U.S. patent application number 16/533102 was filed with the patent office on 2020-02-06 for system and method for item category footage recommendation.
This patent application is currently assigned to Walmart Apollo, LLC. The applicant listed for this patent is Walmart Apollo, LLC. Invention is credited to Ashish GUPTA, Somedip KARMAKAR.
Application Number | 20200042937 16/533102 |
Document ID | / |
Family ID | 69228083 |
Filed Date | 2020-02-06 |
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United States Patent
Application |
20200042937 |
Kind Code |
A1 |
KARMAKAR; Somedip ; et
al. |
February 6, 2020 |
SYSTEM AND METHOD FOR ITEM CATEGORY FOOTAGE RECOMMENDATION
Abstract
A method for computer modeling a retail environment includes:
calculating a space elasticity for an item category in a retail
store, using a constrained linear regression model; calculating a
cross-space elasticity for the item category in the retail store,
using a multiple non-linear regression model; generating a category
space allocation for the item category in the retail store, using a
non-linear multiple-constraint mixed integer optimization model,
based on the space elasticity of the item category and the
cross-space elasticity of the item category; and generating an
electronic planogram for the retail store, based on the category
space allocation of the item category.
Inventors: |
KARMAKAR; Somedip; (Kolkata,
IN) ; GUPTA; Ashish; (Bengaluru, IN) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Walmart Apollo, LLC |
Bentonville |
AR |
US |
|
|
Assignee: |
Walmart Apollo, LLC
Bentonville
AR
|
Family ID: |
69228083 |
Appl. No.: |
16/533102 |
Filed: |
August 6, 2019 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62773611 |
Nov 30, 2018 |
|
|
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G06Q 10/067 20130101;
G06Q 10/0875 20130101 |
International
Class: |
G06Q 10/08 20060101
G06Q010/08; G06Q 10/06 20060101 G06Q010/06 |
Foreign Application Data
Date |
Code |
Application Number |
Aug 6, 2018 |
IN |
201811029541 |
Claims
1. A method for computer modeling a retail environment, comprising:
calculating a space elasticity for an item category in a retail
store, using a constrained linear regression model; calculating a
cross-space elasticity for the item category in the retail store,
using a multiple non-linear regression model; generating a category
space allocation for the item category in the retail store, using a
non-linear multiple-constraint mixed integer optimization model,
based on the space elasticity of the item category and the
cross-space elasticity of the item category; and generating an
electronic planogram for the retail store, based on the category
space allocation of the item category.
2. The method of claim 1, wherein the constrained linear regress
model comprises Log(D)=log(a)+b*log(x), wherein D is a demand of
the item category, x is a number of horizontal footage of the item
category on one or more shelves in the retail store, a is a scale
parameter being=>0, and b is the space elasticity of the item
category being 0<=b<=1.
3. The method of claim 2, wherein the space elasticity is
calculated by fitting the constrained linear regress model on known
data between the demand of the item category and the number of
horizontal footage of the item category.
4. The method of claim 1, wherein the non-linear multiple
regression model is derived from the constrained linear regression
model by including horizontal footage allocations of other item
categories in the retail store.
5. The method of claim 4, wherein the non-linear multiple
regression model is solved using least absolute shrinkage and
selection operator (LASSO) regression analysis method, such that
over-fitting of the multiple regression model is avoided, and
relatively important item categories which influence a demand of
the item category.
6. The method of claim 1, wherein the constrained linear regression
model further comprises parameters including a linear horizontal
footage of the self and a number of the shelves.
7. The method of claim 1, wherein the constrained linear regression
further comprises parameters including clusters of the retail
store.
