Demand Forecasting with Stockouts
and Substitution at The Cornell Store
Vishal Gaur, Joonkyum Lee, Suresh Muthulingam
Acknowledgment: Amr Farahat, Gary Swisher, Deb Barth, Mike Staurowsky
for presentation at the
Revenue Management Conference,
Georgia Tech, May 21-22, 2012
Demand Forecasting with Stockouts
and Substitution at The Cornell Store
Vishal Gaur, Joonkyum Lee, Suresh Muthulingam
Acknowledgment: Amr Farahat, Gary Swisher, Deb Barth, Mike Staurowsky
for presentation at the
Revenue Management Conference,
Georgia Tech, May 21-22, 2012
Business Context
• Non‐profit organization, member of National Association of College Stores (NACS)
• Textbooks
– New/Used/Rental, Custom/Standard
– Sourced from publishers, wholesalers, students
• Competition
– Online stores (Amazon.com), peer‐to‐peer market in used books, local stores around campus
• Scale of business
– 3,500 books per semester for about 2000 course‐instructor combinations
– 2 buyers
Gaur, Lee, Muthulingam / Cornell University
3
Research Objectives
Estimate substitution behavior between new and used textbooks
Improve demand forecast and stocking decisions
• Unique setting – Only censored demand (sales) data are available.
– Occurrence of stockouts is known, but the time of occurrence of stockout is not known.
– The total (potential) number of customers is known (enrollment number).
– Show impact from a pilot implementation at the Cornell Store
Gaur, Lee, Muthulingam / Cornell University
4
Literature Review
 Estimation of demand with stockout‐based substitution
•
•
•
•
•
•
Anupindi, Dada and Gupta (1998)
Kӧk and Fisher (2007)
Fisher and Vaidyanathan (2009)
Musalem et al. (2010)
Conlon and Mortimer (2010)
Vulcano, van Ryzin and Ratliff (2012)
 Stockout decisions with stockout‐based substitution
• Smith and Agrawal (2000)
• Mahajan and van Ryzin (2001)
• Honhon, Gaur and Seshadri (2010)
Gaur, Lee, Muthulingam / Cornell University
5
Data Description
ISBN
Semester
Estimated
Enrollment
New Sales
Used New Used Sales Stockout Stockout
New Price
# of Courses
0‐00‐648595‐2
54
300
82
88
0
0‐00‐648595‐2
54
300
55
135
0‐00‐945000‐B
54
160
97
0‐02‐019985‐6
54
150
0‐02‐019985‐6
54
0‐02‐076200‐3
Avg books
% per course Required
0
18.95
2
11
1
1
18.95
3
44
1
0
25.99
14
82
0
1
220
36
59
0
55
12
3
5
0‐02‐332200‐4
55
54
8
0‐02‐351320‐9
55
300
0‐02‐352960‐1
55
0‐02‐360760‐2
Level
Department
0
1
art_science
14.66667
1
1
hotel
2
3
1
2
management
12
1
19
1
3
art_science
0
12
1
14
1
2
art_science
0
1
8
1
11
1
2
art_science
12
0
0
52.5
1
7
1
4
architecture
92
108
1
1
10
3
18
1
1
art_science
30
11
10
0
0
10.75
1
7
1
3
ecology
55
80
22
34
0
0
6
2
7
1
2
architecture
0‐02‐402150‐4
56
60
14
34
0
0
9.5
1
8
1
3
ilr
0‐02‐427691‐X
56
80
24
26
1
1
104
1
1
1
4
management
0‐02‐427691‐X
56
65
11
19
0
0
107.25
1
1
1
3
art_science
0‐02‐428810‐1
56
600
124
198
0
0
46
1
10
1
2
ilr
• Sales are observed; demand is not.
• There is substitution between new and used books when one of them stocks out.
Gaur, Lee, Muthulingam / Cornell University
6
Data Description continued
Number of ISBNs in each semester
Semester
Spring 05
Fall 05 Spring 06
Fall 06 Spring 07
Fall 07 Spring 08
Fall 08 Spring 09
Fall 09 Required books
3229
3283
3281
3395
3353
3261
3112
3135
2874
3080
Optional books
488
475
586
468
460
432
415
406
353
412
Number of ISBNs per course‐instructor‐semester
Mean
Std Dev
Median
Max
99%
95%
Min
Required
books
3.21
2.93
2
27
13
9
1
Optional books
2.04
1.98
1
29
10
6
1
Gaur, Lee, Muthulingam / Cornell University
7
Forecasting Model
• Customer’s utility from {new, used},
Unj = xj + random noise
– x: forecasting variables or product attributes
• price, course level, department, required/optional, # of other books in course
– β: coefficients or weights of product attributes (parameters to be estimated)
• Choice probability is given by a multinomial logit
formulation
pj S 
Gaur, Lee, Muthulingam / Cornell University
exp  x j 
1  exp  xnew   exp  xused 
8
Timeline illustrating the sequence of events. One
value of total sales can be obtained in many ways.
