Performance benchmarking and sales
forecasting using firm-level data for US
retailers
Vishal Gaur
for presentation at
“Rocket Science” en Retail 2008
Industrial Engineering, University of Chile
June 19, 2008
(C) Vishal Gaur, Cornell University, 2008
1
Outline
1. Applications of public financial data
–
–
Benchmarking of inventory turnover
Forecasting sales using inventory and gross margin data
2. A distribution management problem at a supermarket
chain (Albert Heijn, BV)
3. Experiment design in a retail chain (toy retailer in US)
(C) Vishal Gaur, Cornell University, 2008
2
Importance of Inventory Management in Retailing
•
•
•
More than $300 billion of investment in inventory in the U.S. retailing
industry in 2008 (~$500 billion including motor vehicles and spare
parts).
Inventory represents 36% of total assets and 53% of current assets
of retailing firms.
Inventory turnover
– Routinely used for productivity comparisons by retailers, manufacturers,
consultants and analysts.
•
Benefits of high inventory turnover
–
–
–
–
Lower working capital requirement
Lower inventory holding and obsolescence costs
Greater ability to respond to market dynamics
Fewer stock-outs
(C) Vishal Gaur, Cornell University, 2008
3
Variation in Inventory Turnover
• Within-firms variation
–
Range of inventory turnover of commonly known firms in 19852000:
Best Buy Co. Inc.
2.8 – 8.5
Circuit City Stores, Inc.
4.0 – 5.6
The Gap, Inc.
3.6 – 6.3
Radio Shack Corp.
1.1 – 3.1
Wal-Mart Stores, Inc.
4.9 – 7.2
• Across-firms variation
–
Range of inventory turnover of supermarket chains during the
year 2000: 4.7 to 19.5.
(C) Vishal Gaur, Cornell University, 2008
4
Time-Series Plot of Annual Inventory Turnover of Four Consumer
Electronics Retailers for 1987-2000
Annual Inventory
Turnover
10
9
8
7
6
5
4
3
2
1
0
1986
1988
1990
1992
1994
1996
1998
2000
Time (years)
Best Buy Co.
Circuit City Stores, Inc.
Radio Shack Corp
CompUSA, Inc.
(C) Vishal Gaur, Cornell University, 2008
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Research Questions
•
Why does inventory turnover vary so much
•
•
•
•
Correlation with gross margin, capital intensity
and deviation of sales from forecast.
Characterize the “earns versus turns” tradeoff.
How to benchmark inventory productivity.
Understand how firms make aggregatelevel inventory decisions.
(C) Vishal Gaur, Cornell University, 2008
6
Description of Data
• Data:
– Obtained from S&P’s Compustat database
– 311 firms across 10 retailing segments for years 1985-2000.
– 3407 observations across firms and years; 11 annual
observations per firm.
• Preparation:
– At least five consecutive years of observation for each firm
• Causes of missing data: new entry, mergers, acquisitions,
liquidations.
– Missing data other than at the beginning or the end of the
period
• Bankruptcy and reorganization
– Inventory valuation method
• FIFO, LIFO, Average cost method, Retail method.
(C) Vishal Gaur, Cornell University, 2008
7
Variables
1.
Inventory Turnover IT = Cost of Goods Sold
2.
Gross Margin
GM =
3.
Capital Intensity
Avg Gross Fixed Assets
CI =
Avg Inventory + Avg Gross Fixed Assets
4.
Sales Surprise
SS =
Average Inventory
(C) Vishal Gaur, Cornell University, 2008
Sales - Cost of Goods Sold
Sales
Sales Realized
Sales Forecast
8
Model Specification
logITsit = Fi + c t + b1s logGMsit + b2s logCIsit + b3s logSS sit + ε sit
where
• s denotes segment index, i the firm index, and t the year index.
• Fi : firm-specific fixed effects.
Control for differences in the intercept between firms, such as between their
managerial efficiency, location, accounting policies, marketing, etc.
• ct : year-specific fixed effects.
Control for differences in economic conditions over time.