8. The method of claim 1, wherein the non-linear
multiple-constraint mixed integer optimization model is solved
using genetic algorithm
9. The method of claim 1, wherein the non-linear
multiple-constraint mixed integer optimization model comprises R =
i = 1 n ( p i .alpha. i ( x i L * S ) b i j = 1 .noteq. i n ( x j L
* S ) g ij ) , ##EQU00005## wherein: p.sub.i is a unit price of an
ith item category in the retail store, x.sub.i is category space
allocations of the ith item category and is a positive number, L is
a linear footage per shelf, S is a number of shelves in the retail
store, a.sub.i, b.sub.i are parameters which are solved using the
constrained linear regression model, g.sub.ij is a cross-space
elasticity of the ith item category on a jth item category solved
using the multiple regression model; and
lb.sub.i<=x.sub.i<=ub.sub.i in which lb.sub.i and ub.sub.i
are respectively lower and upper bounds of category space
allocation of the ith item category.
10. The method of claim 9, wherein the lower and upper bounds are
derived from business constraints of 1.5 case pack and 3.5 days of
supply (DOS), and 1 DOS safety stock, to eliminate over-stock and
out-of-stock situations: l b i = max ( 1.5 CP 1 DOS units ) vf i df
i , ub i = max ( 1.5 CP 4.5 DOS units ) vf i df i + 1 ,
##EQU00006## in which 1 DOS units=median of (historical) daily
sales vf.sub.i and df.sub.i are respectively vertical and depth
footage of the ith item category for the shelf.
11. A system for computer modeling a retail environment,
comprising: a processor configured to: calculate a space elasticity
for an item category in a retail store, using a constrained linear
regression model; calculate a cross-space elasticity for the item
category in the retail store, using a multiple non-linear
regression model; generate a category space allocation for the item
category in the retail store, using a non-linear
multiple-constraint mixed integer optimization model, based on the
space elasticity of the item category and the cross-space
elasticity of the item category; and generate an electronic
planogram for the retail store, based on the category space
allocation of the item category.
12. The system of claim 11, wherein the constrained linear regress
model comprises Log(D)=log(a)+b*log(x), wherein D is a demand of
the item category, x is a number of horizontal footage of the item
category on one or more shelves in the retail store, a is a scale
parameter being=>0, and b is the space elasticity of the item
category being 0<=b<=1;
13. The system of claim 12, wherein the space elasticity is
calculated by fitting the constrained linear regress model on known
data between the demand of the item category and the number of
horizontal footage of the item category.
14. The system of claim 11, wherein the non-linear multiple
regression model is derived from the constrained linear regression
model by including horizontal footage allocations of other item
categories in the retail store.
15. The system of claim 14, wherein the non-linear multiple
regression model is solved using least absolute shrinkage and
selection operator (LASSO) regression analysis method, such that
over-fitting of the multiple regression model is avoided, and
relatively important item categories which influence a demand of
the item category.
16. The system of claim 11, wherein the constrained linear
regression model further comprises parameters including a linear
horizontal footage of the self and a number of the shelves.
17. The system of claim 11, wherein the constrained linear
regression further comprises parameters including clusters of the
retail store.
18. The system of claim 11, wherein the non-linear
multiple-constraint mixed integer optimization model is solved
using genetic algorithm
19. The system of claim 11, wherein the non-linear
multiple-constraint mixed integer optimization model comprises R =
i = 1 n ( p i .alpha. i ( x i L * S ) b i j = 1 .noteq. i n ( x j L
* S ) g ij ) , ##EQU00007## wherein: p.sub.i is a unit price of an
ith item category in the retail store, x.sub.i is category space
allocation of the ith item category and is a positive number, L is
a linear footage per shelf, S is a number of shelves in the retail
store, a.sub.i, b.sub.i are parameters which are solved using the
constrained linear regression model, g.sub.ij is a cross-space
elasticity of the ith item category on a jth item category solved
using the multiple regression model; and
lb.sub.i<=x.sub.i<=ub.sub.i in which lb.sub.i and ub.sub.i
are respectively lower and upper bounds of category space
allocation of the ith item category.
