U.S. patent application number 12/147610 was filed with the patent office on 2008-10-23 for system and method to determine the prices and order quantities that maximize a retailer's total profit.
This patent application is currently assigned to International Business Machines Corporation. Invention is credited to Claudia Keser, Tomasz Nowicki, Grzegorz Swirszcz.
Application Number | 20080262903 12/147610 |
Document ID | / |
Family ID | 38862644 |
Filed Date | 2008-10-23 |
United States Patent
Application |
20080262903 |
Kind Code |
A1 |
Keser; Claudia ; et
al. |
October 23, 2008 |
SYSTEM AND METHOD TO DETERMINE THE PRICES AND ORDER QUANTITIES THAT
MAXIMIZE A RETAILER'S TOTAL PROFIT
Abstract
The present invention provides a system and method for
determining the prices and order quantities that maximize a
retailer's expected profit by using a multi-dimensional
distribution of the highest prices that customers are willing to
pay. This is novel, as well in the literature as in the patent
database. Brand switching is dealt with, taking into account that
consumers who come into the store with a-priori preferences for
products build a-posteriori preferences at the point of purchase
based on actual retail prices and availabilities in the store.
Inventors: |
Keser; Claudia; (Shrub Oak,
NY) ; Nowicki; Tomasz; (Briarcliff Manor, NY)
; Swirszcz; Grzegorz; (Ossining, NY) |
Correspondence
Address: |
WHITHAM, CURTIS & CHRISTOFFERSON, P.C.
11491 SUNSET HILLS ROAD, SUITE 340
RESTON
VA
20190
US
|
Assignee: |
International Business Machines
Corporation
Armonk
NY
|
Family ID: |
38862644 |
Appl. No.: |
12/147610 |
Filed: |
June 27, 2008 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
11424958 |
Jun 19, 2006 |
|
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12147610 |
|
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Current U.S.
Class: |
705/7.25 ;
705/7.31; 705/7.35; 705/7.37 |
Current CPC
Class: |
G06Q 10/06315 20130101;
G06Q 30/0283 20130101; G06Q 30/0202 20130101; G06Q 10/06375
20130101; G06Q 30/0206 20130101; G06Q 30/06 20130101 |
Class at
Publication: |
705/10 |
International
Class: |
G06Q 10/00 20060101
G06Q010/00 |
Claims
1-5. (canceled)
6. A system for determining prices and order quantities that
maximize a retailer's total profit for a specific product category
comprising: a computer to determine demand for products based on a
distribution of upper limits of prices each customer is willing to
pay for each of a plurality of products and based on given proposed
retail prices; a computer to determine an amount of products to be
ordered by calculating profit based on one or more of available
wholesale price data, proposed retail prices, and said determined
demand at said proposed retail prices; a computer to determine
retail prices based on available wholesale prices, a distribution
of upper limits of prices each customer is willing to pay for each
of a plurality of products, and said determined demand for given
products and said determined order quantities, both depending on
retail prices; and a computer to provide the resulting list of
quantities and prices as one or more of a printout, a
machine-readable data output to storage, and directly as input to
data processing.
7. The system of claim 6, wherein the computer is connected to a
network.
8. The system of claim 7, wherein the network is the Internet.
9. The system of claim 7, wherein said wholesale price data is
obtained from a database connected to said network.
10. The system of claim 6, wherein said computer-determined retail
prices are profit-maximizing retail prices.
11. A machine-readable medium for determining prices and order
quantities that maximize a retailer's total profit for a specific
product category by: instructing a computer to determine demand for
products based on a distribution of upper limits of prices each
customer is willing to pay for each of a plurality of products and
based on given proposed retail prices; instructing a computer to
determine an amount of each of products to be ordered by
calculating profit based on one or more of available wholesale
price data, proposed retail prices, and said determined demand at
said proposed retail prices; instructing a computer to determine
retail prices based on available wholesale prices, a distribution
of upper limits of prices each customer is willing to pay for each
of given products, and said determined demand for products and said
determined order quantities, both depending on retail prices; and
instructing a computer to provide the resulting list of quantities
and prices as one or more of a printout, a machine-readable data
output to storage, and directly as input to data processing.