• b1s, b2s, b3s: segment-wise coefficients.
b1s ≠ 0 for hypothesis 1, b2s > 0 for hypothesis 2, b3s > 0 for hypothesis 3.
• εsit denotes the error term.
(C) Vishal Gaur, Cornell University, 2008
9
Summary of Data
Retail Industry
Segment
Apparel And
Accessory Stores
Catalog, Mail-Order
Houses
Department Stores
Drug & Proprietary
Stores
Food Stores
Hobby, Toy, And
Game Shops
Home Furniture &
Equip Stores
Jewelry Stores
Radio,TV, Cons
Electr Stores
Variety Stores
Aggregate statistics
# annual
Average Sales Inventory
# of firms observations
Turnover
($ million)
72
786
979.1
4.57
2.13
45
441
439.9
8.60
9.11
23
309
6058.6
3.87
1.45
23
256
2309.5
5.26
2.90
57
650
4573.6
10.78
4.58
10
98
1455.5
2.99
1.08
13
125
391.2
5.44
10.43
15
156
475.2
1.68
0.58
17
200
1585.0
4.10
1.54
36
386
6548.7
4.45
2.92
311
3407
2791.4
6.08
5.41
(C) Vishal Gaur, Cornell University, 2008
Gross
Margin
0.37
0.08
0.39
0.17
0.34
0.08
0.28
0.07
0.26
0.06
0.35
0.07
0.40
0.07
0.42
0.13
0.31
0.11
0.29
0.09
0.33
0.11
Capital
Intensity
0.59
0.14
0.50
0.18
0.63
0.10
0.48
0.12
0.75
0.08
0.46
0.14
0.55
0.16
0.36
0.11
0.44
0.09
0.51
0.15
0.57
0.17
10
Overall Fit Statistics
• Model explains 66.7% of the within-firm variation and
97.2% of the total variation (within and across firms) in
log(IT).
• Intercept of the regression line varies across firms and
across years.
• The coefficients of gross margin, capital intensity and
sales surprise are statistically significant. They differ by
segment.
(C) Vishal Gaur, Cornell University, 2008
11
Coefficients’ Estimates
Segment-wise coefficients
Apparel And Accessory Stores
Catalog, Mail-Order Houses
Department Stores
Drug & Proprietary Stores
Food Stores
Hobby, Toy, And Game Shops
Home Furniture & Equip Stores
Jewelry Stores
Radio,TV,Cons Electr Stores
Variety Stores
Pooled coefficients
Gross Margin
Capital Intensity
Sales Surprise
-0.153
-0.226
-0.310
-0.186
-0.351
-0.571
-0.017*
-0.438
-0.500
-0.313
-0.285
0.977
-0.039*
0.861
0.361
1.085
-0.015*
0.562**
0.038*
0.268
0.106
0.252
0.053
0.225
0.189
0.143
0.179
0.215
0.174
0.279
0.140
0.176
0.143
• Coefficients marked * are not significant, coefficients marked ** have p<0.02, all
other coefficients have p<0.001.
(C) Vishal Gaur, Cornell University, 2008
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Application to Benchmarking
• Tradeoff curve
– model specifies the tradeoff between IT, GM and CI, and
corrects for the effect of sales surprise.
( GM )
0.283
( CI )
−0.252
( SS )
−0.143
IT = Firm-specific constant
× Time-specific constant
• Adjusted Inventory Turnover (AIT)
– equals the residual from the model and shows the distance
of a firm from its tradeoff curve (benchmark).
Residual = log AITsit = log ITsit + 0.285log GM sit
− 0.252 log CI sit − 0.143log SS sit
(C) Vishal Gaur, Cornell University, 2008
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Example 1: Comparison of Four Consumer Electronics
Retailers
10
9
Inventory Turns
8
7
6
5
4
3
2
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Gross Margin (%)
Best Buy Co. Inc.
(C) Vishal Gaur, Cornell University, 2008
Circuit City Stores
Radio Shack
CompUSA
14
Example 1: Values of Adjusted Inventory Turns for different gross margins for
the four consumer electronics retailers
14
Best Buy Co. Inc.