20. The system of claim 19, wherein the lower and upper bounds are
derived from the business constraints of 1.5 case pack and 3.5 days
of supply (DOS), and 1 DOS safety stock, to eliminate over-stock
and out-of-stock situations: l b i = max ( 1.5 CP 1 DOS units ) vf
i df i , ub i = max ( 1.5 CP 4.5 DOS units ) vf i df i + 1 ,
##EQU00008## in which 1 DOS units=median of (historical) daily
sales, vf.sub.i and df.sub.i are respectively vertical and depth
footage of the ith item category for the shelf.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This patent application claims the priority to Indian
Provisional Application No.: 201811029541, filed Aug. 6, 2018, and
U.S. Provisional Application No. 62/773,611, filed Nov. 30, 2018,
contents of which are incorporated by reference herein.
BACKGROUND
1. Technical Field
[0002] The present disclosure relates to space planning, and more
specifically to a system and method for item category footage
recommendation.
2. Introduction
[0003] Shelf space is a scarce resource for a retailer. Shelf space
allocation may involve the distribution of appropriate amount of
shelf space among different item categories, together with their
locations, in a store in such a way that the total profits and/or
customer satisfaction may be maximized. Due to the limited shelf
space, planograms may be one of the most important aspects that are
used to improve financial performance. Planograms are a subset of
the wider domain of space planning which may include more
well-known research areas such as bin packing and knapsack
problems. Electronic planograms can be also used for inventory
control and vendor relation improvement. Further, a computer system
for managing the shelf space can run inefficiently due to
undesirable space planning. In addition, existing computer models
for generating electronic planograms are inefficient and
inaccurate.
[0004] There is a need for correlating relationship between space
and sales both individually for each item category as well as their
inter-relationships to maximize total profit of item categories in
a department, and to improve the computer system for managing the
shelf space.
SUMMARY
[0005] A method of computer modeling a retail environment for
performing concepts disclosed herein can include calculating a
space elasticity for an item category in a retail store, using a
constrained linear regression model; calculating a cross-space
elasticity for the item category in the retail store, using a
multiple non-linear regression model; generating a category space
allocation for the item category in the retail store, using a
non-linear multiple-constraint mixed integer optimization model,
based on the space elasticity of the item category and the
cross-space elasticity of the item category; and generating an
electronic planogram for the retail store, based on the category
space allocation of the item category.
[0006] A system of computer modeling a retail environment
configured as disclosed herein can include: a processor; and a
computer-readable storage medium having instructions stored which,
when executed by the processor, cause the processor to perform
operations comprising: calculating a space elasticity for an item
category in a retail store, using a constrained linear regression
model; calculating a cross-space elasticity for the item category
in the retail store, using a multiple non-linear regression model;
generating a category space allocation for the item category in the
retail store, using a non-linear multiple-constraint mixed integer
optimization model, based on the space elasticity of the item
category and the cross-space elasticity of the item category; and
generating an electronic planogram for the retail store, based on
the category space allocation of the item category.
[0007] A non-transitory computer-readable storage medium configured
as disclosed herein can have instructions stored which, when
executed by a computing device, cause the computing device to
perform operations which include: calculating a space elasticity
for an item category in a retail store, using a constrained linear
regression model; calculating a cross-space elasticity for the item
category in the retail store, using a multiple non-linear
regression model; generating a category space allocation for the
item category in the retail store, using a non-linear
multiple-constraint mixed integer optimization model, based on the
space elasticity of the item category and the cross-space
elasticity of the item category; and generating an electronic
planogram for the retail store, based on the category space
allocation of the item category.
[0008] Additional features and advantages of the disclosure will be
set forth in the description which follows, and in part will be
obvious from the description, or can be learned by practice of the
herein disclosed principles. The features and advantages of the
disclosure can be realized and obtained by means of the instruments
and combinations particularly pointed out in the appended claims.
