U.S. patent application number 09/498911 was filed with the patent office on 2001-08-23 for statistical sampling security methodology for self-scanning checkout system.
Invention is credited to Beadle, Edward, Bridgelall, Raj, Kartz, Joseph, Murrah, Juditth, Shellammer, Stephen J., Swartz, Jerome, Woffinden, Theo.
Application Number | 20010015375 09/498911 |
Document ID | / |
Family ID | 25462906 |
Filed Date | 2001-08-23 |
United States Patent
Application |
20010015375 |
Kind Code |
A1 |
Swartz, Jerome ; et
al. |
August 23, 2001 |
Statistical sampling security methodology for self-scanning
checkout system
Abstract
A statistical basis for use in a self-scanning checkout system
determines how many items to check in a shopper's shopping cart for
incorrect or missing scans as well as which particular or types of
items to check to determine if they were properly scanned, if the
shopper is determined to be audited. The present invention does not
audit every customer, but rather determines whether a given shopper
or customer is to be audited on a given shopping trip based upon
obtaining a minimum checkout loss for such customer. The
methodology determines how many items to check for a given shopper
as well as which particular items to check for that shopper. The
following factors attempt to model the real world of shopping and
may be considered, alone or in varying combinations, in determining
the number of items to check for a particular shopping transaction:
shopper frequency; queue length; prior audit history; store
location; time of day, day of week, date of year; number of times
items are returned to shelf during shopping; dwell time between
scans; customer loyalty; store shopping activity and other factors.
Using statistical decision theory for auditing policies a minimum
loss per shopper transaction improves the security and reduces the
labor of self-check out without being too intrusive to
customers.
Inventors: |
Swartz, Jerome; (Oldfield,
NY) ; Shellammer, Stephen J.; (Lake Grove, NY)
; Kartz, Joseph; (Stony Brook, NY) ; Woffinden,
Theo; (Berkshire, GB) ; Murrah, Juditth;
(St.James, NY) ; Beadle, Edward; (Melbourne,
FL) ; Bridgelall, Raj; (Mount Sinai, NY) |
Correspondence
Address: |
SYMBOL TECHNOLOGIES INC
LEGAL DEPARTMENT
ONE SYMBOL PLAZA
HOLTSVILLE
NY
11742
US
|
Family ID: |
25462906 |
Appl. No.: |
09/498911 |
Filed: |
February 4, 2000 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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09498911 |
Feb 4, 2000 |
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08932779 |
Sep 18, 1997 |
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6092725 |
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08932779 |
Sep 18, 1997 |
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08787728 |
Jan 24, 1997 |
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5877485 |
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60011054 |
Jan 25, 1996 |
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Current U.S.
Class: |
235/383 |
Current CPC
Class: |
G07G 1/0054 20130101;
G07G 3/003 20130101; G06Q 30/06 20130101 |
Class at
Publication: |
235/383 |
International
Class: |
G06K 015/00 |
Claims
1. A method for enhancing the accuracy and reducing audit level of
a self-checkout system while achieving a lowest average loss for a
customer in a system wherein a customer selects a plurality of
items for purchase and registers the plurality of items with a
portable terminal, comprising the steps of: a) generating at least
one state space of possible events that may occur in a
self-checkout by a customer; b) generating at least one action
space in response to each state space; c) generating a loss
function in response to each action space; and d) auditing a
self-check out to obtain a minimum checkout loss for a
customer.
2. In a self-service shopping checkout system wherein a shopper is
provided with a portable self-scanning terminal for scanning of a
bar code of an item selected for purchase prior to depositing the
item into a shopping cart, and wherein a list of items self-scanned
by the shopper is compiled and made available to a cashier for
surveillance and payment purposes, the improvement comprising a
method for enhancing the accuracy and reducing overall audit level
and achieving a lowest average loss of a self-checkout system
wherein a customer selects a plurality of items for purchase and
registers the plurality of items with the portable terminal,
comprising the steps of: a) determining if the customer is to be
audited to obtain the lowest average loss for the customer using
statistical decision analysis; a) determining, as a function of a
plurality of input criteria, the number of items n to be scanned;
b) selecting from the shopper's cart of items presented for
purchase n items to be scanned; c) scanning a bar code located on
each of said n items selected for scanning; and d) allowing the
shopping transaction if each item selected for scanning is present
on the list of self-scanned items compiled by the shopper.
3. The method of claim 2 further comprising the step of disallowing
the shopping transaction if the minimum checkout loss exceeds a
threshold.
4. A self-service shopping checkout system comprising: a) a
plurality of portable self-checkout devices, each of said
self-checkout devices to be used by a customer to scan a bar code
located on an item to be purchased so as to record therein a list
of such items to be purchased, each of said devices comprising bar
code scanning means for scanning and decoding a bar code located on
an item to be purchased, means for compiling a list of items
scanned by said customer, and a data output port for allowing
transfer of said scanned item list to an associated data port
located external to said portable device; b) a stationary dispenser
unit for the releasable containment of said plurality of portable
self-checkout devices, said dispenser unit comprising: (i) a
plurality of device containment slots, each of said slots being
configured for releasable containment of a mating self-scanning
device, each of said slots having associated therewith a data input
port suitable for mating with a data output port located on a
portable self-checkout device; and (ii) a printer for printing a
tally list of items scanned for purchase by said shopper, said
tally list being supplied by a self-checkout device after said
self-checkout device is returned to a device containment slot after
being used by a shopper, said tally list further comprising a
two-dimensional bar code encoded with said items scanned by said
shopper, a unique identification record associated with said
shopper, and the number of items scanned by said shopper; c) a
plurality of point of sale terminals, each of said point of sale
terminal comprising: (i) bar code reading means for reading said
two-dimensional bar code from a tally list presented to a cashier
operating said point of sale terminal, said bar code reading means
providing as output data signals representing said items scanned by
said shopper, said unique identification record associated with
said shopper, and said number of items scanned by said shopper;
said bar code reading means also configured so as to scan select
items presented for checking by said cashier; (d) means for
generating at least one state space of possible events (E) that may
occur in a self-checkout by a shopper; (e) means for generating an
action space in response to each state space; (f) means for
generating a loss function in response to each action space; and
(g) means for auditing a self-check out to obtain a minimum
checkout loss for a customer.
5. The method of claim 1 wherein the state space is a statistical
representation of possible events (E) that may occur in a
self-checkout.
6. The method of claim 1 wherein the action space is a statistical
representation of possible actions that may be taken in response to
the possible events.
7. The method of claim 1 wherein the loss function measures a loss
resulting from an action.
8. The method of claim 1 further comprising the step of determining
and defining an average loss for a self check-out as a Bayes
loss.
9. The method of claim 8 where the Bayes average loss is given by
the equation: 5 B ( a ) = E [ 1 ( , a ) ] = i n L ( i , a ) P ( i )
where .theta..sub.i represents random events.
10. The method of claim 1 wherein the loss function is a function
of L(c) and p where L(c) is the expected inventory loss associated
with a shopper (c) and p is the probability of performing an audit
on the shopper.