Circuit City Stores
CompUSA
Radio Shack
12
Inventory Turns
10
8
6
4
2
0
0
0.1
0.2
0.3
Gross Margin
0.4
0.5
0.6
Note: Figures are drawn using the average values of CI and setting SS = 1.
(C) Vishal Gaur, Cornell University, 2008
15
Example 2: Comparison across years within a firm Ruddick Corp.
IT is decreasing with time, but AIT
is increasing with time.
Gross Margin and Capital Intensity
are increasing with time.
9.5
0.9
9
y = -0.0194x + 8.3937
R2 = 0.0592
0.8
0.7
8.5
0.6
8
0.5
7.5
0.4
0.3
7
0.2
0
1986
y = 0.0704x + 6.2215
R2 = 0.5705
6.5
0.1
6
1988
1990
1992
Gross Margin
1994
1996
1998
Capital Intensity
2000
1987
1989
1991
1995
1997
1999
Time (in years)
Inventory Turnover
(C) Vishal Gaur, Cornell University, 2008
1993
Adjusted Inventory Turnover
16
(C) Vishal Gaur, Cornell University, 2008
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Average stock returns of public retailers & S&P 500 firms
during 1978-2005
257 Retail firms
15.3% average return, 25.8% among
survivors
Number of Firms
Firms in the S&P 500 index in 1978
14.1% average return, 21.7% among
survivors
100
180
90
160
80
140
70
120
60
100
50
80
40
60
30
40
20
20
10
0
0
BNRT
-30
-20
-10
35% retailers
went bankrupt
0
10
20
30
40
50
60
70
80
BNRT
-20
-10
0
10
20
30
40
50
60
70
80
90
100
Average Annual Stock Return (%)
$1000 invested in Wal-mart in 78 worth $706,000 in Dec. 2005
$1000 in Circuit City in 78 worth $828,000 in Dec. 2005
$1000 in Gap in 78 worth $351,500 in Dec. 2005
(C) Vishal Gaur, Cornell University, 2008
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Construction of portfolios of firms
1
Jan 1,
2002
1
Dec 31,
2002
2
Jun 30,
2003
3
Jun 30,
2004
Obtain annual financial statements for fiscal year ending between Jan
1 and Dec 31, 2002. For example, fiscal year 2001 may end on Jan
31, 2002.
In each retail segment, rank firms by chosen metric and divide into 5
or 10 equal portfolios.
2
Invest $1 in each portfolio on June 30, 2003 equally divided among
the firms in the portfolio.
3
Sell holdings on June 30, 2004 and form new portfolios using data
available up to Dec 31, 2003.
(C) Vishal Gaur, Cornell University, 2008
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Variables used to form portfolios
IT:
inventory turnover
[ = closing inventory/cost of goods sold]
ΔIT:
IT for current year – IT for previous year
GM: gross margin
[ = (sales – cost of goods sold)/sales]
ΔGM: GM for current year – GM for previous year
AIT:
adjusted inventory turnover
ΔAIT: AIT for current year – AIT for previous year
Ranking is done within each retail segment for each year
(C) Vishal Gaur, Cornell University, 2008
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Comparison of total returns on portfolios formed
in different ways
Variables used to form portfolios
Portfolio
rankings
IT
ΔIT
GM
ΔGM
AIT
ΔAIT
Low
0.81
0.70
1.21
1.02
0.90
0.77
2
0.84
1.05
0.88
1.14
0.86
0.99
3
1.15
1.04
1.14
1.26
1.03
1.11
4
1.10
1.28
1.04
0.99
1.23
1.18
High
1.54
1.36
1.11
0.98
1.41
1.38
• Table reports average monthly stock return (%) for 5 portfolios each formed on IT, ΔIT, GM,
ΔGM, AIT and ΔAIT.
• Number of observations in a portfolio range between 5253 and 6329.
• Standard deviation of monthly stock returns = 20% (approx.) in each portfolio.
(C) Vishal Gaur, Cornell University, 2008
21
Results of performance-attribution regressions Summary
•
Using AIT
– Estimate of the intercept, α, increases as portfolio rank increases.