12. The machine-readable medium of claim 11, wherein the computer
being instructed is connected to a network.
13. The machine-readable medium of claim 12, wherein the network is
the Internet.
14. The machine-readable medium of claim 12, wherein said wholesale
price data is obtained from a database connected to said
network.
15. The machine-readable medium of claim 11, wherein said
computer-determined retail prices are profit-maximizing retail
prices.
16. A method for determining prices and order quantities that
maximize a retailer's expected profit for a specific product
category comprising the steps of: using a customer survey to
determine prices customers are willing to pay for a product; and
based on said survey, defining a model of customers' in-store brand
choice as a function of a distribution of prices customers are
willing to pay.
17. The method of claim 16, wherein said prices are maximum prices
customers are willing to pay.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present application generally relates to the pricing and
ordering of brand-differentiated products in retailing (in the
consumer durables and services categories).
[0003] 2. Background Description
[0004] While the problem is of great importance in practice, we are
not aware of publications in the professional literature on systems
and methods for establishing optimal prices and order quantities
for brand-differentiated products in retailing. A number of
investigators have considered consumers' brand substitutability.
See, for example, R. E. Bucklin and V. Srinivasan, 1991; A. Ching,
T. Erdem, and M. Keane, 2006; R. A. Colombo and D. G. Morrison,
1989; J. J. Inman and R. S. Winer, 1998; and A. Terech, R. E.
Bucklin, and D. G. Morrison, 2003.
SUMMARY OF THE INVENTION
[0005] An embodiment of this invention relates to a method for
determining prices and order quantities that maximize a retailer's
total profit. This method is based on consumer demand functions
taking cross-price elasticities into account. This kind of demand
function is derived from a model that takes brand switching into
account. We develop a new, simple approach to model customers'
in-store brand choice as a function of a distribution of maximum
prices that they are willing to pay, which can be estimated based
on a survey method. This novel approach to model customers' brand
choice is key for the application of the method, since the
empirical estimation of consumer demand functions has been
difficult due to a lack of historical transaction or panel-type
data for consumer durables and services.
[0006] Brand-choice models in the professional literature mostly
consider repetitive shopping behavior, in particular purchases of
perishable goods in supermarkets, for which extensive data bases
exist (Bucklin and Srivinasan, 1991; Inman and Winter, 1998; Ching
et al., 2005). While some of the brand models that could
potentially be applied for consumer durables classify consumers
into hard-core loyals and potential switchers (Colombo and
Morrison, 1989) or into groups with varying degrees of loyalty
between these two extremes (Terech et al., 2003), our model assumes
that (1) everybody potentially switches brands and (2) that
consumers decide depending on price and availability.
[0007] The present invention thus provides a system and method for
determining the prices and order quantities that maximize a
retailer's total profit by using a multi-dimensional distribution
of the highest prices that customers are willing to pay.
[0008] The present invention provides a model on optimal retail
pricing and order planning for horizontally differentiated products
(brands) in a given product category. To deduce customer demand
functions under multi-brand competition, it also models customer
in-store brand-switching behavior. Based on the deduced demand
functions, the system and method solve the retailer's profit
maximization problem for the considered product category.
[0009] While one simplified version of the model presented herein
considers two horizontally differentiated products (brands), it can
easily be extended to several products. The products may be
consumer durables or services. They could, for example, be consumer
electronics or home appliances--items that are bought occasionally
and for which brand typically matters. They could also be, for
example, service contracts for consumer electronics products and
home appliances.
[0010] Usually, there is a lack of historical transaction or
panel-type data on the purchase of consumer durables, which makes
the estimation of consumer demand functions difficult. This is why
we present a simple model of in-store brand choice, which can be
empirically estimated based on a survey method. The principal
assumption of this model is that customers come into the store with
a priori preferences for the products but then build a posteriori
preferences at the point of purchase based on the actual prices and
availabilities in the store.
[0011] The model assumes a joint multi-dimensional distribution of
customer preferences rather than several one-dimensional
distributions for each of the brands. The model is kept very
simple--e.g., it considers no consumer factors such as age and
income--for three major reasons: [0012] First, the model is
specifically designed for consumer durables, which are purchased
much less frequently than consumable products such as groceries,
with the result that huge data sets are typically not available for
consumer durables. [0013] Second, the model takes into account the
impact of limited product availability on the customers' actual
brand choice. [0014] Third and foremost, the model deduces consumer
demand functions that are plugged into the retailer's profit
maximization function. The analysis is restricted to simple demand
functions in order to keep the retailer's profit maximization
function tractable.
