row 2 of column K so that
Excel’s Data Table command can be used.
•
Enter numbers 0 thru 85 in cells J3–J88. These are the range of values for the order-up-to
points.
•
Highlight cells J2–K88.
•
From the drop-down menu, select “Data,” then “Table.” (For Excel 2007 – From the dropdown menu, select “Data,” then “What-If Analysis,” then “Data Table…”)
•
Enter H2 in “Column input cell,” leave “Row input cel …
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