These and other features of the disclosure will become more fully
apparent from the following description and appended claims, or can
be learned by the practice of the principles set forth herein.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] FIG. 1 illustrates an exemplary diagram of an assumed model
correlating allocated item category space and demand share of the
item category, according to one embodiment of the present
disclosure;
[0010] FIG. 2 illustrates an exemplary diagram of a modified model
correlating allocated item category space and demand share of the
item category, based on actual data, according to one embodiment of
the present disclosure;
[0011] FIG. 3 illustrates an exemplary histogram of category space
elasticity calculated using a model, according to one embodiment of
the present disclosure;
[0012] FIG. 4 illustrates an exemplary histogram of category
cross-space elasticity calculated using a model, according to one
embodiment of the present disclosure;
[0013] FIG. 5 illustrate an exemplary method of recommending
category space in a retail store; and
[0014] FIG. 6 illustrates an exemplary computer system.
DETAILED DESCRIPTION
[0015] Systems, methods, and computer-readable storage media
configured according to this disclosure are capable of recommending
item category footage (space) allocated in a retail store, which
may provide a process for arranging item categories on shelves in
the retail store. Optimized category space allocation using
conventional methods can be recommended to increase the overall
revenue in a product department or in a retail store. However,
different categories may behave differently in terms of change in
sales for similar change in footage. Also the space allocated to
the categories in the department or retail store can influence each
other positively or negatively in terms of change in demand. This
may lead to learn the relationship between space and sales both
individually for each category as well as their
inter-relationships. As used herein, the "sale" and "demand" are
interchangeable. The "category space/footage" may refer to the
number of the horizontal footage allocated to the category for
displaying the category on a fixture (e.g., one or more shelves) in
a retail store.
[0016] Various specific embodiments of the disclosure are described
in detail below. While specific implementations are described, it
should be understood that this is done for illustration purposes
only. Other components and configurations may be used without
parting from the spirit and scope of the disclosure, and can be
implemented in combinations of the variations provided. These
variations shall be described herein as the various embodiments are
set forth.
[0017] When creating a planogram, allocation of space for each
category may be one of the primary areas of focus. However, the
display space allocated to a category may have a different
influence on sales with respect to different categories. In some
embodiments, optimization using space elasticity may be provided.
As used herein, space elasticity of a category may be defined to
indicate a relationship between space allocation of the category
and observed demand of the category. That is, the measurement of
the impact on a category's sales performance by increasing or
decreasing its allocation of space, for example, within a shelf,
may be reflected by the space elasticity of the category. Space
elasticity may be impacted by many variables, including types of
the category, brands, price, seasonality, etc. A high space
elasticity value may indicate that the category sales can be
greatly affected by change in space allocation of the category.
[0018] Category space elasticity may enable retailers to map demand
data against space variables and generate the associated space
elasticity of demand curves. FIG. 1 illustrates an exemplary
diagram of a model correlating category footage and demand based on
space elasticity of the category, according to one embodiment of
the present disclosure. The model may take a general form as sales
share (demand).about.function (elasticity, space share).
[0019] In this embodiment, the model may take a polynomial form.
For the ith category:
D(i)=a(i)*(x(i){circumflex over ( )}b(i)), where a=>0, and
0<=b<=1
where D(i) is the demand share of the ith category, x(i) is the
number of horizontal footage of the ith category, a(i) is a scale
parameter, b(i) is the space elasticity of the ith category. As can
be seen from FIG. 1, the sales of the ith category may increase
with an increase in the space allocated (footage) of the ith
category, but the rate of increase may diminish gradually.
[0020] In some embodiments, through a transformation, the above
model form may be written as: Log(D(i))=log(a(i))+b(i)*log(x(i)),
so that the parameters (i.e., a and b) can then be estimated by a
constrained linear regression (i.e., a=>0, and
0<=b<=1).