The Basic Model
[0015] The basic model considers a retailer who is selling two
products, X and Y. The retailer buys products X and Y at given unit
wholesale prices w.sub.x and w.sub.y, respectively. The
wholesalers' list prices for products X and Y are C.sub.x and
C.sub.y, respectively. The retailer's decision variables are the
unit retail prices, P.sub.x and P.sub.y, and the quantities x and y
that he orders from the wholesalers of products X and Y,
respectively.
[0016] The basic model assumes that the retailer maximizes his
expected profit, denoted as .PI.(.), from selling the two products.
The expected profit is a function of the quantities x and y, the
retail prices P.sub.x and P.sub.y expected customer demand of
product X, D.sub.x, and expected customer demand of product Y,
D.sub.y:
.PI.(x,y,P.sub.x,P.sub.y)=D.sub.xP.sub.x-xw.sub.x+D.sub.yP.sub.y-yw.sub.-
y, (1)
[0017] The treatment of expected demand is discussed below. The
basic model assumes that customers come to the store to buy either
one unit of product X or one unit of product Y or nothing. One may
employ a brand switching model tinder the assumption that customers
come to the retailer's store with a priori preferences, represented
by maximal prices they are willing to pay for either product
(reservation prices). The upper boundary to these reservation
prices is given by the respective list prices. Depending on the
retail prices, P.sub.x and P.sub.y, for X and Y, respectively,
customers then build their a posteriori preferences so that they
choose the product that yields the maximal subjective gain, which
is expressed by the difference of reservation price and actual
retail price. The model deduces expected customer demand functions,
D.sub.x and D.sub.y, which depend on the distribution of the
customers' joint a priori preferences for the two products, the
retail prices and the retailer's capacities for products X and
Y.
Consumer Demand Model
[0018] Customers' behavior may be modeled as follows: The
probabilistic space {.OMEGA.,Prob} describes the set of customers.
The number of customers visiting a store is N. Each customer
.omega..epsilon..OMEGA. carries personal preferences,
g.sub.x(.omega.) and g.sub.y(.omega.), toward product X and Y,
respectively. A customer's preference for a product describes the
maximal price that this customer is willing to pay for the product.
Preferences are modeled by random variables with values between
zero and the respective list price. The upper boundary is due to
the assumption that no individual is willing to buy a product at a
price above its list price. Note that the joint multi-dimensional
distribution of personal preferences builds the foundation of the
consumer demand model.
Case of Unlimited Supply
[0019] To begin with, the consumer demand model assumes that there
is unlimited supply of products X and Y, so that every customer who
decides to buy a product can get this product. Each customer
.omega. decides to buy either product X or Y or neither of them in
the following way. First he evaluates his subjective gain
W.sub.x(.omega.)=g.sub.x(.omega.)-p.sub.x for product X, and
W.sub.y(.omega.)=g.sub.y(.omega.)-p.sub.y for product Y. If both
subjective gains, W.sub.x and W.sub.y, are negative, the customer
buys nothing. Otherwise, he buys the product with the larger gain.
If both gains are equal, we assume that he buys product X. This is
an arbitrary tie-breaking rule. It is unimportant, though, given
the assumption of zero probability for such an event to occur.
[0020] The expected demand function, D.sub.x, for product X is
given by the probability that W.sub.x is positive and larger (or
equal) than W.sub.y, multiplied by the number of customers N.
Similarly, the expected demand function, D.sub.y, for product Y is
given by the probability that W.sub.y is positive and larger than
W.sub.x, multiplied by the number of customers N.