Time of stock‐out not observed
Used book stocks out
New book stocks out
NEW
NEW
NEW
USED
USED
USED
New and used books are available
‐ Some students buy new books
‐ Some students buy used books
‐ Some students buy nothing
New book sales
Used book sales
Gaur, Lee, Muthulingam / Cornell University
Total number of customers
Time line
Only new books are available
No books
‐ Some students buy new books
‐ Some students substitute new books for used books
‐ Some students buy nothing
‐ No sales
Total new book sales
Total used book sales
New book sales
9
Enumerate sample paths to account for
stockouts and substitution (new/used books)
•
Maximize likelihood
max

•

i observations
Pr  textbook i' s sales  observed sales
Probability that we observe a given sales of a textbook
– Example: Both new and used books stock out.
– Pr(New book sales=Sn, Used book sales=Su | Number of enrollment=N)
Case 1: used books stock out first and new book stocks out Case 2: new books stock out first and used book stocks out Sn 1 N Sn Su
k 0
j 0
Su 1 N Sn Su
k 0
j 0
Su 1 k j ! k S u j
P P P
Su 1 ! k! j! n u 0
Sn 1 k j ! S n k j
P P P
Sn 1 ! k! j! n u 0
Sn new book sales
k used book sales
j students buy nothing
Assortment: new and used book
Beginning of sales
Gaur, Lee, Muthulingam / Cornell University
N Sn Su j
l 0
N Sn Su j
l 0
Sn 1 k l !
P
Sn 1 k ! l! n,u
Sn k
Su 1 k l !
P
Su 1 k ! l! u,n
P0,u l
Su k
P0,n l
Su‐k used book sales
l students buy nothing
Assortment: used books only
New book stock‐out
Used book stock‐out
No books
N customers
10
Evaluation of our method against alternative
demand forecasting methods
• Alternative Method 1. Use only uncensored observations – Use only those observations in which no stockout occurred)
– Analyze low demand observations only.
• Alternative Method 2. Ignore stockout and substitution
– Assume demand = sales. – Example: Both new and used books stock out.
Pr(New book sales=Sn, Used book sales=Su | Number of enrollment=N) =
Pn S n Pu S u P0 N
Sn Su
• Alternative Method 3. Uncensoring without modeling substitution
– Account for stockout information.
– After a stockout occurrence, do not account for substitute demand.
Gaur, Lee, Muthulingam / Cornell University
11
A simulation experiment to evaluate the
demand forecasting methods
Given demand model (KNOWN )
% GAP
Compare results with true demand model
Generate random observations
• Product characteristics
• Inventories
• Customer Arrivals
• Sales occurrence
Estimate parameters using our model and alternative models
• Estimates of mean demand
• Estimates of choice parameters 
Gaur, Lee, Muthulingam / Cornell University
12
Simulation Setup
Six parameters (β) to be estimated
• Constant, Price, 1000Level for new and used books • True value of β = (‐1.2, ‐0.2, 0.7, ‐1, ‐0.1, 0.4)
Random values for product attributes (x)
• Enrollment number ~ 500*beta(2,18)
• Normalized Price ~ Normal(1,0.2)
• 1000Level ~ Bernoulli(0.3)
• 10,000 observations are generated
Stocking levels
• Stocking level with respect to the expected demand={0.5, 0.75, 1, 1.25, 1.5, 1.75, 2}
• We try these 7 different stocking levels to assess the effect of stockouts on forecast accuracy and computation time.
Gaur, Lee, Muthulingam / Cornell University
13
MPE in expected demand (New and used books)
Result 1: Evaluation of demand forecast with
respect to the true mean
30%
20%
10%
0%
‐10%
‐20%
‐30%
‐40%
‐50%
‐60%
‐70%
‐80%
‐90%
‐100%
Mean Percentage Error in Expected Demand
0.5
(96.6%)
0.75
(89.3%)
1
(61.6%)
1.25
(28.0%)
1.5
(11.5%)
1.75
(5.3%)
2
(2.3%)
Stocking Level as a fraction of expected demand (overall stockout rate shown in parentheses)
Model 1: Use only uncensored observations
Model 2: Ignore stockout and substitution
Model 3: Ignore substitution
Our model: account for stockout and substitution
With stockout information, true demand can be estimated even when there is a high incidence of stockouts.
Gaur, Lee, Muthulingam / Cornell University
14
Result 2 (Parameter Recovery): Comparison of
estimated parameters with the true values
% gap between true parameters and estimates obtained by different methods for stocking level = 0.75 (stockout rate = 98.3%) New Books
Used Books
Price elasticity
Whether 1000 level
‐1.0
‐0.1
0.4
0.72
2.6%
‐1.01
‐1.6%
‐0.08
17.3%
0.40
0.3%
‐0.24
‐18.2%
0.81
15.4%
‐0.89
11.3%
‐0.11
‐13.0%
0.52
29.2%
‐1.68
‐40.0%
‐0.18
7.6%
0.64
‐8.9%
‐1.47
‐47.4%
‐0.08
19.8%
0.33
‐18.4%
‐2.0
‐66.5%
‐0.43
‐116.1%
0.67
‐4.1%
‐1.77
‐77.3%
‐0.20
‐100.9%
0.32
‐20.1%
Intercept
Price elasticity
True Parameters
‐1.2
‐0.2
0.7
Account for stockout and substitution
‐1.17
2.4%
‐0.22
‐9.8%
Ignore substitution
‐1.04
13.6%
Ignore stockout and substitution
Use only uncensored observations
Gaur, Lee, Muthulingam / Cornell University
Whether Intercept
1000 level
15
Price elasticity of demand has a larger estimation
error when stockouts are more frequent
True values: ‐0.2 for new books and ‐0.1 for used books.