11. A method of selecting a best action for auditing a customer in
a self-check out system comprising the steps of: a) generating at
least one state space of possible events that may occur in a
self-checkout by the customer; b) generating at least one action
space in response to each state space; c) generating a loss
function in response to each action space; and d) selecting the
action that gives the smallest loss function on the average.
12. A method of selecting a best action for auditing a customer in
a self-check out system comprising the steps of: a) generating at
least one state space of possible events that may occur in a
self-checkout by the customer; b) generating at least one action
space in response to each state space; c) generating a Bayes' loss
function in response to each action space; and d) randomly
selecting the action with the probability inversely proportional to
the Bayes' loss associated with taking that action.
13. A method of selecting a best action for auditing a customer in
a self-check out system comprising the steps of: a) determining if
the customer is to be audited for items on a given shopping trip
based upon a lowest average loss to the self-check out system; and
b) determining how many items to audit based on a statistical
decision analysis applied to self shopping if step a) determines
the customer should be audited.
14. In a customer self-check out system, a method of estimating the
probability of a customer making an error comprising the steps of:
a) scanning into the self-check out system a customer history of
prior audit results; and b) estimating the probability of the
customer making an error in a self-check out using the prior
history results.
15. In a self-check out system, a method of determining the average
loss for a customer in a self-check out, comprising the steps of:
a) identifying a plurality of factors including store busy; level
of audit (full, patial, none) and affecting the self-check out; b)
selecting a at least one of the plurality of the events; and c)
calculating the average loss for the customer in the self-check out
using a Bayes' loss factor based upon the selected at least
plurality of events.
16. A self-service shopping checkout system for enhancing the
accuracy and reducing overall audit level while achieving a lowest
average loss of a self-checkout by a customer, comprising: a) means
for registering a plurality of items by the customer using a
portable terminal; b) means for determining if the customer is to
be audited to obtain the lowest average loss for the customer using
statistical decision analysis; c) means for determining, as a
function of a plurality of input criteria, which items n and the
number thereof to be scanned; d) means for selecting from the
shopper's cart of items presented for purchase n items to be
scanned; e) means for properly scanning a bar code located on each
of said n items selected for scanning; and f) means for allowing
the shopping transaction if each item selected for scanning is
present on a list of self-scanned items compiled by the
shopper.
17. The system of claim 16 further comprising: a) means for
disallowing the transaction if any item selected for scanning is
not present on the list of self-scanned items compiled by the
shopper.
18. An article of manufacture, comprising: a computer usable medium
having computer readable program code means embodied therein for
enhancing the accuracy and reducing overall audit level while
achieving a lowest average loss of a self-checkout by a customer in
a self-check out system including a plurality of portable
self-checkout devices, each of said self-checkout devices to be
used by a customer to scan a bar code located on an item to be
purchased so as to record therein a list of such items to be
purchased, each of said devices comprising bar code scanning means
for scanning and decoding a bar code located on an item to be
purchased and means for compiling a list of items scanned by said
customer, the computer readable program code means in said article
of manufacturing, comprising: (a) computer readable program code
means for registering a plurality of items by the customer using a
portable terminal; b) computer readable program code means for
determining if the customer is to be audited to obtain the lowest
average loss for the customer using statistical decision analysis;
c) computer readable program code means for determining, as a
function of a plurality of input criteria, which items n and the
number thereof to be scanned; d) computer readable program code
means for selecting from the shopper's cart of items presented for
purchase n items to be scanned; e) computer readable program code
means for properly scanning a bar code located on each of said n
items selected for scanning; and f) computer readable program code
means for allowing the shopping transaction if each item selected
for scanning is present on a list of self-scanned items compiled by
the shopper or disallowing the transaction if each item selected
for scanning is not present on the list of self-scanned items
compiled by the shopper.
Description
[0001] This application is a continuation-in-part of Ser. No.
08/787,728, filed Jan. 24, 1997, which parent application claims
the benefit of U.S. Provisional Application No. 60/011,054, filed
Jan. 25, 1996, assigned to the same assignee as that of the present
application, and is incorporated fully herein by reference.
BACKGROUND OF THE INVENTION
[0002] This invention relates to self-service shopping, and in
particular to a methodology for improving the security of a
self-service shopping system by the use of statistical sampling of
shoppers and their purchases.
[0003] Self-service shopping systems are desired for their ability
to offload service-oriented functions from human labor forces and
provide automatic assistance to the shopper for increase in
response time, efficiency, throughput, lower cost, and the like.
For example, systems in the prior art provide each shopper with a
portable bar code scanning device, which is used to scan the bar
code located on a product in order to determine the price by
accessing a locally stored look-up table and keep a tally list of
all items selected for purchase. When the shopper is finished
selecting items for purchase and scanning the bar codes on the
items, he places the self-scanner into a recess in a stationary
(i.e., wall-mounted) cradle, wherein a list of items selected is
printed out for a receipt and provided to the shopper. The shopper
then brings the list along with the cart of selected items to a
clerk for tender of final payment and, possibly, an audit of items
selected for purchase in order to ensure that all items selected
and placed in the cart were properly scanned. This self-service
scenario speeds shoppers through the store quicker than the
conventional conveyor belt/cashier environment typical in stores
today.
[0004] Security in a self-service shopping system as described
above is a major concern of retailers. Shoppers who fail to scan
the bar code of an item placed in their shopping cart will bring
the item home without proper payment, whether such failure to scan
the item is intentional or inadvertent. In addition, shoppers may
scan an item but place a different (i.e. more expensive) item in
their cart. Therefore, some methodology of checking shoppers'
purchases must be implemented in order to satisfy security
criteria.
[0005] Two goals of a self-checkout system are to increase shopper
throughput and to save in labor costs. Ideally, a shopper can scan
his items when selected from the shelf and save scanning time at
the checkout line. In addition, stores would require less human
labor since there is a reduction in the number of cashiers
required. However, there is still a requirement to scan some items
from a shopper's cart if a shopper is determined to be audited in
order to flag an attempted theft as well as to provide deterrence
against pilferage. Thus, some labor is required to scan at least
some of the items leaving the store. At one extreme, a system where
every shopper has all of his purchase items re-scanned is not
feasible since there is no net time savings in such a system (all
purchases are scanned by a cashier anyway). There is therefore a
need to determine whether a shopper needs to be audited and how
many and which items are to be scanned in order to maximize the
potential for catching pilferage, provide maximum deterrence
against theft, minimize labor costs in checking the shoppers'
scanned items, maintain the increased throughput achieved by the
self-checkout system, and avoid the negative inferences inherently
made by shoppers whose items are checked by an exit cashier or
security guard.
[0006] Prior art proposals for checkout security require a cashier
to check only certain shoppers, but to scan their entire cart full
of goods. This type of system is unsatisfactory for those shoppers
who are selected for full checking, since they must wait for the
entire cart to be re-scanned (thus defeating the purpose of the
self-checkout system), suffer potential embarrassment at being
singled out by the store for security checking, etc. Thus, an
entirely new methodology is needed to supplant this security
checking system.