Case of Limited Supply
[0021] Customers, however, may face shortages in the supply of
products X and/or Y. Five different decisions are possible for each
customer: [0022] (1) If W.sub.x(.omega.)<0 and
W.sub.y(.omega.)<0, customer .omega. buys nothing [0023] (2) If
W.sub.x(.omega.)>W.sub.y(.omega.)>0, customer .omega. buys
product X if available; otherwise he tries to buy product Y [0024]
(3) If W.sub.y(.omega.)>W.sub.x(.omega.)>0, customer .omega.
buys product Y if available; otherwise he tries to buy product X
[0025] (4) If W.sub.x(.omega.)>0>W.sub.y(.omega.), customer
.omega. buys product X if available, nothing otherwise [0026] (5)
If W.sub.y(.omega.)>0>W.sub.x(.omega.), customer .omega. buys
product Y if available, nothing otherwise
[0027] Define potential expected demands, U.sub.x and U.sub.y, for
products X and Y, respectively, as the expected demand in the
unlimited supply case. Hence, U.sub.x is the expected number of
customers making either decision (2) or (4). In other words, these
are the customers with product X as their first choice. Similarly,
U.sub.y is the expected number of customers making either decision
(3) or (5). In other words, these are the customers with product Y
as their first choice.
U.sub.x=NProb{.omega.:decision(.omega.) is (2) or (4)}
U.sub.y=NProb{.omega.:decision(.omega.) is (3) or (5)} (2)
[0028] Define T.sub.x as the expected number of customers making
decision (2), (3), or (4). These are the customers who would
consider buying product X even if not in the first place.
Similarly, T.sub.y is the expected number of customers making
decision (2), (3), or (5). These are the customers who would
consider buying product X even if not in the first place.
T.sub.x=NProb{.omega.:decision(.omega.) is (2), (3), or (4)}
T.sub.y=NProb{.omega.:decision(.omega.) is (2), (3), or (5)}
(3)
[0029] Remark 1: Potential expected demands depend on the actual
retail prices, P.sub.x and P.sub.y, because the prices influence
the subjective gains and therefore the probabilities of the
particular decision.
[0030] In order to establish the actual expected demand functions,
it is necessary to consider what happens when one of the products
is not available anymore. Our model represents consumer demand as
the flow of customers purchasing products over time and assumes
that in such a flow the customers' preferences are independent of
the arrival moment.
[0031] Three cases are distinguishable, covering the various
possible situations.
[0032] Case 1: If potential expected demands U.sub.x and U.sub.y
are smaller than order quantities x and y, then the actual expected
demands are identical to the potential expected demands.
D.sub.x=U.sub.x
D.sub.y=U.sub.y
[0033] Case 2: Otherwise, suppose that the product X exhausts
first. This means that x<U.sub.x, but it also means that
x/U.sub.x<y/U.sub.y. The portion of customers who already
visited the store is given by x/U.sub.x at the moment when product
X exhausts. The portion of customers who have not yet visited the
store is 1-x/U.sub.x. The amount of product Y sold up to this
moment is equal to U.sub.y x/U.sub.x. In this case, the expected
demand for product X is equal to order quantity x. The expected
demand for product Y is the minimum of the order quantity y and the
sum of the demand up to the exhaustion moment, U.sub.y x/U.sub.x,
and the expected demand after this moment, (1-x/U.sub.x) multiplied
by T.sub.y, the number of customers who would consider buying
product Y even if not in the first place.
D.sub.x=x
D.sub.y=min[y,U.sub.yx/U.sub.x+(1-x/U.sub.x)T.sub.y]
[0034] Case 3: Similarly, if the product Y exhausts first,
y<U.sub.y and y/U.sub.y<x/U.sub.x:
D.sub.x=min[x,U.sub.xy/U.sub.y+(1-y/U.sub.y)T.sub.x]
D.sub.y=y
Demand for all three cases may be written in a more compact
way.
D.sub.x=min[x,U.sub.xy/U.sub.y+(1-y/U.sub.y).sup.+NProb{.omega.:decision-
(.omega.) is (4)}]
D.sub.y=min[y,U.sub.yx/U.sub.x+(1-x/U.sub.x)+NProb{.omega.:decision(.ome-
ga.) is (5)}] (4)
where the + sign in the superscript means that we take the value of
the expression if it is positive and zero otherwise.
Retailer's Profit Maximization
[0035] The retailer's expected profit maximization (equation (1))
yields optimal retail prices P.sub.x* and P.sub.y* and optimal
order quantities x* and y*.