New book price elasticity
Stocking level
0.5
(stockout rate)
(96.6%)
Account for stockout and substitution ‐0.14
Ignore substitution
‐0.17
0.75
1
1.25
1.5
(89.3%) (61.6%) (28.0%) (11.5%)
1.75
(5.3%)
2
(2.3%)
‐0.22
‐0.21
‐0.23
‐0.21
‐0.20
‐0.23
‐0.24
‐0.23
‐0.23
‐0.22
‐0.20
‐0.24
Ignore stockout and substitution
‐0.17
‐0.18
‐0.22
‐0.23
‐0.21
‐0.20
‐0.24
Use only uncensored observations
6.21
‐0.43
‐0.24
‐0.23
‐0.21
‐0.20
‐0.24
1.75
(5.3%)
2
(2.3%)
Used book price elasticity
Stocking level
0.5
(stockout rate)
(96.6%)
Account for stockout and substitution ‐0.13
Ignore substitution
‐0.15
0.75
1
1.25
1.5
(89.3%) (61.6%) (28.0%) (11.5%)
‐0.08
‐0.14
‐0.13
‐0.11
‐0.08
‐0.10
‐0.11
‐0.15
‐0.13
‐0.12
‐0.08
‐0.09
Ignore stockout and substitution
‐0.07
‐0.08
‐0.12
‐0.13
‐0.11
‐0.08
‐0.09
Use only uncensored observations
11.75
‐0.20
‐0.09
‐0.12
‐0.10
‐0.08
‐0.09
Gaur, Lee, Muthulingam / Cornell University
16
Pilot implementation
• 3 groups to compare performance
– Group 1: business as usual (control group)
– Group 2: we provide demand forecasts
– Group 3: we provide suggested stocking level
• 30 sets of matching textbooks for each group
– Drop 6 sets because of dropped courses or changes in parameters.
– Use 24 sets (72 textbooks), accounting for 3.4% of the books for the Spring 2012 semester. Gaur, Lee, Muthulingam / Cornell University
17
Matching process
proportion of the sets with identical attributes
average (median)
maximum difference
Price of a new book (V)
8.3%
7.1% (6.8%)
Number of courses (Q)
95.8%
2.8% (0.0%)
Average number of books per course (B)
95.8%
1.3% (0.0%)
Proportion required (R) 100.0%
0.0% (0.0%)
Enrollment (E)
91.7%
2.1% (0.0%)
New ISBN (W)
91.7%
‐
Course level (L)
100.0%
‐
Odd semester (O)
100.0%
‐
Department (D)
100.0%
‐
Gaur, Lee, Muthulingam / Cornell University
18
Demand information provided for group 2
1. If new and used books are stocked in plenty
Expected Demand
Standard
Deviation
2. If only new books are stocked in plenty
3. If only used books are stocked in plenty
Expected
Demand
Standard
Deviation
Expected
Demand
Standard
Deviation
Group
Set
ISBN
New book
Used book
Total
New book
Used book
New book
New book
Used book
Used book
2
1
9780205711499
1.2
4.3
5.5
1.1
1.8
1.6
1.2
4.6
1.8
2
2
9780030327162
5.9
28.2
34.1
2.3
4.3
9.2
2.8
30.4
4.3
2
3
9781556520747
1.8
7.2
9.0
1.3
2.1
3.0
1.6
8.0
2.1
2
4
9780141441474
14.7
61.5
76.3
3.6
6.0
25.0
4.6
68.2
6.1
2
5
9780195042399
1.4
7.7
9.1
1.1
2.1
2.5
1.5
8.4
2.1
2
6
9780679721888
1.5
7.0
8.5
1.2
2.1
2.5
1.5
7.6
2.1
2
7
9781566564151
2.1
7.8
9.9
1.4
2.1
3.7
1.7
8.8
2.1
2
8
9780071546058
5.0
16.0
21.0
2.1
3.3
7.5
2.5
17.8
3.3
2
9
9780679723417
4.7
15.2
19.9
2.1
3.2
7.1
2.4
16.9
3.2
2
10
9780822200161
9.9
33.0
42.9
3.0
4.7
15.1
3.6
36.8
4.8
Gaur, Lee, Muthulingam / Cornell University
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Process of finding suggested stocking level
for group 3
Step
Example
Provide initial suggested stocking level
For set 1
30 new books
70 used books
base on the ABS heuristic and neighborhood search using simulation Update availability information
Usually used‐book availability is limited
Other attributes (e.g., price or enrollment) might change Provide revised suggested stocking level
Solve the optimization problem with restrictions on availability (and others)
Gaur, Lee, Muthulingam / Cornell University
Only 50 used books are available
40 new books
50 used books
20
Result of the pilot experiment:
Comparison of realized profit
Total Profit
Total profit
Group 1
Group 2
Group 3
1611.59
1747.03
1775.48
Profit Difference
Group 2 ‐ Group 1
Group 3 ‐ Group 1
Group 3 ‐ Group 2
Mean paired difference in profit
5.6431
6.8285
1.1854
p‐value of paired t‐test
0.0711
0.0938
0.4280
Median paired difference in profit
7.2137
3.5463
‐0.2625
p‐value of Wilcoxon signed‐rank test
0.0678
0.0476
0.4527
p‐value of sign test
0.0758
0.0320
0.5000
Group 2 and 1
Group 3 and 1
Group 3 and 2
17.80% (10.41%)
6.33% (‐1.71%)
* The p values are one‐tailed
Percentage Gap
Mean (median) percentage gap in profit 11.89% (16.68%)