SUMMARY OF THE INVENTION
[0007] The present invention proposes the implementation of a
statistical basis for use in a self-scanning checkout system for
determining whether a shopper or customer should be audited and how
many items to check in a shopper's shopping cart for incorrect or
missing scans as well as which particular or types of items to
check to determine if they were properly scanned. In the present
invention, a fraction of the shoppers, depending upon an algorithm,
will be checked by a cashier or security guard, but only a limited
and select number of items will be checked for each shopper. The
present methodology determines how many items to check for a given
shopper as well as which particular items to check for that
shopper. The following factors may be considered, alone or in
varying combinations, in determining the number or type of items to
check for a particular shopping transaction: shopper frequency (the
number of times the shopper has visited that store), queue length
(the length of the checkout line at that time); prior history
(check more items if the shopper has had errors in the past, check
less items if the shopper has had no errors in the past), store
location (check more items in stores located in areas with a high
risk of pilferage); time of day, day of week, date of year
(determine if pilferage more likely at certain times of day or
year); number of times items are returned to shelf during shopping;
dwell time between scans, and other factors.
[0008] In a method aspect of the present invention, provided is a
method for use in a self-service shopping checkout system wherein a
shopper is provided with a self-scanning terminal for the scanning
of the bar code of an item selected for purchase prior to
depositing the item into a shopping cart, and wherein a list of
items self-scanned by the shopper is compiled and made available to
a cashier for surveillance and payment purposes. The method
performs a security check to determine if the shopper did not
likely fail to scan an item prior to depositing the item into the
shopping cart. The method comprises the steps of determining, as a
function of a plurality of input criteria, whether a shopper should
be audited and the number of items n to be scanned, selecting from
the shopper's cart of items presented for purchase n items to be
scanned, scanning a bar code located on each of said n items
selected for scanning, allowing the shopping transaction if each
item selected for scanning is present on the list of self-scanned
items compiled by the shopper, and disallowing the shopping
transaction if any item selected for scanning is not present on the
list of self-scanned items compiled by the shopper. The number of
items n is determined as a function of the criteria mentioned
above. The method further comprises the steps of selecting items at
random system checks and determining whether more items are needed
to be checked until statistical significance is achieved.
[0009] In a systems aspect, the present invention comprises several
alternative embodiments. In each embodiment, a self-service
shopping checkout system comprises a plurality of portable
self-checkout devices, wherein each of the self-checkout devices is
to be used by a customer to scan a bar code located on an item to
be purchased so as to record therein a list of such items to be
purchased. In one embodiment, a stationary dispenser unit is used
for the releasable containment of said plurality of portable
self-checkout devices and transmission of data stored in the
devices by wireline to a host computer for processing; and a
plurality of point-of-sale terminals using the host processing to
check out the customer. In another embodiment, the portable device
contains a wireless transceiver for transmitting the data stored in
the device directly to the host computer in lieu of storing the
data in the device and using the dispenser to transmit the stored
data to the computer. In still another embodiment, the portable
device is a dumb terminal for collecting and storing the shopping
data which may be used in conjunction with a kiosk to determine the
prices and cost of items selected for purchase. The kiosk contains
a display and a rack for receiving the dumb terminal to communicate
with the host computer by wireline or a wireless link. In response
to customer inputs, the desired information is presented on the
display. Alternatively, the customer may place the dumb terminal in
a cradle at the checkout stand. The cradle loads the data in the
dumb terminal into the host computer for processing and check out
of the customer.
[0010] In the present system, each of the portable self-checkout
devices comprises bar code scanning means for scanning and decoding
a bar code located on an item to be purchased, means for compiling
a list of items scanned by said customer, and a data output port
for allowing transfer of said scanned item list to an associated
data port located in a dispenser external to said portable device
or by wireless link directly to a host computer for processing the
shopper's items selected for purchase. In one embodiment, the
dispenser unit of the system comprises a plurality of device
containment slots, each of said slots being configured for
releasable containment of a mating self-scanning device, each of
said slots having associated therewith a data input port suitable
for mating with a data output port located on a portable
self-checkout device, and a printer for printing a tally list of
items scanned for purchase by said shopper, said tally list being
supplied by a self-checkout device after said self-checkout device
is returned to a device containment slot after being used by a
shopper, said tally list further comprising a bar code encoded with
said items scanned by said shopper, a unique identification record
associated with said shopper, and the number of items scanned by
said shopper. Each of the point-of-sale terminals in the present
system comprises bar code reading means for reading said
two-dimensional bar code from a tally list presented to a cashier
operating said point-of-sale terminal, said bar code reading means
providing as output data signals representing said items scanned by
said shopper, a unique identification record associated with said
shopper, and the number of items scanned by said shopper. Each of
the point-of-sale terminals in the present system comprises bar
code reading means for reading said two-dimensional bar code from a
tally list presented to a cashier operating said point-of-sale
terminal, said bar code reading means providing as output data
signals representing said items scanned by said shopper, said
unique identification record associated with said shopper, and said
number of items scanned by said shopper; said bar code reading
means also configured so as to scan select items presented for
checking by said cashier; means for determining, as a function of
said number of items scanned by said customer and an internally
stored check number unique to said customer, the number of items n
to be scanned by the cashier; means for comparing the identity of
the items scanned by said cashier with the list of items scanned by
said customer; means for allowing the shopping transaction if each
item selected for scanning by the cashier is present on the list of
self-scanned items compiled by the shopper; and means for
disallowing the shopping transaction if any item selected for
scanning by the cashier is not present on the list of self-scanned
items compiled by the shopper.
[0011] The present invention may be further enhanced using other
auditing factors as a basis for statistical techniques for
self-check out. Among the audit factors for such self-checkout are
shopper audit history, loyalty of shoppers, regional differences
and other factors which attempt to model the real world to obtain
the minimum checkout loss for a shopper. After a determination
whether a shopper should be audited and, if so, how many items
should be selected for audit, a shopping transaction is allowed
according to a statistical decision if the minimum check-out loss
for the transaction is less than a threshold defined by a loss
function L(c) and (p), where L(c) is the expected inventory loss
associated with the shopper and (p) is the probability of
performing an audit on the shopper.
BRIEF DESCRIPTION OF THE DRAWING
[0012] FIG. 1 is a diagram of the input criteria used in the
present invention;
[0013] FIG. 2 is a flow chart of the method of the present
invention;
[0014] FIG. 3 is a block diagram of the system of the present
invention;
[0015] FIG. 4 is a block diagram of the self-scanning terminal of
the present invention; and
[0016] FIG. 5 is a block diagram of the host computer of the
present invention.
DESCRIPTION OF THE PREFERRED EMBODIMENT
[0017] In FIG. 1, the present methodology determines how many items
to check for a given shopper transaction as well as which
particular items to check for that shopper, using the following
input criteria which may be considered, alone or in varying
combinations: shopper's prior history A (check more items if the
shopper has had errors in the past, check less items if the shopper
has had no errors in the past); store location and demographics B
(check more items in stores located in areas with a high risk of
pilferage); number of shopper's in checkout queues or queue length
C (the length of the checkout line at that time); shopper's scan
habits D or the number of times items are returned to shelf during
shopping, and dwell time between scans; time of day, day of week
date of year E (determine if pilferage more likely at certain times
of day or year); and types of items scanned F. Other factors may
include, shopping frequency (the number of times the shopper has
visited that store).