Properties of the Model with Two Products
[0036] We cannot present a closed-form solution to the retailer's
expected profit maximization problem because of its complexity.
Thus, in general, the solution has to be found numerically.
Nonetheless, the closed-form solution for a specific customer
preference distribution is discussed in the example below.
[0037] In general, we are able to identify a number of properties
of the retailer's profit function. We formulate them for product X
but they hold analogously for product Y.
[0038] Property 1: The expected potential demand U.sub.x as a
function of the retail prices, P.sub.x and P.sub.y, is
non-increasing in P.sub.x and non-decreasing in P.sub.y. These are
the customers whose first choice would be X, given the prices
P.sub.x and P.sub.y.
[0039] Property 2: The expected number of customers who would
consider buying product X even if not in the first place is
non-increasing in P.sub.x and independent of P.sub.y.
[0040] Property 3: If the retailer is not obliged to order positive
quantities, then his optimal expected profit is non-negative. This
implies that the optimal solution might require zero order
quantities in some situations. These situations may be caused by
the wholesale price exceeding the preferences of all customers.
They may also be caused by a much lower profit margin for one
product than for the other product, so that the retailer's interest
is to drive as many customers as possible to the more profitable
product.
[0041] Property 4: There always exists an optimal solution with
retail prices not below the wholesale prices.
[0042] Property 5: For any retail prices, P.sub.x and P.sub.y, and
any order quantity x, ordering more than
U.sub.yx/U.sub.x+(1-x/U.sub.x).sup.+N Prob{.omega.:
decision(.omega.) is (5)} yields a lower expected profit than
ordering exactly this amount:
.PI.(x,y,P.sub.x,P.sub.y).ltoreq..PI.(x,D.sub.y,P.sub.x,P.sub.y)
(5)
[0043] Property 6: For prices and order quantities maximizing the
retailer's expected profit, we have
D.sub.y(x*,y*,P.sub.x*,P.sub.y*)=y* (6)
In other words, the expected demand for product Y is equal to the
order quantity of product Y if the prices and order quantities are
optimal.
[0044] Property 7: Ordering both products, X and Y, above expected
potential demands yields lower expected profit than ordering
exactly expected potential demands of both products.
[0045] If
P.sub.x>w.sub.x, and P.sub.y>w.sub.y, and x.gtoreq.U.sub.x,
and y.gtoreq.U.sub.y, (7)
[0046] then
.PI.(x,y,P.sub.x,P.sub.y).ltoreq..PI.(U.sub.x,U.sub.y,P.sub.x,P.sub.y)
[0047] Property 8: There are cases where the order quantity for one
of the two products larger than the expected potential demand for
this product yields a higher expected profit than ordering the
expected potential demand. In this case, the order quantity for the
other product is zero.
[0048] Assume that
P.sub.x>w.sub.x, and P.sub.y>w.sub.y, and x<U.sub.x.
[0049] If
U.sub.x(P.sub.x-w.sub.x)<NProb{.omega.:decision(.omega.) is
(2)}(P.sub.y-w.sub.y), (8)
[0050] then
.PI.(x,y,P.sub.x,P.sub.y).ltoreq..PI.(0,T.sub.y,P.sub.x,P.sub.y),
[0051] otherwise
.PI.(x,y,P.sub.x,P.sub.y).ltoreq..PI.(U.sub.x,U.sub.y,P.sub.x,P.sub.y).
[0052] Property 9: For given retail prices, the optimal order
quantity of a product is equal either to zero (and then the product
is not offered at all) or to the expected number of customers for
whom this product is the first choice.
Extension of the Model to More Than Two Products
[0053] When more than two products are available the search for the
optimal solutions (largest retailer's profit) may be very
complicated due to the highly non-linear dependence of the profit
from the proposed retail prices. In addition, the domain of the
definition of the profit function is partitioned into regions (of
the different quantities) where it has different forms. Moreover,
it is important to consider the brand-switching phenomenon at the
moment when the supply does not meet the demand. Fortunately, only
a finite set of possible procurement quantities comes into
consideration. Namely, for each group of proposed retail prices,
and therefore for each distribution of subjective gains, it is
enough to check the collection of subset of products the retailer
wishes to order from the wholesaler. For each such subset, the
optimal quantities for any product are determined by the number of
customers whose first preference is this product (assuming it will
be provided). Thus, the optimum to be calculated is not an optimum
over all retail prices and all quantities but is instead an optimum
over all retail prices and all the (finite) subsets of products to
be procured from the wholesaler.