Both group 2 and group 3 perform significantly better than group 1
Gaur, Lee, Muthulingam / Cornell University
21
Result of the pilot experiment 2:
Sales to stock ratio and stockout rate
Sales to stocking level ratio
Mean (median) sales to stocking level ratio
Total
New books
Used books
Group 1
Group 2
Group 3
0.60 (0.59)
0.42 (0.40)
0.75 (0.88)
0.58 (0.61)
0.55 (0.50)
0.70 (0.75)
0.72 (0.85)
0.86 (1.00)
0.70 (0.80)
• Total and new‐book sales to stock ratio of group 3 is significantly higher than those of other groups
• Total sales to stock ratios of group 1 and group 2 are similar but they have different configuration
Stockout rate
Total
New books
Used books
Group 1
12.50%
7.14%
17.86%
Group 2
12.50%
7.14%
17.86%
Group 3
39.29%
50.00%
28.57%
• Stockout rate of group 3 is significantly higher than those of other groups
Gaur, Lee, Muthulingam / Cornell University
22
Result of the pilot experiment 3:
Drivers – Stocking level and product mix
Difference in stocking level and product mix
Group 1
Group 2
Group 3
Mean (median) total stocking level to estimated enrollment ratio
0.53 (0.50)
0.56 (0.53)
0.38 (0.41)
Mean (median) used‐book stocking level to total stocking level ratio
0.46 (0.51)
0.55 (0.72)
0.70 (0.82)
• The total and the relative used‐book stocking level of group 1 is substantially lower than those of other groups
• The relative used‐book stocking level of group 2 is considerably lower than that of group 3
Gaur, Lee, Muthulingam / Cornell University
23
Reasoning – Difference between group 1 and 2
• Different product mix: – Group 1 stocks relatively more new books and group 2 stocks relatively more used books.
– When none of new and used books stocks out: overage cost of a new book is high  profitability of group 1 is worse
– When either type of book stocks out  substitution starts to occur substitution rate from used books to new books is higher than that from new books to used books (even though margin of a new book is better)
price
cost
salvage
overage cost underage cost
critical ratio
new book
1
0.6
0.48
0.12
0.4
0.769
used book
0.75
0.375
0.3
0.075
0.375
0.833
Note. The numbers are normalized to set new‐book price to 1. The numbers are averaged ones over all book titles.
Gaur, Lee, Muthulingam / Cornell University
24
Reasoning – Difference between group 1 and 3
• Total stocking level of group 1 is high
– Stocking level from solving newsvendor problems for new and used books independently is too high when critical fractile is high (Honhon et al. 2010)
• Impact of ignoring the substitution rate
– Usually the availability of used books is limited. – The buyers tend to make up for the shortfall of used books by buying additional new books to match the initial total stocking level. – However, the substitution rate from used books to new books is typically low (0.2 ~ 0.4)
Gaur, Lee, Muthulingam / Cornell University
25
Summary
• Accurate demand forecasts can be obtained by incorporating stockout information in the model even if the stock‐out rate is significantly high(~90%).
• Enrollment (traffic) data are valuable for estimation.
• Pilot implementation shows the interdependence between stocking levels of the new and used books.
• Splitting the dataset improves computational efficiency, but increases error.
‐ Use safety stock to compensate for the error.
• Ongoing work ‐ Extending the analysis to more than two products
Gaur, Lee, Muthulingam / Cornell University
26
Gaur, Lee, Muthulingam / Cornell University
27
Summary
•
Our method recovers parameters more accurately than other methods.
– Even if the stock‐out rate is significantly high(~90%), accurate demand forecasts can be obtained by incorporating stockout information in the model.
•
Pilot implementation shows that our method can make significant improvement in profitability.
– Accounting for substitution effect drives different stocking level and product mix.
•
Our method can be applied dynamically under the restrictions on product availability.
•
Splitting the dataset improves computational efficiency, but increases error.
– Use safety stock to compensate for the error.