[0018] In FIG. 2, a method for performing a security check to
determine if the shopper did not likely fail to scan an item prior
to depositing the item into the shopping cart comprises the steps
of G generating a plurality of input criteria for self-check out; H
determining if the customer is to be audited, i.e items to be
re-scanned; I performing a statistical determination of which items
(R) to be selected and scanned; J performing a statistical
determination of how many items of the selected items to check in a
shopper's basket; K generating a list of items to check; L
selecting from the shopper's cart of items presented for purchase n
items to be scanned including M the step of properly scanning a bar
code located on each of said n items selected for scanning from the
chart for proper scanning; N allowing the shopping transaction if
each item selected for scanning is present on the list of
self-scanned items compiled by the shopper; O disallowing the
shopping transaction if any item selected for scanning is not
present on the list of self-scanned items compiled by the shopper;
and P adjusting the security parameters for the next shopping
transaction and providing the adjusted security parameters to the
input criteria. In an alternate embodiment, the system may advise
the cashier or security guard as to the number of items to check in
step J without specifying which items to check.
[0019] FIG. 3 illustrates a block diagram of the secure
self-service shopping system of the present invention. The system 2
comprises, at the top level, a scanner dispenser 2, a host computer
system 4, and a plurality of point of sale (POS) terminals 6. The
host computer 4 is a standard computer system well known in the
prior art and found in retail establishments such as supermarkets
for controlling operations of the supermarket, as modified as
described below to carry out the methods and functions of the
present invention. In particular, the host computer 4 is capable of
interfacing with the scanner dispenser 2 for data communications
therebetween in accordance with the present invention as will be
described more fully below. Likewise, each POS terminal 6 is a
standard POS computer system well known in the prior art and found
in retail establishments such as supermarkets for controlling
checkout functions of the supermarket, such as purchase item entry
and payment tender functions, as modified as described below to
carry out the methods and functions of the present invention. In
particular, the POS terminal 6 is capable of interfacing with the
host computer 4 for data communications therebetween in accordance
with the present invention as will be described more fully
below.
[0020] The scanner dispenser 2 is a stationary, i.e., wall-mounted
chassis, which comprises a plurality of interface slots 10
configured to physically and electrically mate with an associated
portable scanning terminal 100, shown in detail in FIG. 4. Each
terminal 100 is placed within an associated recess in the dispenser
2 for data transfer functions, battery recharge, etc., after the
shopper has used the scanning terminal for self-service scanning
functions. After data has been transferred between the terminal 100
and the dispenser 2, as will be described below, and the terminal
power supply (i.e. battery) is deemed to be suitable for re-use,
then the dispenser 2 will allow a subsequent shopper to select that
terminal for use in his or her shopping functions. The dispenser 2
also comprises a control processing section 12, a memory section
14, a printer 16, a card reader 18, a host I/O section 20, and a
display 22, all of which will be described below in further
detail.
[0021] When a shopper desires to obtain a scanning terminal 100
from the dispenser 2, he accesses the system by presenting a coded
identification card to the card reader portion of the dispenser 2.
The card reader may be a magnetic stripe reader, which is well
known in the art. In this case, the shopper presents a "loyalty
card" having an associated encoded magnetic stripe, comprising data
indicative of the identity of the shopper. The shopper may also
present a credit card, smart card, debit card or the like having a
suitable encoded magnetic stripe. In an alternative embodiment, the
card reader 18 may be a bar code symbol scanning device, suitable
for reading a one or two dimensional bar code symbol printed on a
loyalty card, driver's license or the like, for obtaining therefrom
the required identification data. Any type of technology which
lends itself towards the use of automatic identification may be
implemented by this system.
[0022] Once the control section 12 of the dispenser 2 has
determined that the requesting user is allowed to access a terminal
100 (i.e. the shopper is a member of the self-service shopping
system), a terminal is assigned to the user and the identity of the
assigned terminal is signaled to the user in any of various ways.
For example, an LED associated with and in close proximity to the
assigned terminal may be caused to blink on and off, thus catching
the attention of the shopper and indicating that he should select
that terminal. Likewise, appropriate instructions may be displayed
to the shopper via the display 22, such "Please take terminal
number 17" or the like. Concurrently therewith, a locking mechanism
which may be used for terminal security purposes to prevent
unauthorized removal of the terminal will be disabled by the
dispenser control logic 12, thus enabling the removal of the
assigned terminal 100 from the dispenser 2 by the shopper.
[0023] The scanning terminal 100 shown in block diagrammatic form
in FIG. 4 is a lightweight, portable, hand-holdable device well
suited for carrying by the shopper and performing data entry
functions such as keypad entry and/or bar code scanning of items
selected for purchase. The terminal 100 comprises a scanning module
102, a decoder 104, a keypad 106, a display 108, a dispenser
interface section 110, a control section 112, an items scanned
memory section 114, a price look-up table 116, and, optionally, a
wireless transceiver 118 and antenna 120, all of which function in
operative association with bus 122 as further described.
[0024] The scanning module 102 and decoder 104 operate in
conjunction in a manner well known in the art to allow the user to
scan a bar code located on an item selected for purchase and input
onto bus 122 for subsequent processing. For example, in the
preferred embodiment, the scanning module 102 is a laser bar code
scanner which utilizes a laser light source, a scanning means such
as a mirror mounted on a miniature motor, and a photosensor for
receiving light reflected from a target bar code and for converting
the received reflected light into an electrical signal indicative
of the degrees of reflectivity of the various portions of the bar
code. The scanning module also comprises signal processing which
digitizes the signal from the photosensor so that the decoder may
perform an analysis thereon to determine the data represented by
the bar code. A laser scanning device such as this is well known in
the art and may be found, for example, in U.S. Pat. No. 5,479,000,
which is incorporated by reference herein. In addition, the
scanning module may be of the CCD type, which utilizes a linear or
two-dimensional CCD array for capturing the reflected light
(ambient or otherwise) from the target bar code and for generating
an associated signal which is processed in accordance with
techniques well known in the art.
[0025] After the user has scanned a bar code from a target item,
the decoded data signal indicative of the data represented by the
target bar code is output by the decoder onto the bus 122. The
decoded data is used to fetch price and item description
information from the price look-up table 116, which is in turn sent
to the display 108 for display to the user. The price and
description data is also sent to the item scanned memory 114 for
storage therein such that the item scanned memory 114 will compile
a tally list of all items scanned by the user in that shopping
trip.
[0026] If desired, the user may delete an item from the tally list
by scanning the bar code of the item and depressing an appropriate
function key found on the keypad, e.g. a "minus" key, to signal to
the control logic 112 that the associated scanned bar code is to
removed from, rather than added to, the tally list in the memory
114. Thus, when the user changes his mind about the purchase of an
item scanned, he may re-scan the item, press the appropriate return
key, place the item back on the shelf, and the tally list will
reflect accurately only those items intended to be purchased by the
user.
[0027] The user may, at any desired time, obtain a subtotal of the
items scanned for purchase and resident in memory 114 by depressing
an appropriate key on the keypad 106, e.g. a "subtotal" key. This
key will cause the control logic section 112 to fetch the price of
each item from the memory 114, add the prices together, and display
the total on the display 108. This enables the user to ensure that
he has not exceeded a certain spending limit.