An Example with Closed-Form Solution
[0054] This example assumes that the distribution of preferences is
perfectly negatively correlated, so that, for each customer
.omega.,
g.sub.x(.omega.)/C.sub.x+g.sub.y(.omega.)/C.sub.y=1.
This means that the pair of preferences (g.sub.x, g.sub.y) lies for
each customer on the segment of the straight line between the
points (C.sub.x,0) and (0,C.sub.y). Moreover, it is assumed that on
this segment the distribution is uniform.
[0055] This allows one to calculate the probabilities of the
customers' decisions (1) through (5), which will uniquely depend on
the retail prices:
TABLE-US-00001 Deci- sion Buy Probability (1) Nothing Max{0,
P.sub.x/C.sub.x + P.sub.y/C.sub.y - 1} (2) X, otherwise Y
Max{C.sub.x/(C.sub.x + C.sub.y)(1 - P.sub.x/C.sub.x -
P.sub.y/C.sub.y), 0} (3) Y, otherwise X Max{C.sub.y/(C.sub.x +
C.sub.y)(1 - P.sub.x/C.sub.x - P.sub.y/C.sub.y), 0} (4) X,
otherwise nothing Min{P.sub.y/C.sub.y, 1 - P.sub.x/C.sub.x} (5) Y,
otherwise nothing Min{P.sub.x/C.sub.x, 1 - P.sub.y/C.sub.y}
[0056] The first choices in the Max and Min expressions correspond
to the case that P.sub.x/C.sub.x+P.sub.y/C.sub.y<1, while the
second choices correspond to the case that
P.sub.x/C.sub.x+P.sub.y/C.sub.y>1.
[0057] Plugging these probabilities into the retailer's profit
function and using the properties discussed above, one finds the
optimal profit
.PI.(x*,y*,P.sub.x*,P.sub.y*)=N/4[(C.sub.x-w.sub.x).sup.2/C.sub.x+[(C.su-
b.y-w.sub.y).sup.2/C.sub.y] (9)
[0058] at
x*=N(1-P.sub.x/C.sub.x)
y*=N(1-P.sub.y/C.sub.y)
P.sub.x*=(C.sub.x+w.sub.x)/2
P.sub.y*=(C.sub.y+w.sub.y)/2
An Application to More General Distributions
[0059] As stated above, it is in general not possible to find a
closed-form solution and recourse must be made to numerical
methods.
[0060] Suppose that the distribution of customer preferences is
given in form of a table. In the case of two brands, it is a
two-dimensional table. The rows and columns of this table represent
the intervals of the preferences of the two products. The entries
of the table represent the number of customers with preferences in
those intervals.
[0061] Assume a pair of wholesale prices. For each pair of retail
prices above or equal to the respective wholesale prices, one can
calculate the number of customers making a decision (1) through
(5), making interpolations if necessary (assuming uniform
distribution in each cell). Using the formulas for demand and the
properties discussed above, one may calculate the optimal
quantities for each pair of retail prices and the corresponding
retailer's profit, thus making it possible to choose the optimal
pair of retail prices.
[0062] The present invention thus provides a system, a method, and
a machine-readable medium for providing instructions for a
computer, which [0063] given a distribution of upper limits of
prices a consumer is willing to pay for each of a plurality of
products given their list prices, and [0064] given wholesale price
data for a plurality of products, determines profit-maximizing
retail prices and amounts of products to be ordered and provides
the resulting list of quantities and prices as one or more of a
printout, a machine-readable data output to storage, and directly
as inputs to data processing. The computer may be connected to a
network, and the network may be the Internet. Said wholesale price
data and the distribution of customer preferences may be obtained
from a database connected to such a network.