•
Enrollment (traffic) data are valuable for estimation.
•
Further work
– Extending the model to more than two products
Gaur, Lee, Muthulingam / Cornell University
28
Data Description - 2
• 61,032 observations across 10 semesters
–
–
–
–
–
–
Course, Course level, Instructor, ISBN, Required/Optional text
New book price, Used book price, New book cost
Estimated and actual enrollment
To Provide (Stock‐up‐to level)
Sales of new and used books, Returns of new and used books
Publisher, Vendor, Buyer code
• Contextual information
– Types of contracts with different publishers and wholesalers
Gaur, Lee, Muthulingam / Cornell University
29
Customer Purchase Process
Buy new
NEW
USED
p
q
Buy used
1-p-q
Don’t buy any
When new books are out‐of‐stock:
NEW
q' > q
USED
Buy used
1-q
Don’t buy any
An analogous process occurs when used books are out‐of‐stock.
Gaur, Lee, Muthulingam / Cornell University
30
Challenges in estimating
the forecasting model
• Demand is not observed, only sales are. This is due to stockouts.
• Number of books (of the other type) sold before a stockout occurs is not known. Only total sales are known.
Gaur, Lee, Muthulingam / Cornell University
31
Identifying the opportunity for improvement by
estimating lost sales and excess inventory
•
•
The demand forecast model and the store’s ordering decisions can be used to estimate excess inventory and lost sales
Picture shows estimation results for 100 test observations (model estimated on 2,361 observations).
0.9
0.8
Estimated excess inventory and lost sales as % of total enrollment
Excess Inventory/Enrollment
Lost Sales/Enrollment
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
‐0.1 0
Gaur, Lee, Muthulingam / Cornell University
0.2
0.4
0.6
0.8
1
1.2
1.4
Total inventory of new and used books as % of total enrollment
32
Stock-out rates also differ between new and used
textbooks, showing substitution patterns
Didn’t order used book
Didn’t order new book
N/A
Stocked out
Ordered new Didn’t stock book
out
Ordered used book
N/A
Stocked out
Didn’t stock out
0%
1%
5%
6%
7%
8%
8%
22%
34%
21%
16%
71%
41%
30%
29%
100%
• Substitution: Most but not all students prefer to buy used books. In 8% of cases, the bookstore stocked out of new books, but not old.
• Profit margin on new books = 25%
Profit margin on used books = 35%.
• Used books stock out about half the time. New books stock out about 25% of the time. Thus, the bookstore could benefit by stocking more used books, if available.
Gaur, Lee, Muthulingam / Cornell University
33
0.8
Excess Inventory/Enrollment
Lost Sales/Enrollment
0.6
0.4
0.2
0
‐0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
‐0.4
‐0.6
‐0.8
Gaur, Lee, Muthulingam / Cornell University
34
Objectives of the study
For the store
For us
 Assess the current performance of the bookstore and find areas for improvement
 Devise a method for demand forecasting and improve ordering of new and used books
 Add to algorithm in the system
 Improve competitiveness in sourcing used books from students
 Improve effectiveness of a brick & mortar store competing with online
channels
 Advancement in forecasting and planning
 Issues related to managerial behavior in operational decisions
 Modeling prices and supply in the sourcing of used books
 Performance effects of the contracts between the store and publishers/wholesalers
Gaur, Lee, Muthulingam / Cornell University
35
Example: One Text for Multiple Courses
DEPT
COURSE SECTION
TITLE
AUTHOR
INSTRUCTOR
REQ/OPT EST ENROLL.
QTY
ACT ENROLL.
TOTAL SALES
GOVT
1101
103
ELEMENTS OF STYLE STRUNK
PEPINSKY
R
17
202
18
145
GOVT
1101
102
ELEMENTS OF STYLE STRUNK
KEMERLI
R
17
202
18
145
GOVT
1101
104
ELEMENTS OF STYLE STRUNK
BENSEL
O
17
202
17
145
PHIL
1111
102
ELEMENTS OF STYLE STRUNK
KYLE
O
17
202
18
145
PHIL
1112
104
ELEMENTS OF STYLE STRUNK
STAPLETON
R
17
202
18
145
ENGL
1127
102
ELEMENTS OF STYLE STRUNK
TORRES
R
17
202
17
145
ENGL
1158
109
ELEMENTS OF STYLE STRUNK
VAUGHN
O
17
202
18
145
ENGL
1185
109
ELEMENTS OF STYLE STRUNK
MCQUEEN‐
THOMSON
R
17
202
16
145
ILRIC
2301
1
ELEMENTS OF STYLE STRUNK
COOK
R
17
202
11
145
ENGL
2700
101
ELEMENTS OF STYLE STRUNK
SCHWARZ
R
17
202
14
145
ENGL
2710
102
ELEMENTS OF STYLE STRUNK
FRIED
R
18
202
18
145
GOVT
3303
1
ELEMENTS OF STYLE STRUNK
TURNER
O
200
202
53
145
ILRIC
4330
1
ELEMENTS OF STYLE STRUNK
TURNER
O
200
202
129
145
ILRIC
6330
1
ELEMENTS OF STYLE STRUNK
TURNER
O
12
202
14
145
8 R
600
202
379
145
14 courses
Gaur, Lee, Muthulingam / Cornell University
36
Example: One Text for Many Courses
DEPT
COURSE SECTION
TITLE
AUTHOR
INSTRUCTOR
REQ/OPT EST ENROLL.