[0028] In another embodiment, as an alternative to looking up the
price and description of the scanned item from a terminal-resident
memory such as the look-up table 116, the terminal 100 may employ
wireless communication with the host computer 4 via the optional
wireless transceiver 118 and antenna 120. In such an embodiment,
the price and item description information is stored in the price
look-up table 210 at the host computer 4, as shown in FIG. 5. The
decoded bar code data is sent via the transceiver 118 to the
associated antenna 203 and transceiver 202 at the host computer 4,
which fetches the price and item description from its price look-up
table 210 and sends it back to the terminal 100 via the wireless
link. This type of embodiment eliminates the need for a look-up
table to be stored in each terminal 100, and changes to the data in
the price look-up table may be made at the host rather than
requiring each terminal 100 to be revised when the price or item
description is changed.
[0029] In addition, when a wireless data link is used to allow
communications between the terminal 100 and the host 4, then the
tally list of items scanned may be kept in an appropriate memory
location in the items scanned memory 212 at the host computer 4
rather than utilizing an on-board memory 114. Deletion of an item
and acquisition of a subtotal may be likewise executed through the
wireless link rather than performing those functions at the
terminal 100.
[0030] The wireless link may be accomplished via an RF (radio
frequency) link, which is well known in the art and is described in
detail in U.S. Pat. No. 5,157,687; which is incorporated by
reference herein. In an RF based scenario, the host transceiver
would likely be physically located near the host since
communications with the terminals need not be in close proximity.
In the alternative, other wireless technologies such as infrared
communications may be implemented, with transceiver stations
strategically located throughout the store for communications with
each terminal 100 as the shopper proceeds through the store.
[0031] In still another embodiment, the terminal 100 may be used in
conjunction with a kiosk located in the store to provide the
customer for information purposes only a list of the items scanned,
the item prices and the cost of purchase. In such case, the
terminal 100 maybe a "dumb terminal" and simplified to eliminate
costly functions, such as control, display and other functions. The
kiosk contains a receptacle for receiving the terminal; a display
and a keyboard for communication with the host computer. In use,
the terminal would be loaded into the receptacle and the scanned
items loaded into the host computer for processing in accordance
with customer inputs through the keyboard. The processing results
would be shown on the display. The kiosk may communicate with the
host computer by wireline or wireless link, as previously
indicated. As an alternative, the customer may load the "dumb
terminal" into a cradle at the checkout stand whereupon the scanned
items would be loaded into the host computer for check-out
processing.
[0032] Returning to FIG. 3, when the shopper has completed scanning
items for purchase, terminal 100 is returned back to the scanner
dispenser 2 and placed within an appropriate mating recess for
communications with the scanner interface 10. When the terminal has
implemented an on-board look-up table 116 and memory 114, then the
tally list of items scanned is downloaded from the memory 114 to
the host computer 4 for further processing. Along with the tally
list, data indicative of the identity of the shopper, which is
obtained when the shopper initially requests a terminal 100 from
the dispenser 2 as described above, is downloaded to the host 4.
The host 4 thusly has stored therein the identity of the shopper
along with data indicative of the items selected for purchase. If
the system is operating in wireless communications mode, then the
items scanned memory 212 at the host computer will contain the
tally list of items scanned for purchase for that particular
shopper without the need for downloading from the scanning terminal
at the dispenser interface.
[0033] After determining that the shopper has completed selecting
and scanning items for purchase, the host computer proceeds to
determine, in accordance with the present invention, the items to
be checked by the checkout cashier (or security guard or the like).
Referring to FIG. 5, the host computer has stored in a security
criteria memory 214 a plurality of security criteria which are used
to determine the items to check by the cashier, if the shopper is
determined to be audited. The security criteria include, but are
not limited to, the following:
[0034] 1. Shopper frequency: The frequency of visits of the shopper
is a factor to consider in determining the number of items to
check. A counter is kept in memory for each member of the
self-service system, which is incremented every time the shopper
has visited the store. In general, the more the shopper has visited
the store, the lower the number of items will be checked and the
probability of checking the shopper will be lower, since so-called
loyal shoppers will be given the benefit of having less items
checked.
[0035] 2. Queue length: The host computer will know the approximate
length of the queue by observing the number terminals have been
used and returned to the dispenser, but which have not yet been
checked out at the POS terminal. Since a goal of the system is to
maintain a high throughput of shoppers, it may be postulated that
less items will be checked when the queue length is long.
[0036] 3. Prior history: The specific prior history of the
particular shopper is stored and used to factor in the
determination of the number of items to be checked. That is,
shoppers with a prior history of scanning errors, as determined by
the security check at the POS terminal, will have more items
checked than shoppers with less errors in the past and the
probability of re-scanning items of such shopper is higher.
[0037] 4. Store location: Demographic indicia linked to the
likelihood that pilferage will occur more frequently in a certain
geographic location may be factored into the determination of the
number of items to be checked.
[0038] 5. Time of day/day of week/date of year: Statistical
analysis of pilferage as it may be linked to the time of day, day
of week or date of year may be factored into the determination.
[0039] 6. Item returns: The host computer will have information
available to it as to the number of times a shopper has depressed
the minus key, which indicates a scanned item has been returned to
the shelf. A likelihood exists that a shopper who has depressed
this key an excessive amount of times is more likely to have failed
to actually return the item to the shelf. Thus, the number of items
to be checked should increase as this factor increases. This factor
increases the probability of re-scanning and the number of items to
be checked.
[0040] 7. Dwell time between scans: The elapsed or dwell time
between scans by the shopper may be examined by time-tagging the
scans and analyzing the shopping pattern. Thus, for example, it may
be statistically determined that shoppers should scan an item once
every minute. When a shopper takes five minutes to scan the next
item, it may be presumed that items may have been selected for
purchase but not scanned in that interim. Those shoppers with
inordinate dwell times may have more items checked.
[0041] After the host computer 4 has used the security criteria as
described above in order to ascertain, via the security
determination logic means 216, the specific number of items to
check for scan accuracy by the cashier or security guard, it
proceeds to determine if this shopper is to be re-scanned (audited)
or not, and if so, which types of items the cashier or security
guard should look for in selecting the items to check. Factors to
consider in determining which items to look for from among the
shoppers purchases include the following:
[0042] 1. Statistical determination of highly pilfered items:
Historically, certain items such as batteries or razors (high cost,
small package size) have a higher percentage of pilferage than
other items such as watermelons (low cost, large package size).
[0043] 2. Prior history: The specific prior history of the
particular shopper is stored and used to factor in the
determination of which items should be checked. That is, shoppers
with a prior history of scanning errors for certain items, as
determined by the security check at the POS terminal, will have
those particular items checked.
[0044] 3. Store location: Demographic indicia linked to the
likelihood that pilferage of certain items will occur more
frequently in a certain geographic location may be factored into
the determination of the specific items to be checked.
[0045] 4. Time of day/day of week/date of year: Statistical
analysis of pilferage of certain types of items as it may be linked
to the time of day, day of week or date of year may be factored
into the determination.