– Low ranked portfolios have significantly negative intercept, showing belowaverage returns.
– Five out of ten portfolios have statistically significant intercept (p=0.10)
– Abnormal return on a zero investment portfolio (buy top 30% and short-sell
bottom 30% firms at the beginning of each year) = 0.9 bp/month = 11.25% per
year. (p<0.01)
•
Using IT
– Estimate of the intercept, α, has a less evident trend as portfolio rank increases.
– Two out of ten portfolios have statistically significant intercept (p=0.10)
– Abnormal return on a zero investment portfolio is not statistically significant.
•
All regressions yield significant F-statistics (p<0.01) with R2 ranging
between 36.5% and 61.2%.
(C) Vishal Gaur, Cornell University, 2008
22
Incorporating Price and Inventory
Endogeneity in Firm-Level
Sales Forecasting
Saravanan Kesavan
Vishal Gaur
Ananth Raman
23
(C) Vishal Gaur, Cornell
23
Sales, Inventory, and Margin for a
Retailer are Interrelated
• Customer purchases depend
on product availability,
variety, and prices.
Sales
• Sales are input into retailer’s
decisions on inventory and
margin.
• Inventory and Margin
influence each other.
Inventory
Margin
The variables Sales, Inventory, and Margin are measured for a given firm for a
given year. Margin (or relative markup) is used as a measure for price.
(C) Vishal Gaur, Cornell University, 2008
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24
Implications of Interrelationships
among Sales, Inventory, and Margin
Data are the joint outcome of all six interrelationships!!
z
z
Simple correlation among sales, inventory, and
margin insufficient to determine causation
Change to one variable affects the other two
variables
¾
z
Not possible to evaluate observed practices easily
Time-series methods for forecasting sales ignoring
inventory and margin are inadequate
¾
Past sales managed using inventory and margin
(C) Vishal Gaur, Cornell University, 2008
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25
Measurement of Endogenous
Variables
Let i = firm index, t = year index, q = quarterly index
[Cost of goods sold]it
Average sales per store,
CSit =
[Number of stores]it
4
Average inventory per store, ISit =
Margin,
∑ Ending inventory
itq
q=1
4*[Number of stores]it
MUit =
Revenueit
[Cost of goods sold]it
Notes:
1. Sales measured at cost and not at price since revenue encompasses margin.
2. Normalization of data by the number of stores.
3. Inventory and COGS adjusted for LIFO reserves.
(C) Vishal Gaur, Cornell University, 2008
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26
Predetermined Variables
SGA per store,
SGA it =
[Selling, general & administrative expenses]it
[Number of stores]it
4
Proportion of new inventory, PIit =
∑ [ Accounts payable]
itq
q=1
4
∑ [Ending inventory ]
itq
q=1
Store growth,
Git =
[Number of stores]it
[Number of stores]i,t-1
4
∑ [Net property, plant, & equipment]
itq
Capital investment per store,CAPSit =
q=1
[ 4*Number of stores]it
Others: Index of consumer sentiment (ICS); Lagged sales per store; Lagged margin
Notes:
1. Net property, plant, & equipment is adjusted for operating leases.
2. Proportion of new inventory differs from days of inventory.
(C) Vishal Gaur, Cornell University, 2008
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27
Predetermined variables
Lagged SGA per store, sgait-1
Lagged index of consumer
sentiment, icsi,t-1
Sales per
store, csit
Store growth, git
Lagged proportion of new
inventory, pii,t-1
Inventory per
store, isit
Lagged sales per store, csi,t-1
Lagged cap. investment per
store, pii,t-1
Gross
margin, muit
Lagged gross margin, gmi,t-1
(C) Vishal Gaur, Cornell University, 2008
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Model Specification: Structural
Equations
cs: Sales per store
is: Inventory per store
z
Aggregate Sales Equation
Inventory
Elasticity
mu: Margin
Price
Elasticity
⎧Index of ⎫
⎧Proportion
⎫
⎪
⎪
csit = Fi + α11isit + α12 muit + α13 {SGA per store}it −1 + α14 ⎨
⎬ + α15 {Store Growth}it + α16 ⎨Consumer ⎬ + ε it
⎩of new inventory ⎭i ,t −1
⎪Sentiment ⎪
⎩
⎭t −1
z
Aggregate Inventory Equation
Stocking
Propensity
to Sales
Stocking
Propensity
to Margin
⎧ Proportion of ⎫
⎧Capital Inv.⎫
isit = J i + α 21csit + α 22 muit + α 23 {Sales per store}i ,t −1 + α 24 ⎨
⎬ + α 25 {Store Growth}it + α 26 ⎨
⎬ + ηit
⎩ new inventory ⎭i ,t −1
⎩ per store ⎭i ,t −1
z
Gross Margin Equation
Markup
Propensity
to Sales
Markup
Propensity
to Inventory
muit = H i + α 31csit + α 32isit + α 33 {Store Growth}it + α 34 {Margin}it −1 + υit
(C) Vishal Gaur, Cornell University, 2008
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29
Application to Forecasting
z
Reduced Form Model
¾
¾
Forecasts simultaneously for sales per store, inventory per store, and
margin
We evaluate forecasts of sales revenue per store and total sales revenue
(C) Vishal Gaur, Cornell University, 2008
30
Comparison with financial
analysts
z
z
z
Consensus analysts’ forecast of sales obtained from
I/B/E/S
Use forecasts generated 11-12 months before the
fiscal year-end date
For our model:
¾
z
Expected number of new store openings taken from
previous year’s 10-K statement
Exclude observations in which number of stores
changed by more than 30%
¾
M&A, bankruptcies.
(C) Vishal Gaur, Cornell University, 2008
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Results of comparison with financial analysts
IBES
12 months
Reduced
Form
Model
ARIMA
Model
(1,1,1)
Double
Exponential
Smoothing
Model
Year
“n”
MAPE
MAPE
MAPE
MAPE
2004
77
4.97%
4.77%
5.24%
6.04%
2005
79
4.63%
4.15%
5.31%
5.56%
2006
64
5.18%
4.03%
4.86%
5.63%
(C) Vishal Gaur, Cornell University, 2008
32
Is forecast error correlated with the principles of
our model?
Positive analyst
bias for current
year
Over-inventoried
Inventory/store
residual in the
previous year
Negative analyst
bias for current
year
Under-inventoried
Underpriced
Overpriced
Gross margin residual in the previous
year
Regression results show that both types of bias are present in analysts’
forecasts and are statistically significant.
(C) Vishal Gaur, Cornell University, 2008
33
Uses of our model
z
To financial analysts / outside experts
¾
z
To firms
¾
¾
z
For forecasting future sales of firms
in aggregate planning
In performance analysis
Enable better communication between the
firm and its investors
(C) Vishal Gaur, Cornell University, 2008
34
(C) Vishal Gaur, Cornell University, 2008
35
An Optimization Algorithm for the Inventory
Routing Problem and Its Implementation at a
Supermarket Chain
Vishal Gaur, Marshall L. Fisher
(C) Vishal Gaur, Cornell University, 2008
36
Albert Heijn Store and DC Locations
650 Albert Heijn stores +
350 other stores
4 Regional DCs
1 National DC
(C) Vishal Gaur, Cornell University, 2008
37
Problem Definition
• Givens
– A set of stores served by a single distribution center (DC)
– A one week planning horizon; time is divided into discrete epochs
of one hour each
– Demand forecast for each hour at each store
– Travel times and costs between all locations
• Objective: to determine a periodic weekly delivery
schedule specifying the times when each store should be
replenished and the vehicle routes that service these
requirements at minimum cost.
(C) Vishal Gaur, Cornell University, 2008
38
Albert Heijn Supply Chain and Problem Definition
Suppliers
National
DC
Slow moving items
Suppliers
Regional
DCs
4 DCs
Fast moving items
Stores
650 Albert Heijn
stores +
350 other stores
Short-term Problem (frequency: at least once a day)
Solve VRPTW using actual order volumes and planned delivery times.
Long-term Problem (frequency: once in 3 months)
Determine delivery times and vehicle routes using forecasted volume.