[0021] Other variables may also impact the demand of a category,
such as store location, and shelf height. The above model may be
expanded to include an effect of the total modular footage per
shelf and the number of shelves of a retailer store. Other
explanatory variables like store clusters may also be added to
improve the model. For example, let L and S denote the linear
footage of a shelf and the number of shelves of the store, and c(i)
and d(i) are parameters indicating effects of the linear footage L
and the number S of shelves on the sales, respectively, the updated
model may be
log(D(i))=log(a(i))+b(i)*log(x(i))+c(i)*log(L)+d(i)*log(S), which
may be subject to constraints: 0<=b(i)<=1. Thus, category
space elasticity may be measured, mapped and utilized to enable
retailers to predict profit return on space.
[0022] In some embodiments, the actual sales data of categories may
be validated against the model assumptions to check the proportion
of conformity of the model, and accordingly the
variables/parameters may be updated to improve the model's
validation and accuracy. The proportion of conformity can measure
the categories, for which, unconstrained regression model parameter
estimates, conform or match with the model assumptions of a>0,
0<b<1.
[0023] In other embodiments, instead of the actual sales, category
share of sales and share of space may be used for examining
compliance of a model. Specifically, instead of regressing the
logarithm of actual category sales on logarithm of actual category
space, the share of sales and space are used. For example, a
category X has sales of $20M, and has 10 items. Item 1 has sales
$1M, so item 1 has a share of sales 1/20, i.e. 5% sales share.
Similarly out of 20 ft allocated to category X, 2 ft is allocated
to item 1, so the item 1 has 2/20, i.e. 10% space share. Using
these modified features, improved accuracy and model conformity can
be obtained.
[0024] Also the model mentioned above can be simplified to the
following two cases: effect of total space instead of separated
effects of number of shelves and footage per shelf, i.e.,
c(i)=d(i); and elasticity calculated as effect of space share,
i.e., c(i)=d(i)=-b(i). The parameters c and d represent the effects
of number of shelves and shelf footages. When the share of space
instead of the actual space is considered, a new variable is
created: space share=facings/(number of shelves*shelf footages). So
inherently the unknown variables c and d are the same in magnitude
as the elasticity parameter b and of opposite sign. For a set of
universal product codes (UPCs), the UPCs that demonstrate the
model's compliance (referred to as the compliant UPCs), may be
analyzed using a linear regression model, while constrained
regression may be used for the other UPCs that do not demonstrate
the model's compliance. The results can be validated on categories
of UPCs, as shown in Table 1 below.
TABLE-US-00001 Model Variables Compliance Total Sales 11% Sales
Share 54% Total space 62% Share of facings 80%
[0025] FIG. 2 illustrates an exemplary diagram of a modified model
correlating category footage and demand, based on actual data,
according to one embodiment of the present disclosure. As can be
seen from FIG. 2, the model fits the data well. By fitting this
model on the data, the space elasticity of each category may be
estimated, with the constraint of 0<=space elasticity of
category<=1.
[0026] FIG. 3 illustrates an exemplary histogram of category space
elasticity calculated using a model, according to one embodiment of
the present disclosure. In this embodiment, 27 UPCs are used to fit
the model, the distribution of elasticity results are as shown in
FIG. 3. As can be seen, 12 UPCs have a space elasticity value
ranging from 0 to 0.05 (302); 3 UPCs have a space elasticity value
ranging from 0.05 to 0.1 (304); 7 UPCs have a space elasticity
value ranging from 0.1 to 0.15 (306); 2 UPCs have a space
elasticity value ranging from 0.15 to 0.20 (308); 1 UPCs has a
space elasticity value ranging from 0.25 to 0.30 (310); and 2 UPCs
have a space elasticity value ranging from 0.3 to 0.35 (312). This
model may explain about 74% of the variability on demand on an
average.
[0027] The relative change in sales of a category may be very much
dependent on the space allocated to that category. But the space
allocated to the other categories in the same department/store can
also have some influence over it. That is, the space allocated to
categories in a department/store may influence each other
positively or negatively in terms of change in demand. To take into
this effect, a cross-space elasticity of the category may be used
in determining space allocation. As used herein, the cross-space
elasticity may be referred to as a change in demand of one category
in response to the change in space of the other categories.