QTY
ACT ENROLL.
TOTAL SALES
GOVT
1101
103
ELEMENTS OF STYLE STRUNK
PEPINSKY
R
17
202
18
145
GOVT
1101
102
ELEMENTS OF STYLE STRUNK
KEMERLI
R
17
202
18
145
GOVT
1101
104
ELEMENTS OF STYLE STRUNK
BENSEL
O
17
202
17
145
PHIL
1111
102
ELEMENTS OF STYLE STRUNK
KYLE
O
17
202
18
145
PHIL
1112
104
ELEMENTS OF STYLE STRUNK
STAPLETON
R
17
202
18
145
ENGL
1127
102
ELEMENTS OF STYLE STRUNK
TORRES
R
17
202
17
145
ENGL
1158
109
ELEMENTS OF STYLE STRUNK
VAUGHN
O
17
202
18
145
ENGL
1185
109
ELEMENTS OF STYLE STRUNK
MCQUEEN‐
THOMSON
R
17
202
16
145
ILRIC
2301
1
ELEMENTS OF STYLE STRUNK
COOK
R
17
202
11
145
ENGL
2700
101
ELEMENTS OF STYLE STRUNK
SCHWARZ
R
17
202
14
145
ENGL
2710
102
ELEMENTS OF STYLE STRUNK
FRIED
R
18
202
18
145
GOVT
3303
1
ELEMENTS OF STYLE STRUNK
TURNER
O
200
202
53
145
ILRIC
4330
1
ELEMENTS OF STYLE STRUNK
TURNER
O
200
202
129
145
ILRIC
6330
1
ELEMENTS OF STYLE STRUNK
TURNER
O
12
202
14
145
8 R
600
202
379
145
14 courses
Gaur, Lee, Muthulingam / Cornell University
37
Example contd.: Time-series data for
“Elements of Style”
Sales
Semester
Estimated Enrollment
Qty
Actual Enrollment
54
281
217
228
95
104
199
62
221
188
174
93
43
136
64
407
292
339
111
93
204
72
256
183
173
84
40
124
74
312
193
278
101
90
191
82
356
223
271
75
77
152
84
290
233
259
95
91
186
92
252
118
133
28
37
65
94
600
202
379
84
61
145
Gaur, Lee, Muthulingam / Cornell University
38
Another Example: One Course with Multiple Texts
Course / Dept
1101 PSYCH
Title
Author
Reqd/
Optional
Instructor
Estimated Enrollment
Qty
Actual Enrollment
Total Sales
MBTI FORM M 6165
‐
R
MAAS
1355
1117
1095
845
POWER SLEEP
MAAS
R
MAAS
1280
938
1020
712
FRONTIERS OF PSYCHOLOGY MAAS
R
MAAS
1280
1050
1020
825
ICLICKER
R
MAAS
10775
4985
9164
3662
O
MAAS
1280
100
1020
98
R
MAAS
1280
1100
1020
701
ICLICKER
POWER NAP KIT COLLEGE GELB
EDITION
3 PK: PSYCHOLOGY W/ SG, MYERS
PSYCH PORTAL
Gaur, Lee, Muthulingam / Cornell University
39
Performance Evaluation
• % Gap between true expected demand and forecasted expected demand
True 
Draw N, price, 1000Level
observations Estimation using MLE
ˆ1 , ˆ2 , ˆ3
Draw N, price, 1000Level
for estimation
True

Gaur, Lee, Muthulingam / Cornell University
% GAP
ˆ1 , ˆ 2 , ˆ 3
40
Numerical Experiment:
Simulation Process
There are 7 stocking levels. For each stocking level, we have 10 sets of observations. A set of observations consists of 1,000 textbooks. Draw random enrollment, price, and 1000level
Identify stock‐out information and sales of new and used books
Gaur, Lee, Muthulingam / Cornell University
Compute choice probabilities, expected demand, and inventory level
Find estimates of parameters
Each customer observes current assortment and makes purchasing decision
Adjust remaining inventory Sample a new set of 100,000 textbooks
Find expected demand using true beta and estimates
41
Planning cycle for the Spring semester
Mid‐Nov
Mid‐Dec
Semester begins
Mid‐Feb
time
Selling season
Faculty place requests for books for the Spring semester
Source used books from students and wholesalers
Gaur, Lee, Muthulingam / Cornell University
Procure new books
Monitor stock outs and get expedited shipments as needed
Manage returns
42
Result 2 (Parameter Recovery): Comparison of
estimated parameters with the true values
% gap between true parameters and estimates obtained by different methods for stocking level = 0.75 (stockout rate = 98.3%) New Books
Used Books
Price elasticity
Whether 1000 level
‐1.0
‐0.1
0.4
0.72
2.6%
‐1.01
‐1.6%
‐0.08
17.3%
0.40
0.3%
‐0.24
‐18.2%
0.81
15.4%
‐0.89
11.3%
‐0.11
‐13.0%
0.52
29.2%