[0046] 5. Item returns: The host computer will have information
available to it as to the number of times a shopper has depressed
the minus key for certain items, which indicates that scanned item
has been returned to the shelf. A likelihood exists that a shopper
who has depressed this key an excessive amount of times is more
likely to have failed to actually returned the item to the shelf,
and thus that item should be checked.
[0047] 6. Dwell time between scans: The elapsed or dwell time
between scans by the shopper may be examined by time-tagging the
scans and analyzing the shopping pattern. Thus, for example, it may
be statistically determined that shoppers should scan an item once
every minute. When a shopper takes five minutes to scan the next
item, it may be presumed that items may have been selected for
purchase but not scanned in that interim. By analyzing the store
location as a function of dwell time increase (by checking adjacent
scans and extrapolating the interim location of the shopper), it
can be determined which items should be checked.
[0048] Once the analysis has been made by the host computer as to
which specific (or types of) items should looked for by the cashier
or security guard, then data indicative thereof is stored along
with the number of items to be checked for that shopper in the
memory of the host computer 4. This data is available for download
to the appropriate POS terminal selected for final checkout by the
shopper after he has resumed the scanning terminal 100 to the
dispenser 2.
[0049] The shopper may then proceed to an appropriate POS terminal
6, which is manned by a cashier for tender of payment and security
checking of the items selected for purchase. When the shopper
reaches the POS station, he presents his loyalty card (or other
suitable automatic identification card) to the cashier, who will
present the card to an appropriate card reader for automatic
identification of the shopper. The shopper's identification data is
used to fetch from the host computer 4 the tally list of items
scanned and the data indicative of the number of items to be
checked as well as the identity of specific items or types of items
to look for in performing the audit process.
[0050] The cashier or security guard reads from the display at the
POS terminal the list of items to check (or from a printed version
of the list) and selects the items for checking. The cashier scans
the bar code of each item, and if any item scanned is not on the
tally list, the cashier or security guard is alerted that the
shopper has made an error in scanning. In this case, the retail
establishment may opt to re-scan the entire shopping cart, may
simply add the item to the tally list, or may take some other act
it deems appropriate for the situation. Data indicative of the
mis-scanned item is then transmitted from the POS terminal back to
the host computer and stored in its security criteria memory 214
for subsequent processing and subsequent criteria
determination.
ADDITIONAL SELF CHECKOUT AUDITING PROCESSES OR POLICIES
[0051] A more advanced auditing policy will increase security and
further reduce labor. Many factors can be used in developing such a
policy. Some of the factors that can be used in an advanced
auditing policy are listed hereinafter in Section A. How these
factors are taken into account by a system operator determines the
auditing policy. Several auditing policies are proposed. One policy
is based on statistical decision theory and is described in Section
B1. A policy based on different customers response to auditing is
given in Section B2. A policy based on Neural Networks is described
in Section B3.
[0052] A. Factors used in an Advanced Auditing Policy
[0053] There are many heuristic rules that can be applied in an
auditing policy. In the prior art there is one implicit rule. The
rule can be stated something like this: People who have failed an
audit (either due to theft or due to innocent errors) are more
likely to do so in the future, therefore they should be audited
more often. To develop a better auditing policy we need to use
additional rules that model the real world more completely.
[0054] In this section we summarize the rules that will be used in
subsequent sections to develop advanced auditing policies. The
following is a list of the rules and a short description of
each.
[0055] Audit History:
[0056] The audit history of a given customer is a good indication
of his future checkout accuracy. One may use the recent audit
history or possibly the entire audit history. This is the rule used
in the prior art.
[0057] Loyal Customers:
[0058] Customers who shop frequently at the store are likely more
honest and should be audited less. Some of this falls out from the
previous rule; however, we may want to give the loyal customer an
additional level of trust and further reduce the audit
frequency.
[0059] Regional Differences:
[0060] Different regions of the country or the world will have
different likelihood of theft. Regions with a high theft level may
require more stringent security so the level of auditing should be
higher in those regions.
[0061] Store Shopping Activity:
[0062] To reduce waiting a long time in audit lines the store may
want to reduce the average auditing level during times when the
store is very busy. This will increase the throughput of the store
at the risk of slightly increased theft.
[0063] Weight & Size of Items:
[0064] These qualities may be factor in the rate of pilferage.
[0065] Seasonal:
[0066] During different seasons people may be more likely to
attempt theft or make errors.
[0067] Time of Day:
[0068] During different times of the day people may be more likely
to attempt theft or make errors.
[0069] High Rate of Returns:
[0070] If the customer is deleting a lot of items from the checkout
list he may be more likely to be attempting theft.
[0071] Scan Frequency:
[0072] Long time spans between scan items could be an indication of
attempted theft.
[0073] B1. Statistical Decision Theory Based Auditing Policy
[0074] The approach taken here is to use statistical decision
theory to implement an auditing policy based in whole or in part on
the above rules. A description of statistical decision theory is
given in Appendix I, references [1, 2].
[0075] The first parameter that is required in setting up a
decision rule is a description of the state space, which is the set
of possible states of nature [2]. This is all the information that
we have at our disposal to make a decision. The state space,
.theta., which we will use consists of a finite set of possible
events that can occur. As an example we will consider a state space
of four events which consist of all combinations of two independent
events. The first event to consider is whether there is an error in
the self checkout that was performed by the customer. This event,
E.theta., represents an error in the self checkout data; its
complement {overscore (E)}.theta., means there is no error. The
second event indicates whether the store is busy or not. The event,
B.theta., means the store is busy and the event {overscore
(B)}.theta. means the store is not busy.
[0076] Taking combinations of E, {overscore (E)}, B, and {overscore
(B)}, the state space can be partitioned into four mutually
exclusive events,
.theta.={.theta..sub.1, .theta..sub.2, .theta..sub.3,
.theta..sub.4} (1)
[0077] where the states are as follows,
.theta..sub.1=E.andgate.B
.theta..sub.2={overscore (E)}.andgate.B
.theta..sub.3=E.andgate.{overscore (B)}
.theta..sub.4={overscore (E)}.andgate.{overscore (B)} (2)
[0078] So .theta..sub.1 means that the customer has made an error
in his checkout and the store is busy, .theta..sub.2 means self
checkout is correct and the store is busy, etc.
[0079] In developing a decision rule we also need to define the
possible actions that we can take. Since we are trying to determine
whether to audit a customer or not, our actions involve levels of
auditing. Each time a customer shops at the store we have several
options. We can let the customer leave without an audit, we can
audit the customers entire cart, or we can perform a limited audit
by checking only some of the items the customer has in his
cart.
[0080] For this example, we will consider a action space consisting
of these three actions,
A={a.sub.1, a.sub.2, a.sub.3}. (3)
[0081] The three actions are,
a.sub.1: No Audit
a.sub.2: Limited Audit (e.g. check 10% of items)
a.sub.3: Full Audit (4)
[0082] Finally, we need to define a loss function associated with
taking action a.sub.i given that event .theta..sub.j occurs. This
loss function measures the loss (either financial or otherwise)
incurred by taking such an action. In the self checkout problem
there are several factors that effect loss. First, there is the
actual loss incurred due to theft. There is a loss associated with
a low throughput of customers that may incur due to excessive
auditing during busy times. There is the labor costs associated
with performing the audit. And finally, there is loss associated
with customer dissatisfaction due to excessive auditing or having
to wait a long time.