[0065] The method, system, and machine-readable medium thus
provided according to the present invention determine prices and
order quantities that maximize a retailer's expected profit for a
specific product category by: using a computer to determine
expected demand for products based on a distribution of upper
limits of prices each customer is willing to pay for each of a
plurality of products and based on given proposed retail prices;
using a computer to determine an amount of products to be ordered
by calculating profit based on one or more of available wholesale
price data, proposed retail prices, and said determined demand at
said proposed retail prices; using a computer to determine retail
prices based on available wholesale prices, a distribution of upper
limits of prices each customer is willing to pay for given
products, and said determined demand for products and said
determined order quantities, both depending on retail prices; and
providing a list of quantities and prices as one or more of a
printout, a machine-readable data output to storage, and directly
as input to data processing. The computer may or may not be
connected to a network, and the network may or may not be the
Internet. The wholesale price data may or may not be obtained from
a database connected to such a network. The retail prices
determined by the computer may or may not be profit-maximizing
retail prices.
[0066] The present invention provides a computer-implemented method
for determining prices and order quantities that maximize a
retailer's expected profit for a specific product category
comprising the steps of: using a customer survey to determine
prices customers are willing to pay for a product; and based on
said survey, using a computer to define a model of customers'
in-store brand choice as a function of a distribution of prices
customers are willing to pay. The prices determined by this method
may or may not be maximum prices customers are willing to pay.
BRIEF DESCRIPTION OF THE DRAWINGS
[0067] FIG. 1 shows a schematic for maximization of retailer's
expected profit (simply denoted as profit hereafter) given
wholesale prices and customers' preferences.
[0068] FIG. 2 shows a schematic for determination of optimal
quantities when retail and wholesale prices are known.
[0069] FIG. 3 shows a schematic for determination of the
distribution of customer preferences depending of retail
prices.
[0070] FIG. 4 shows an example of a system according the claimed
invention, in which wholesale price data is obtained over a
network.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE
INVENTION
[0071] The present invention produces the prices and order
quantities that maximize a retailer's total profit for a specific
product category, taking the distribution of customer preferences
into account, under the following given conditions: [0072] There is
a joint multi-dimensional distribution of the highest prices
customers are willing to pay, estimated based on survey or
historical data (described, for example, as a multi-index table or
a database), the number of indices in such a table would correspond
to the number of brands while the dimension of each index would
correspond to the number of considered price-intervals for the
respective brand. The entries of such a table would be the
percentage of customers for whom the respective prices are the
maximally acceptable prices for each of the brands. [0073] There is
a known monetary cost of each brand to the retailer, including the
unit wholesale price, shipping, storage, shelf and others. [0074]
There is a the list price of each of the brands, representing caps
to the multi-index preference table. [0075] There is a given
estimated total number of customers visiting the store. Taking
those conditions as given, the procedure of the present invention
is as follows. [0076] A. For any proposed list of retail prices,
using the distribution of highest prices customers are willing to
pay, determine the distribution of subjective gains. Each customer
orders the products he is willing to buy by the highest,
nonnegative subjective gain, assuming that it is available. [0077]
B. Using the distribution of customers with the same ordering for
the proposed retail prices and for each subset of available
products, determine the demands for each product. This will
constitute the amounts of each product to be ordered. [0078] C.
Using the calculated amounts to be ordered, given wholesale prices
and proposed retail prices, calculate the profit of the retailer.
[0079] D. Maximize the profit by choosing the list of retail prices
that yields the highest profit. The result of this procedure is a
list of order quantities and prices, which may be provided as a
graphic or nongraphic printout, and/or as machine-readable data
output to storage or directly as input to data processing, for use
in ordering and pricing application.
[0080] Referring now to the drawings, and more particularly to FIG.
1, which shows the complete process, there is shown the
maximization of retailer's profit given wholesale prices and
customers' preferences. Starting with proposed retailer prices for
all products, as shown in step 210, the proposed retail prices are
used as input, as shown in step 211, to establish the distribution
of customers' subjective gains, as shown in step 430. Also used as
input for step 430 is the knowledge of the distribution of the
highest prices each customer is willing to pay for each of the
products, as shown in step 410. Both the distribution of customers'
subjective gains, as shown in step 430, and the knowledge of
wholesale prices, as shown in step 229, are used to calculate
quantities that maximize a retailer's profit, as shown in step 227.