Previously solved by a hierarchical approach.
(C) Vishal Gaur, Cornell University, 2008
39
Characteristics of Store Demand
Variation in demand during a week
Demand Rate
(units/hour)
3.5
Variation in demand during the year
Total Weekly
Sales Volume
140
3.0
120
2.5
100
2.0
80
1.5
60
1.0
40
0.5
Mon
Tue
Wed Thu
Fri
20
Sat
0
0
0
12
24
36
48
Time (in hours)
60
72
0
10
20
30
40
50
60
Time (in weeks)
Demand varies considerably by hour but the same pattern
repeats every week. Coefficient of variation of demand is about
5%.
(C) Vishal Gaur, Cornell University, 2008
40
Use of generalized minimum weight matching on non-bipartite
graphs when each cluster is restricted to at most two stores
• Matching: A subset of edges in a graph with the property that every
vertex has at most one edge in the subset incident to it.
• Types of matching problems:
– Maximum weight matching
– Minimum weight perfect matching
• Generalized minimum weight matching problem: minimize the sum
of the costs of the edges in the matching plus the sum of the costs of
the unmatched vertices.
• We convert our problem into a maximum weight matching problem.
Algorithms for this problem include Edmonds O(n4), Gabow O(n3),
Micali and Vazirani O(m√n).
(C) Vishal Gaur, Cornell University, 2008
41
Sequential application of the generalized minimum weight matching
algorithm gives us clusters with progressively larger number of stores.
First iteration
Second iteration
3
2
5
3
4
1
1
2
5
7
7
6
6
(C) Vishal Gaur, Cornell University, 2008
4
42
Flowchart of the Randomized Algorithm
For stores i, j, and iteration l,
Tijl = number of times i and j have combined together up to iteration l.
Pijl = 1/(1 + Tijl) = probability of splitting a route at link (i, j) in iteration l.
Randomly split some clusters
Minimum Weighted Matching
Update probabilities of
combination of store pairs
Construct new routes and delivery
schedule
Termination Criteria
(C) Vishal Gaur, Cornell University, 2008
43
Additional Constraints for the Implementation at
Albert Heijn, BV
• Time window constraints
• Store-vehicle restrictions
• Loading-unloading time delays and cost
• Traffic delays
• Delivery time variability
• Vehicle waiting time restrictions and cost
• Time between departure and last stop
(C) Vishal Gaur, Cornell University, 2008
44
Assignment of routes to a heterogeneous fleet of trucks
• Deterministic scheduling of jobs with arrival times and due
times on parallel machines.
• NP-Hard. Heuristics do not even guarantee a feasible
solution.
• Three phase heuristic
– Lagrangian relaxation with fixed penalty cost assigned to each
truck type
– Progressive reduction of problem size
– Face validity: pair-wise exchange of routes between trucks
(C) Vishal Gaur, Cornell University, 2008
45
Implementation
• Began in June 1999.
• Phased implementation to facilitate testing and get buy-in
from the company
– Solve VRPTW with existing delivery times and at most two stores
per route
– Solve VRPTW with existing delivery times and unlimited number
of stores per route
– Solve IRP with at most two stores in a cluster and restricted
delivery times
– Solve IRP with unrestricted cluster size and delivery times.
• Main activities: pilot implementation and testing, training
of route planners, design of graphical user interface.
(C) Vishal Gaur, Cornell University, 2008
46
Summary of Computational Results
Each problem has 207 stores across 6 days, vehicle capacity 26 units,
and daily store demand ranging between 3 units and 68 units.