[0028] Typically, substitutes may have a negative cross-space
elasticity on a category, whereas complements (or variety
substitutes) may have a positive cross-space elasticity on the
category. For example, the cross-space elasticity of local Spirits
on canned Spirits (traditional substitute) can be -0.014 and beer
on the canned Spirits (variety substitute) can be 0.03.
[0029] In some embodiments, the model for calculation for space
elasticity of a category may be expanded to a multiple regression
problem by including the footage allocations of the other
categories in the department/store as features. This may transform
the demand model to a parameter-heavy complex model, which can be
solved using least absolute shrinkage and selection operator
(LASSO) regression, to avoid over-fitting. In addition, the
variable-selection property of this model may be beneficial in
picking out the relatively important categories which influence the
demand of the target category. For some embodiment, on an average,
this model can explain 95.38% variability in demand shares.
[0030] FIG. 4 illustrates an exemplary histogram of category
cross-space elasticity calculated using a model, according to one
embodiment of the present disclosure. As can be seen from FIG. 4,
some categories have negative cross-space elasticity on other
categories of the same department; some categories have positive
cross-space elasticity on other categories of the same department.
As defined the above, a negative cross-space elasticity may
indicate that demand for a category may be negatively affected by
its replacement with another category of the same department.
Similarly, a positive cross-space elasticity may indicate that
demand for a category may be positively affected by its replacement
with another category of the same department.
[0031] The space elasticity and cross-space elasticity may then be
used to determine the optimal number of footage allocation of each
category in a department/store, that is, to determine category
space, such that the overall revenue of the department/store may be
increased. For determining the optimal number of footage
allocation, the vertical and depth space of categories may be
assumed as constant for each category based on the shelf space
availability of the store. The following non-linear,
multi-constraint optimization problem can be solved to arrive at
these recommendations: maximize: Total Revenue.about.function
(category footage, space elasticity, cross-space elasticity): such
that category footage is a bounded integer and sum (category
footage)=department footage. Specifically: [0032] Maximize:
[0032] R = i = 1 n ( p i .alpha. i ( x i L * S ) b i j = 1 .noteq.
i n ( x j L * S ) g ij ) , ##EQU00001## that is, total revenue R of
the department may be maximized. The total revenue R can refer to
as a sum of unit price of each category*demand for each
category.
[0033] where, .SIGMA..sub.i=1.sup.nx.sub.if.sub.i=L*S, L is a
vector having elements L that is the total linear footage per
shelf, and S is a vector having elements S that is the number of
shelves. That is, L*S represents a sum of total allocated space for
categories of the department that is equal to the total available
space.
[0034] lb.sub.i<=x.sub.i<=ub.sub.i may indicate that
horizontal footage of ith category may be bounded by business
constraints.
x.sub.i's are positive integers, p.sub.i is the unit price, x.sub.i
is the horizontal footage, f.sub.i is the front-facing length of
ith category, L is the total linear footage per shelf and S is the
number of shelves. a.sub.i, b.sub.i are parameters which were
solved in the earlier elasticity model and g.sub.ij is the
cross-space elasticity of ith category on jth category. lb.sub.i
and ub.sub.i are respectively the lower and upper bounds of
horizontal footage of the ith category.
[0035] The lower and upper bounds can be derived from business
constraints. For one example, 1.5 case pack and 3.5 Days of Supply
(DOS) and 1 DOS safety stock may be used as constraints, to
eliminate over-stock and out-of-stock situations:
l b i = max ( 1.5 CP 1 DOS units ) vf i df i , ub i = max ( 1.5 CP
4.5 DOS units ) vf i df i + 1 ##EQU00002##
where 1 DOS units=median of (historical) daily sales, and vf.sub.i
and df.sub.i are respectively the vertical and depth footage of the
ith category for the chosen modular plan.