[0083] As an example, Table 1 lists the different losses that
occur. The actual values for that table would depend on what store
this system is being used in and could be adjusted to fit their
circumstances. Combining the losses listed in this table it is
possible to build a loss function. As an example, loss function
L(.theta., a) is given in Table 2.
[0084] Lets see in Table 2 how the loss function is built up from
the losses in Table 1. For example, whether the store is busy or
not, there is an average inventory loss of $5.00 if the customer
has made an error in his self checkout and we chose not to audit.
If he has not made an error and we do not audit then their is no
loss since there is no error to find. There are no other types of
losses when you do not perform an audit. If the store is busy and
we chose to do a limited audit, and the customer made an error,
then we have a $2.00 loss of inventory, a $0.50 loss in potential
sales, a loss of $0.50 in labor costs, and finally a loss of $0.50
in customer dissatisfaction. Under the same conditions, except that
the customer did not make an error, then we have all the same
losses, except the $2.00 loss of inventory. The other terms of the
loss function are developed in a similar manner. So in this loss
function we have summarized the four types of loss: inventory loss,
potential sales loss, labor costs, and customer
dissatisfaction.
[0085] Now, given the state space, the action space, and the loss
function we need a criterion for selecting the "best" action. We
choose to select the action that gives the smallest loss on the
average. We cannot be guaranteed to always select the smallest loss
because we do not know if the customer has made an error (if we did
it would make the audit decision very easy). This lack of knowledge
can be modelled statistically. We model the events in the state
space as random and with some distribution as to their likelihood.
Now in the state space we have set up there are two factors:
whether the customer has made an error and whether the store is
busy. The first is an unknown and the second is know. So in this
case all we have to model as random are the events E and {overscore
(E)}.
[0086] There are many possible models that could be used to
represent this probabilistically. For example, it could change with
time and other factors. We will make the simple assumption
1TABLE 1 Different Losses Occurring In A Loss Function Loss Value
Inventory loss when no audit is performed and customer made $5.00
an error Inventory loss when limited audit is performed and
customer made $2.00 an error Inventory loss when full audit is
performed $0.00 Potential sales lost when store is busy and full
audit is performed $1.00 Potential sales lost when store is busy
and partial audit $0.50 is performed Potential sales lost when
store is not busy and partial audit $0.25 is performed Potential
sales lost when no audit is performed $0.00 Labor costs for full
audit $1.00 Labor costs for partial audit $0.50 Labor costs for no
audit $0.00 Customer dissatisfaction with full audit when store is
busy $1.00 Customer dissatisfaction with partial audit when store
is busy $0.50 Customer dissatisfaction with full audit when store
is not busy $0.50 Customer dissatisfaction with partial audit when
store is not busy $0.25 Customer dissatisfaction with no audit
$0.00
[0087]
2TABLE 2 Types of losses and their financial value .theta..sub.1 =
E .andgate. B .theta..sub.2 = {overscore (E)} .andgate. B
.theta..sub.3 = E .andgate. {overscore (B)} .theta..sub.4 =
{overscore (E)} .andgate. {overscore (B)} a.sub.1 (No audit) 5.0
0.0 5.0 0.0 a.sub.2 (Limited 3.5 1.5 3.0 1.0 Audit) a.sub.3 (Full
Audit) 3.0 3.0 2.0 2.0
[0088] that for each customer there is a probability that he will
make and error and that probability is fixed. Later we could use a
more elaborate model. So for a given customer we will define the
p.sub.e as that probability of making such an error,
p.sub.e=P(E)=1-P({overscore (E)}). (5)
[0089] If we know this probability (and actually we have to
estimate it) we can use it to find the best action. To do this we
have to define the Bayes loss [2] as the average loss, 1 B ( a ) =
E [ l ( , a ) ] = i n L ( i , a ) P ( i ) . ( 6 )
[0090] where L represents loss which is a function of types of
losses and the auditing decision of Table 2.
[0091] Since we can assume that we know whether the store is busy
or not we can simplify this formula. If the store is busy we have,
P(B)=1 and P({overscore (B)})=0. So,
B(a)=L(.theta..sub.1,
a)P(.theta..sub.1)+L(.theta..sub.2,a)P(.theta..sub.2-
)+L(.theta..sub.3,a)P(.theta..sub.3)+
L(.theta..sub.4,a)P(.theta..sub.4)
B(a)=L(.theta..sub.1,a)P(E)+L(.theta..sub.2,a)P({overscore
(E)})
B(a)=L(.theta..sub.1,a)p.sub.e+L(.theta..sub.2,a)(1-p.sub.e)
(7)
[0092] And if the store is not busy we have, P(B)=0 and
P({overscore (B)})=L. So,
B(a)=L(.theta..sub.1,
a)P(.theta..sub.1)+L(.theta..sub.2,a)P(.theta..sub.2-
)+L(.theta..sub.3,a)P(.theta..sub.3)+
L(.theta..sub.4,a)P(.theta..sub.4)
B(a)=L(.theta..sub.3,a)P(E)+L(.theta..sub.4,a)P({overscore
(E)})
B(a)=L(.theta..sub.3,a)p.sub.e+L(.theta..sub.4,a)(1-p.sub.e)
(8)
[0093] The best action to take is the action that minimizes the
Bayes loss [2]. That action is called the Bayes action,
a.sub.B,
B(a.sub.B)=min.sub.j B(a.sub.j) (9)
[0094] We will now show how to get the probability of this customer
making an error. We will use our prior audit history to estimate
that probability. The simplest estimator is just the relative
frequency. If the customer has been audited N.sub.a times and has
failed the audit (i.e. had an error) N.sub.e times then we can
estimate the probability of an error as the ratio of those two
numbers, 2 p ^ e = N e N a ( 10 )
[0095] We may choose to only use the recent audit history so that
if p.sub.e has changed recently we can detect it. If we want to do
that then we use only the last 10 audits for example, and then
N.sub.a=10 and N.sub.e is the number of errors in those audits.
[0096] In summary, one estimates p.sub.e using Equation 10. If the
store is busy one uses Equation 7 for the Bayes loss, substituting
{circumflex over (p)}.sub.e for p.sub.e,
B(a)=L(.theta..sub.1a,){circumflex over
(p)}.sub.e+L(.theta..sub.2,a)(1-{c- ircumflex over (p)}.sub.e)
(11)
[0097] If the store is not busy one uses Equation 8 for the Bayes
loss, substituting {circumflex over (p)}.sub.e for p.sub.e,
B(a)=L(.theta..sub.3,a){circumflex over
(p)}.sub.e+L(.theta..sub.4,a(1-{ci- rcumflex over (p)}.sub.e)
(12)
[0098] Select the Bayes action, a.sub.B, that minimizes the Bayes
loss as in Equation 9,
B(a.sub.B)=min.sub.j B(a.sub.j) (13)
[0099] In the example given here only two variables were
considered: the customer making an error and whether the store is
busy. Clearly the other factors listed in Section A.2 can all be
included in the auditing policy. This involves having more
variables in the loss function. Note, however that the only unknown
is whether the customer has made an error. So the only probability
that has to be estimated is the probability of such an error. All
other parameters of the loss function would be known to the system.