Profit is then calculated based on proposed retail prices and
calculated demands and quantities, as shown in step 131. In step
135, a determination is made whether all retail prices have been
checked. If no, then a new proposition of retail prices is chosen
as shown in step 137, with the new proposition being used to update
the proposed retail prices for all products in step 211. Steps are
reiterated, beginning with step 430, using the updated step 211 as
input. When step 135 determines that all retail prices have been
checked, the retail prices and implicit quantities that maximize
the retailer's profit are found, as shown in step 140, and the
process is ended, as shown in step 250.
[0081] FIG. 2 details step 227, showing the determination of
optimal quantities to order when retail and wholesale prices are
known. Beginning with knowledge of the distribution of customers'
highest prices, as shown in step 410, and proposed retail prices
for all products, as shown in step 211, the distribution of
customers' subjective gains is established, as shown in step 430. A
Subset of products is then chosen, as shown in step 313, and, for
each product in this subset, the number of customers with the
highest preference for that product is estimated, as shown in step
315. Taking the number of customers with the highest preference for
a product as the quantity to be ordered, as shown in step 321, the
retailer's profit is calculated, as shown in step 331, based on
knowledge of wholesale prices, as shown in step 229, as well as on
proposed retail prices, the above established quantities, and the
given subset of products. In step 335, a determination is made
whether all subsets have been checked. If no, then a new subset is
chosen as shown in step 337, with the new subset being used to
update the choice of subset of products in step 313. Steps are
reiterated, beginning with step 315, for the updated choice of step
313. When step 335 determines that all subsets have been checked,
the subset and implicit quantities which maximize the retailer's
profit for given prices are found, as shown in step 227 in FIG.
1.
[0082] Referring to FIG. 3, which details step 430, there is shown
the determination of the distribution of customer preferences
depending on proposed retail prices. This figure shows in greater
detail how knowledge of customers' highest prices and the retail
prices for all, as shown in steps 410 and 211 of FIG. 2, is used as
input to establish the distribution of customers' subjective gains,
as shown in step 430 of FIG. 2. An investigation of the
distribution of the highest prices each customer is willing to pay
is undertaken, as shown in step 110, resulting in knowledge of the
distribution of the highest prices each customer is willing to pay,
as shown in step 410. That knowledge is used as input for step 423,
in which each customer compares the retail prices of each product
with the price the customer is willing to pay. Also used as input
for step 423 is the retail price for each product, as shown in step
121. Based on the customer comparison of step 423, the comparison
produces a determination of subjective gains a customer expects
from a product, as shown in step 424. For each product, if the
subjective gain does not pass some threshold, then the product will
not be purchased, as shown in step 425; by contrast, all the
products that do pass the threshold are ordered according to the
size of the subjective gain, as shown in step 426. All the
customers are then grouped by the order in which they prefer the
products, as shown in step 430. The result, as shown in step 430,
is to establish a distribution of the groups of customers with the
same ordered preferences.
[0083] FIG. 4 shows an example of a system according the claimed
invention, in which wholesale price data is obtained over a
network. A computer 500 has a machine-readable medium 510 for
providing instructions. An operator 540 is able to provide input
via a keyboard 521 or mouse 525, and the computer is able to
provide output via a monitor 531 or a printer 535. The computer is
connected to a network 550 to which is connected a database 560
from which the computer may obtain wholesale price data. Other data
may be obtained from other databases 570a, 570b, and 570c connected
to the network 550.
[0084] The manager 540 of a retail store who wants to determine
order quantities and retail prices of a number of products in a
specific category may thus use the computer 500, which runs
software based on the present invention. The program pulls
information on customer preferences from a remote data base 570a,
and the manager enters information on wholesale prices using the
keyboard 521 or copies it from a portable memory device 510. This
is one example; data input may be provided in many different ways.
The manager 540 then employs the computer-implemented method of the
present invention to determine profit-maximizes prices and order
quantities. The resulting list of optimal retail prices and optimal
quantities to order is displayed on the screen 531, printed out on
printer 535 and stored in a database 560. The data stored in
database 560 can be streamlined into other software.
[0085] While the invention has been described in terms of a single
preferred embodiment, those skilled in the art will recognize that
the invention can be practiced with modification within the spirit
and scope of the appended claims.
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