[0036] FIG. 5 illustrate an exemplary method 500 of recommending
category footage in category department/store. A category of
interest is identified. The space elasticity for the category is
determined. Cross-space elasticity for the category is determined.
The space elasticity and cross space elasticity are then used to
determine the optimal number of footage allocated for the category.
The method 500 may be implemented in the above disclosed systems,
may include the following steps, and thus some details may be
repeated herein.
[0037] At step 502, a space elasticity for an item category in a
retail store is calculated, using a constrained linear regression
model. The constrained linear regress model may comprise
Log(D)=log(a)+b*log(x), wherein D is a demand of the item category,
x is a number of horizontal footage of the item category on one or
more shelves in the retail store, a is a scale parameter
being=>0, and b is the space elasticity of the item category
being 0<=b<=1. The space elasticity of the category may be
calculated by fitting the constrained linear regress model on known
data between the demand of the item category and the number of
horizontal footage of the item category
[0038] The constrained linear regression model may further comprise
parameters including a linear horizontal footage of the self and a
number of the shelves. In addition, the constrained linear
regression may further comprise parameters including clusters of
the retail store.
[0039] At step 504, a cross-space elasticity for the item category
in the retail store is calculated, using a non-linear multiple
regression model. The multiple non-linear regression model may be
derived from the constrained linear regression model by including
horizontal footage allocations of other item categories in the
retail store. The non-linear multiple regression model may be
solved using least absolute shrinkage and selection operator
(LASSO) regression analysis method, such that over-fitting of the
non-linear multiple regression model is avoided, and relatively
important item categories of the retail store which influence a
demand of the item category.
[0040] At step 506, a category space allocation for the item
category in the retail store may be generated, using a non-linear
multiple-constraint mixed integer optimization model, based on the
space elasticity of the item category and the cross-space
elasticity of the item category. The non-linear multiple-constraint
mixed integer optimization model may be solved using genetic
algorithm.
[0041] The non-linear multiple-constraint mixed integer
optimization model may comprise
R = i = 1 n ( p i .alpha. i ( x i L * S ) b i j = 1 .noteq. i n ( x
j L * S ) g ij ) , ##EQU00003##
wherein: p.sub.i is a unit price of an ith category in the store,
x.sub.i is category space allocations of the ith category and is a
positive number, L is a linear footage per shelf, S is a number of
shelves in the retail store, a.sub.i, b.sub.i are parameters which
are solved using the constrained linear regression model, g.sub.ij
is a cross-space elasticity of the ith category on a jth category
solved using the multiple regression model; and
lb.sub.i<=x.sub.i<=ub.sub.i in which lb.sub.i and ub.sub.i
are respectively lower and upper bounds of category space
allocation of the ith item category.
[0042] The lower and upper bounds may be derived from the business
constraints of 1.5 case pack and 3.5 days of supply (DOS), and 1
DOS safety stock, to eliminate over-stock and out-of-stock
situations:
l b i = max ( 1.5 CP 1 DOS units ) vf i df i , ub i = max ( 1.5 CP
4.5 DOS units ) vf i df i + 1 , ##EQU00004##
in which 1 DOS units=median of (historical) daily sales, vf.sub.i
and df.sub.i are respectively vertical and depth footage of the ith
item category for the shelf.
[0043] At step 508, a planogram of the retail store may be
generated, based on the category space allocation of the item
category. Such planogram may maximize the revenue R of all
categories in the same store/department, as described the
above.
[0044] Example results by using the above systems and methods are
demonstrated on a sample of 8 categories for 297 stores. The
projected revenue is demonstrated to have 4.8% gain with 10.94%
change in footage allocation and 99.94% average area covered.
[0045] FIG. 6 illustrates an exemplary computer system or device
that may perform the above systems and methods. With reference to
FIG. 6, an exemplary system 600 can include a processing unit (CPU
or processor) 620 and a system bus 610 that couples various system
components including the system memory 630 such as read only memory
(ROM) 640 and random access memory (RAM) 650 to the processor 620.