Problem Scenarios
1
Cost ($)
A
Albert Heijn's solution
242,751.39
B
VRPTW with at most 2
deliveries per route
221,732.78
C
D
Savings (%)
Cost ($)
3
Savings (%)
247,501.22
Cost ($)
Savings (%)
243,146.80
8.66%
227,687.77
8.01%
223,889.22
7.92%
VRPTW with unlimited
215,414.55
number of deliveries per route
11.26%
220,400.90
10.95%
217,094.64
10.71%
IRP with at most 2 stores per
208,323.03
cluster
14.18%
214,054.01
13.51%
209,983.17
13.64%
Savings with respect to B
E
2
IRP with unlimited number of
stores per cluster
6.05%
200,463.69
Savings with respect to C
(C) Vishal Gaur, Cornell University, 2008
17.42%
6.94%
5.99%
205,939.19
16.79%
6.56%
6.21%
202,440.14
16.74%
6.75%
47
Personal Experience of Jeroen Hirdes:
A Route Planner’s Perspective
• Working with the latest developments
• Better understanding of route scheduling algorithms
• Benefits of storing data to create long term history
• Better judgement of store behaviour
(C) Vishal Gaur, Cornell University, 2008
48
Example
VRSA Routes
Intertour routes
(C) Vishal Gaur, Cornell University, 2008
49
Summary
• Lessons from the implementation
- Decision support role: enabling Albert Heijn to evaluate the cost impact
of tactical decisions such as delivery frequency constraint, time window
constraint, etc.
- Performance analysis: determine the cost of order variability at stores,
and deviations from scheduled delivery times.
• Further issues addressed by the application
– Assignment of routes to trucks,
– Load balancing at the warehouse,
– Determining which DC to assign to a store,
– Management of deliveries from suppliers to stores.
(C) Vishal Gaur, Cornell University, 2008
50
In-store experiments to determine the impact of
price on sales
Objectives
• Select a subset of stores in a retail chain for conducting an
experiment
– Short lifecycle products
• Estimate price elasticity of the demand for the retail chain
(C) Vishal Gaur, Cornell University, 2008
51
Sample Data – Total Store Sales
Sales ($)
Store
101
102
104
105
106
107
108
109
110
111
201
202
203
Opening
Year
91
92
93
93
94
94
96
95
95
96
94
94
94
Month to date
This Year
243360.89
200584.79
161107.45
167564.02
166967.08
156529.29
159969.72
138550.52
199359.06
204735.67
281504.57
127881.34
159432.69
(C) Vishal Gaur, Cornell University, 2008
Month to date
Last Year
225825.43
161526.19
135974.13
125992.23
134297.03
110326.95
125368.47
108505.13
140331.28
168748.16
271636.39
88210.31
144225.67
Year to date This
Year
774970.63
680822.05
494684.61
492248.49
542107.98
523500.39
481693.31
426937.44
595843.71
633289.33
904793.24
403403.03
537945.19
Year to date
Last Year
776310.7
616936.85
497567.43
462623.69
506260.25
472678.06
480267.04
433574.55
538571.22
598483.91
913364.1
339888.69
522730.67
52
Sample Input Data – Fraction of Sales from
Each Product Category
Store
101
102
104
105
106
107
108
109
110
111
201
202
203
20
5.2
6.5
5.9
5.0
16.1
5.2
19.0
5.0
11.0
14.9
6.2
5.8
6.8
(C) Vishal Gaur, Cornell University, 2008
Product Categories
10
15
22
6.0
11.2
6.0
7.4
12.4
7.7
5.2
8.2
5.9
4.0
8.7
6.2
3.3
9.2
8.1
3.9
10.6
7.6
3.0
9.2
6.3
5.1
6.7
6.4
3.2
11.1
6.7
4.4
9.3
5.9
5.3
13.3
9.3
4.3
9.8
7.9
5.3
11.4
7.9
40
9.1
9.2
7.0
9.1
6.1
6.3
7.4
8.3
8.2
10.0
10.3
9.7
9.0
53
Experiment Design
Store Selection Problem – Block Design
We select 3 stores from each cluster such that
• They are relatively isolated from other stores in the chain
• They are similar in age and size
Prices
High
Clusters
Medium
Low
1
2
3
4
5
6
(C) Vishal Gaur, Cornell University, 2008
54
How to group stores using historical sales mix:
distance metric
Distance estimates obtained for a
sample of 6 stores
Distance between two stores
=
(
fi1 − f j1
) (
2
+ fi2 − f j2
) (
2
+ fi3 − fj3
)
2
where fi1 = fraction of sales of store i from
department 1,
fi2 = fraction of sales of store i from
department 2, etc.