‐1.68
‐40.0%
‐0.18
7.6%
0.64
‐8.9%
‐1.47
‐47.4%
‐0.08
19.8%
0.33
‐18.4%
‐2.0
‐66.5%
‐0.43
‐116.1%
0.67
‐4.1%
‐1.77
‐77.3%
‐0.20
‐100.9%
0.32
‐20.1%
Intercept
Price elasticity
True Parameters
‐1.2
‐0.2
0.7
Account for stockout and substitution
‐1.17
2.4%
‐0.22
‐9.8%
Ignore substitution
‐1.04
13.6%
Ignore stockout and substitution
Use only uncensored observations
Gaur, Lee, Muthulingam / Cornell University
Whether Intercept
1000 level
43
Result 3: Taming the computation time
# of textbooks
Computation Time (sec)
# of iterations
100
29
37
500
232
36
1,000
422
33
5,000
2,285
19
10,000
24,251
72
• Computation time increases dramatically with # of observations
• Types of observations that are more time‐intensive:
– When both new & used books stockout: Likelihood function involves triple summation
– When enrollment is large
• Splitting the data set improves computational efficiency, but with a small sacrifice of estimation accuracy
Gaur, Lee, Muthulingam / Cornell University
44
Performance assessment of the store and differences between buyers
Criteria used by buyers to determine stock-up-to levels
Stock‐up‐to level for an ISBN is a function of 1. Total estimated enrollment across all courses that request the textbook,
2. Course level,
3. Price of textbook,
4. Whether required/optional,
5. Number of requested books in the course
Gaur, Lee, Muthulingam / Cornell University
46
These criteria are confirmed by the data
regression results for all ISBNs with enrollment between 100 and 400 (inclusive)
Log model
Linear model
Optional ISBN
Required ISBN
Optional ISBN
Required ISBN
# of observations
579
4834
586
4904
R2
51%
61%
21%
54%
rmse
0.71
0.45
35.06
42.45
cv of dep var
24.89
10.58
119.33
49.47
1.49***
1.56***
18.96***
41.14***
0.02*
0.03***
0.00*
0.00*
NewPrice
‐0.36***
‐0.14***
‐0.07**
‐0.12***
Actual Enrollment
0.70***
0.69***
0.20***
0.55***
Total # of books per course
‐0.44***
‐0.11***
‐1.17***
‐1.40***
Intercept
AvgCourselevel
Gaur, Lee, Muthulingam / Cornell University
47
Regression results for the entire data set also confirm the criteria used by the buyers
EST1
 ToProvide= α + Est_Enrolli*β + Diff_Enrolli*γ + New Pricei* δ + avg booksi* φ + # of coursesi* λ + New ISBNi*
η + Controls i* μ + εi
ACT1  ToProvide= α + Act_Enrolli*β + New Pricei* δ + avg booksi* φ + # of coursesi* λ + New ISBNi* η + Controls i* μ
+ εi
EST_REQ & ACT_REQ and EST_OPT & ACT_OPT  EST1 & ACT1 models for Courses that use Required and Optional
Texts
Controls  ( semester) Coefficient estimates for controls are not provided below!
EST1
est_enroll
diff_enroll
.56***
(.0016)
.41***
(.0037)
act_enroll
new price
Avg Books/~e
# of courses
_Ireqopt_2
New ISBN
R_Sq
Adj_R_Sq
Number
ACT1
EST_REQ
ACT_REQ
.58***
(.0017)
.42***
(.0039)
.0061
(.0049)
.016
(.02)
-.55***
(.15)
23***
(.53)
1**
(.35)
.57***
(.0016)
.0036
(.005)
-.074***
(.021)
2.3***
(.14)
23***
(.54)
.7
(.36)
0.81***
0.81
35950
0.80***
0.80
35950
-.0018
(.0051)
.0012
(.021)
-1.6***
(.15)
EST_OPT
ACT_OPT
.22***
(.003)
.25***
(.0056)
.59***
(.0017)
-.005
(.0053)
-.1***
(.022)
1.6***
(.14)
1.6***
(.37)
1.2**
(.38)
0.83***
0.83
31794
0.82***
0.82
31794
-.054***
(.007)
-.22***
(.038)
4.2***
(.24)
.22***
(.003)
-.053***
(.0071)
-.21***
(.038)
3.7***
(.22)
3***
(.54)
3***
(.54)
0.61***
0.61
4154
0.61***
0.61
4154
* p<0.05, ** p<0.01, *** p<0.001
Gaur, Lee, Muthulingam / Cornell University
48
Stock-out rates differ between optional and
required textbooks
A rough benchmark for stockout rate: Margin on a book = 25%, Salvage value = 80% of cost = 60% of price