For example, the system would know whether it was being used in a
safe neighborhood or not. So the calculation of the Bayes action
would still be quite simple.
[0100] In this example we have made a number of simplifications.
For example, we have described the business of the store as either
busy or not busy. We could easily have many levels of how busy the
store is and define a loss function that takes into account all
those different levels.
[0101] Using statistical decision theory we always select the
action that gives the lowest average loss. From a mathematical
point of view this is the optimum thing to do. However, if a
customer has a relatively fixed probability of error and visits the
store under similar conditions every time (e.g. level of business)
then it is likely that we will take the same action most of the
time. This may not be the best thing to do from a psychological
point of view. The customer may start to try to second guess the
system and change his actions. For this reason we may want to
randomize our actions a bit. One way to do this is to assign a
probability of performing each action and then select the action
according to that probability law. Let us define p.sub.i as the
probability of taking action a.sub.i. Then one way to select those
probabilities so that they are inversely proportional to the loss
associated with taking that action, 3 p i = 1 / B ( a i ) 1 / B ( a
i ) + 1 / B ( a 2 ) + 1 / B ( a 3 ) For i = 1 , 2 , 3. ( 14 )
[0102] Then we take action a.sub.i with probability p.sub.i. This
may not be the optimum from a mathematical point of view but it may
be better from a psychological point of view.
[0103] B2. Audit Policy Based on Customer's Response to Audit
[0104] Another approach that can be taken in developing an auditing
policy is to quantify the customers reaction to being audited and
use his reaction to govern your audit policy.
[0105] To illustrate this idea we will define A as the cost of
performing an audit. Let L(c) be the expected inventory loss
associated with customer c if an audit is not performed. This
expected loss takes into account both the average loss if an error
is made and the probability that he will make an error. The
objective of this auditing policy it to select a probability of
performing an audit to minimize the average overall loss. Then once
that probability is calculated an audit is performed with that
probability. Let the probability of performing an audit be p.sub.a.
If the loss is independent of the probability of performing an
audit then the average loss is given by,
L.sub.ave=p.sub.aA+(1-p.sub.a)L(c). (15)
[0106] This is easy to see since you perform an audit with
probability p.sub.a and when you do it costs A; similarly you skip
an audit with probability (1-p.sub.a) and it costs L(c) each time.
So we have just averaged those two possibilities.
[0107] What if L(c) is also actually a function of the audit
probability? Then we write the inventory loss as a function of both
the customer and the frequency of auditing, so the loss has two
parameters: L(c,p.sub.a). There are many possible functions that
can be used to model the customers response to being audited. For
example, many customers will be more likely to make less errors if
they are audited, whereas others may continue to make errors even
if audited frequently. Let us try the following loss function,
L(c,p.sub.a)=B(c)(1-p.sub.a).sup.n (16)
[0108] where B(c) is the loss when the customer is never audited
and n is positive integer. The larger n the more likely the
customer will make less errors when audited frequently. So a loss
function with a large value of n models a customer who is highly
deterred from making an error by the threat of an audit. This can
be seen by noticing that for large n the loss, L(c), drops off
faster with an increase in p.sub.a. In this way we can model
different customers response to being audited.
[0109] Given this formula for L(c,p.sub.a) we can select p.sub.a to
minimize the average loss. Substituting this new inventory loss
function into Equation 15 for average loss we get,
L.sub.ave=p.sub.aA+(1-p.sub.a)L(c, p.sub.a)
L.sub.ave=p.sub.aA+(1-p.sub.a).sup.(n+1)B(c). (17)
[0110] To minimize this we differentiate with respect to p.sub.a
and set it equal to zero,
A-(n+1)(1-p.sub.a).sup.nB(c)=0 (18)
[0111] which can be solved for the probability, 4 p a = 1 - ( A ( n
+ 1 ) B ( c ) ) 1 / n ( 19 )
[0112] Since a probability must be nonnegative we must have,
A<(n+1)B(c) (20)
[0113] and if we do not satisfy that equation we should just set
p.sub.a=0 Thus Equation 19 gives the formula for the optimum audit
probability.
[0114] In Equation 15 the only probability density function was
p.sub.a. If the losses A and L were also random we can generalize
Equation 15 by averaging over those distributions also,
L.sub.ave=.intg..intg.(p.sub.aA+(1-p.sub.a)L(c))p(a)p(l)dadl
(21)
[0115] where p(a) is the probability density function of A and p(l)
is the density function of L. Then the same procedure as above is
applied to find the best auditing probability.
[0116] B3. Artificial Neural Network Based Auditing Policy
[0117] Artificial Neural Networks have been applied to sales
forecasting, industrial process control, customer research, data
validation, risk management, target marketing, medical diagnosis
and other problems were the system transfer function depends in the
input variables, and changes over time. For example, Mellon Bank
installed a neural network credit card fraud detection system and
the realized savings were expected to pay for the new system in six
months. See Appendix I, references [3, 4]. Essentially, a Neural
Network is used to learn patterns and relationships in data. The
data here can be information about the customer and the output can
be whether or not the customer is to be audited.
[0118] The input variables may be fuzzified. For example, the
customer's age may be fuzzified to {teenager, young, middle aged or
aged.} The shape of the membership functions may be learned and
generated via a neural net in order to minimize some cost
function--usually from a teacher (expert). The fuzzy rule base may
also be adaptable over time. Genetic Algorithms may be applied to
this rule base such that rules that work well will mutate and spawn
children that will perform better over time. See Appendix I,
reference [5]. References on Genetic Algorithms may be found in
texts that describe "Evolutionary Programming" concepts.
[0119] Summarizing, the advanced auditing policies of the present
invention, as reflected in the auditing rules which model the real
world and statistical decision theory based auditing, is not to
audit every customer. Instead, the present invention determines
whether a given shopper or customer is to be audited on a given
shopping trip based upon obtaining a minimum checkout loss for such
customer thereby providing an audit policy which is not too
intrusive to customers or shoppers, but which is a significant
deterrent to theft and unintentional errors.
APPENDIX 1
[0120] References
[0121] [1] B. W. Lindgren, Elements of Decision Theory. Macmillen
Co., 1971.
[0122] [2] B. W. Lindgren, Statistical Theory. Macmillen Co., third
ed., 1976.
[0123] [3] Z. Solutions, "An introduction to neural networks."
http://www.mindspring.com/ zsol/mgrguid.html.
[0124] [4] N. M. McCord and W. T. Illingworth, A Practical Guide to
Neural Nets. Addison-Wesley, 1990.
[0125] [5] "Genetic algorithms archive."
http://www.aic.nrl.navy.mil/galis- t/.
[0126] It should be apparent to those skilled in the art that while
the invention has been described with respect to a specific
embodiment, various changes may be made therein without departing
from the spirit and scope of the invention as described in the
specification and defined in the claims.
[0127] We claim:
* * * * *
References