101
102
103
104
102
0.24
103
0.25
0.26
104
0.41
0.41
0.55
105
0.14
0.16
0.13
0.45
106
0.48
0.34
0.48
0.29
105
0.43
Principle for grouping stores: Two stores are said to be similar if the distance
between them is small, otherwise they are said to be dissimilar.
We wish to group stores into clusters such that stores within a cluster are
similar to each other and stores in different clusters are dissimilar from each
other.
(C) Vishal Gaur, Cornell University, 2008
55
How to group stores using previous sales mix:
clustering
•
Objective function:
– Minimize sum of all distances within
clusters
•
Decision variables
– Whether a store is the ‘seed’ for a cluster
– Whether store i is clustered with store j, for
all pairs (i,j)
•
This picture is a schematic of clusters. All
interconnections are not shown to avoid
cluttering the graph.
(C) Vishal Gaur, Cornell University, 2008
Constraints
– Each store must be in at least one cluster
– If store i is clustered with store j, then store j
must be a seed
– Minimum number of clusters
– Minimum size of a cluster
56
List of stores selected for the experiment
Cluster
Store
1
102
103
204
105
108
402
205
302
303
325
401
526
107
326
527
110
503
504
2
3
4
5
6
Year To
Opening
Date Sales
Year
($ '000)
92
680.8
93
610.5
94
514.1
94
492.2
96
481.7
94
477.9
95
466.2
94
432.6
95
434.1
96
561.8
94
644.1
96
556.1
94
523.5
96
438.1
96
441.8
95
595.8
96
547
96
553.3
(C) Vishal Gaur, Cornell University, 2008
% Sales from each category
1
2
3
4
5
11.3
5.4
8.1
8.5
7.9
9.9
11.6
6.8
10.1
10.1
8.9
6
7.5
10.5
10.5
11
6.1
7.9
8.4
8.9
9.7
5
6.4
11.4
12.3
11.3
8.9
7.9
8.4
7.5
57
Summary Statistics of Products Tested
Prices ($)
Purchase Cost ($)
Low
Medium
High
A: Family Game Center
19.99
24.99
29.99
11.00
B: Phonics Traveler
24.99
29.99
34.99
18.00
C: Headset Walkie Talkie
14.99
19.99
24.99
11.00
Regular Prices
(C) Vishal Gaur, Cornell University, 2008
58
Assignment of Products to Stores
Products are assigned to stores using a randomized block design to
avoid systematic interactions between products.
Cluster 1
Cluster 2
Store 1
Store 2
Store 3
Store 4
Store 5
Store 6
Product A
29.99
24.99
19.99
24.99
19.99
29.99
Product B
24.99
29.99
34.99
29.99
24.99
34.99
Product C
14.99
19.99
24.99
19.99
14.99
24.99
Control Stores
Precautions taken during the experiment
• Price labels were changed to reflect new prices
• Store managers were not informed about the experiment to control
for execution differences.
(C) Vishal Gaur, Cornell University, 2008
59
Sample Output Data from the Zany Brainy Study
Product C
Week ending 10/3
Beginning
# of
Sales
Inventory
Transactions
Week ending 11/7
Beginning
# of
Sales
Inventory
Transactions
Cluster 1
Store 1
3
0
2794
53
7
362
Store 2
Store 3
12
30
1
0
2565
2365
35
31
9
3
330
324
Store 4
8
3
2037
38
6
252
Store 5
Store 6
7
6
1
0
2020
1883
37
36
6
2
238
279
Store 7
11
1
1685
35
5
248
Store 8
Store 9
6
11
0
1
1681
1612
36
34
6
3
220
218
Cluster 2
Cluster 3
Total Test Period = 6 weeks
(C) Vishal Gaur, Cornell University, 2008
60
Results of the Zany Brainy experiment Sales Data
Total Unit Sales for the 3 test products at each of the 3 Price Levels
80
70
60
50
40
30
20
10
0
Low
Product A
(C) Vishal Gaur, Cornell University, 2008
Medium
Price
Product B
High
Product C
61