Newsvendor critical fractile = 62.5%
Stockout rate = 37.5%
Optional books
# obs.
5,567
Average Stockout rate
35.3%
Required books
# obs.
40,898
Average Stockout rate
17.1%
Gaur, Lee, Muthulingam / Cornell University
49
There are consistent differences between the two
buyers in their stock-up-to levels
Qty/ Estimated Enrollment
Required
Optional
Semester
Alice
Rachel
A&R
Alice
Rachel
A&R
Alice
Rachel
A&R
3
0.62
0.56
0.59
0.69
0.63
0.67
0.21
0.19
0.28
4
0.62
0.61
0.64
0.68
0.67
0.69
0.22
0.21
0.23
5
0.60
0.58
0.58
0.65
0.63
0.63
0.21
0.21
0.19
6
0.61
0.60
0.54
0.66
0.65
0.64
0.20
0.19
0.23
7
0.59
0.56
0.57
0.65
0.61
0.60
0.20
0.19
0.21
8
0.62
0.64
0.63
0.66
0.68
0.68
0.21
0.19
0.27
9
0.59
0.59
0.54
0.63
0.63
0.59
0.19
0.21
0.20
10
0.60
0.60
0.64
0.65
0.65
0.67
0.20
0.19
0.12
• Alice stocks more than Rachel in 11 out of 16 cases.
• A 1% difference in stocking levels can result in a significant difference in expected
profits, esp. when demand uncertainty and in-stock rates are high.
Gaur, Lee, Muthulingam / Cornell University
50
Differences between buyers are confirmed in a regression on various control variables
EST1  ToProvide/Est Enrollment = α + New Pricei* δ + avg booksi* φ + # of coursesi* λ + New ISBNi* η + Racheli* π +
Alice & Racheli* ψ + Controls i* μ + εi
ACT1  ToProvide/Act Enrollment = α + New Pricei* δ + avg booksi* φ + # of coursesi* λ + New ISBNi* η + Racheli* π +
Alice & Racheli* ψ + Controls i* μ + εi
EST_REQ & ACT_REQ  EST1 & ACT1 models for Courses which use Required Texts
EST_OPT & ACT_OPT  EST1 & ACT1 models for Courses which use Optional Texts
Controls  ( semester) Coefficient estimates for controls are not provided below!
EST1
new price
-.00035***
(.000042)
Avg Books/~e
.0053***
(.00018)
# of courses
-.077***
(.0011)
_Ireqopt_2
.4***
(.0049)
Rachel
-.013***
(.0033)
A&R
.015**
(.0053)
New ISBN
.051***
(.0033)
R_sq
R_Sq_A
Number
0.36***
0.36
23187
ACT1
EST_REQ
ACT_REQ
-.003***
-.0003***
-.0032***
(.00016)
(.000046)
(.00018)
-.0035***
.0059***
-.0037***
(.0007)
(.00019)
(.00076)
-.01*
-.081***
-.012*
(.0044)
(.0012)
(.0048)
.77***
(.019)
.019
-.014***
.015
(.013)
(.0037)
(.015)
-.017
.012*
-.026
(.021)
(.0058)
(.023)
-.18***
.05***
-.2***
(.013)
(.0036)
(.014)
0.10***
0.10
22672
0.23***
0.23
20565
0.03***
0.03
20097
EST_OPT
ACT_OPT
-.00085***
(.000071)
-.003***
(.0004)
-.024***
(.0023)
-.0015***
(.00025)
.00097
(.0014)
.0087
(.0079)
-.0023
(.0057)
.026**
(.0092)
.037***
(.0056)
0.12***
0.11
2620
.049*
(.02)
.044
(.032)
-.019
(.02)
0.04***
0.04
2573
* Comment
p<0.05, ** p<0.01, *** p<0.001
1.
2.
Rachel stocks less than Alice (Significant in models EST1, EST_REQ, and ACT_OPT)
When both buyers are involved stocking levels are higher
Gaur, Lee, Muthulingam / Cornell University
51
Further work
• Develop a forecasting model using the criteria identified by buyers
• Compute stock‐up‐to levels and evaluate performance in the next academic year
• Characterize differences between the two buyers
Gaur, Lee, Muthulingam / Cornell University
52
Main Takeaways
•
•
•
A potential exists for improved pricing policies that adjust for competition and used book supply.
The used book market is advantageous to the Store.
Alternative buyback models exist that explicitly encourage the purchase of new books from the Store. Next steps:
•
Test robustness of above insights (alternative demand models, Store expertise, …)
•
Translate insights into actionable pricing tactics (starting with directional guidelines)
Examine the degree of substitutability between new and used books and develop a testable demand function.
•
Gaur, Lee, Muthulingam / Cornell University
53
Overall Summary
• Develop a forecasting model using the criteria identified by buyers
• Compute stock‐up‐to levels and evaluate performance in the next academic year
• Characterize differences between the two buyers
• Test robustness of pricing insights (alternative demand models, Store expertise)
• Develop actionable pricing tactics (starting with directional guidelines)
• Examine the degree of substitutability between new and used books and develop a testable demand function
Gaur, Lee, Muthulingam / Cornell University
54