The system 600 can include a cache of high speed memory connected
directly with, in close proximity to, or integrated as part of the
processor 620. The system 600 copies data from the memory 630
and/or the storage device 660 to the cache for quick access by the
processor 620. In this way, the cache provides a performance boost
that avoids processor 620 delays while waiting for data. These and
other modules can control or be configured to control the processor
620 to perform various actions. Other system memory 630 may be
available for use as well. The memory 630 can include multiple
different types of memory with different performance
characteristics. It can be appreciated that the disclosure may
operate on a computing system 600 with more than one processor 620
or on a group or cluster of computing devices networked together to
provide greater processing capability. The processor 620 can
include any general purpose processor and a hardware module or
software module, such as module 1 662, module 2 664, and module 3
666 stored in storage device 660, configured to control the
processor 620 as well as a special-purpose processor where software
instructions are incorporated into the actual processor design. The
processor 620 may essentially be a completely self-contained
computing system, containing multiple cores or processors, a bus,
memory controller, cache, etc. A multi-core processor may be
symmetric or asymmetric.
[0046] The system bus 610 may be any of several types of bus
structures including a memory bus or memory controller, a
peripheral bus, and a local bus using any of a variety of bus
architectures. A basic input/output (BIOS) stored in ROM 640 or the
like, may provide the basic routine that helps to transfer
information between elements within the computing system 600, such
as during start-up. The computing system 600 further includes
storage devices 660 such as a hard disk drive, a magnetic disk
drive, an optical disk drive, tape drive or the like. The storage
device 660 can include software modules 662, 664, 666 for
controlling the processor 620. Other hardware or software modules
are contemplated. The storage device 660 is connected to the system
bus 610 by a drive interface. The drives and the associated
computer-readable storage media provide nonvolatile storage of
computer-readable instructions, data structures, program modules
and other data for the computing system 600. In one aspect, a
hardware module that performs a particular function includes the
software component stored in a tangible computer-readable storage
medium in connection with the necessary hardware components, such
as the processor 620, bus 610, output device 670 as display, and so
forth, to carry out the function. In another aspect, the system can
use a processor and computer-readable storage medium to store
instructions which, when executed by the processor, cause the
processor to perform a method or other specific actions. The basic
components and appropriate variations are contemplated depending on
the type of device, such as whether the system 600 is a small,
handheld computing device, a desktop computer, or a computer
server.
[0047] Although the exemplary embodiment described herein employs
the hard disk as the storage device 660, other types of
computer-readable media which can store data that are accessible by
a computer, such as magnetic cassettes, flash memory cards, digital
versatile disks, cartridges, random access memories (RAMs) 650, and
read only memory (ROM) 640, may also be used in the exemplary
operating environment. Tangible computer-readable storage media,
computer-readable storage devices, or computer-readable memory
devices, expressly exclude media such as transitory waves, energy,
carrier signals, electromagnetic waves, and signals per se.
[0048] To enable user interaction with the computing system 600, an
input device 690 represents any number of input mechanisms, such as
a microphone for speech, a touch-sensitive screen for gesture or
graphical input, keyboard, mouse, motion input, speech and so
forth. An output device 670 can also be one or more of a number of
output mechanisms known to those of skill in the art. In some
instances, multimodal systems enable a user to provide multiple
types of input to communicate with the computing system 600. The
communications interface 680 generally governs and manages the user
input and system output. There is no restriction on operating on
any particular hardware arrangement and therefore the basic
features here may easily be substituted for improved hardware or
firmware arrangements as they are developed.
[0049] The various embodiments described above are provided by way
of illustration only and should not be construed to limit the scope
of the disclosure. Various modifications and changes may be made to
the principles described herein without following the example
embodiments and applications illustrated and described herein, and
without departing from the spirit and scope of the disclosure.
* * * * *