Survey of E-Commerce Modeling and Optimization ... - IEEE Xplore

TSINGHUA SCIENCE AND TECHNOLOGY ISSN 1007-0214 03/15 pp 761 - 7 7 1 V o l u m e 10 , N u m b e r S I , D e c e m b e r 2 0 0 5

Survey of E-Commerce Modeling and Optimization Strategies * WANG Dingwei

* * , NUTTLE Henry L. W. \

FANG Shu-Cherng

1

S c h o o l of I n f o r m a t i o n S c i e n c e a n d E n g i n e e r i n g , N o r t h e a s t e r n U n i v e r s i t y , S h e n y a n g 1 1 0 0 0 4 , C h i n a ; f D e p a r t m e n t of Industrial E n g i n e e r i n g , N o r t h C a r o l i n a State U n i v e r s i t y , R a l e i g h , N C 2 7 6 9 5 , U S A

Abstract:

Electronic commerce is impacting almost all commercial activities. The resulting emerging

commercial activities bring with them many new modeling and optimization problems. This survey reviews pioneering works in this new area, covering topics in advertising strategy, web page design, automatic pricing, auction methods, brokerage strategy, and customer behavior analysis. Mathematical models for problems in these areas and their solution algorithms are discussed.

In addition to presenting and

commenting on these works, we also discuss possible extensions and related problems. The objective of this survey is to encourage more researchers to pay attention to this emerging area. Keywords:

electronic commerce; modeling and optimization; advertising; web link; pricing; auction; brokerage; customer behavior

retailing ' ' ' . [ 1

Introduction model

and

pushing

"information e c o n o m y " commerce

the

world

toward

an

In r e c e n t y e a r s , electronic

( E-commerce )

development.

6

This

7 ]

breadth

of impact

provides

a

great challenge to r e s e a r c h e r s of various technologies.

T h e information revolution is dramatically r e s h a p i n g the business

4

has

experienced

By year 2 0 0 4 , I n t e r n e t - r e l a t e d

rapid

business

Within any new a r e a , study " h o w

to

do

the first stage is always to

it".

The

earlier

works

on

E-

c o m m e r c e are also focused on how to c o n d u c t b u s i n e s s on the Internet. qualification

The business m o d e ,

certification,

realization,

growing knowledge of " h o w to do i t " , a large n u m b e r

E - c o m m e r c e h a s attracted a n u m b e r of r e s e a r c h e r s and

of E - c o m m e r c e c o m p a n i e s s p r a n g u p around the world.

engineers

H o w e v e r , in the stormy climate of the stock

attention Ul

to

a

diverse wide

backgrounds

range

of

to

direct

E-commerce

their related

topics

Ε-wallet

. T h e rapid d e v e l o p m e n t of

with

active

security,

and

US$

1 - 3

all

trade

h a d grown to over U S $ 1 5 0 0 billion p e r year from only 1 billion in 1995

were

Ε-banking

[ 6 - 8 ]

.

With

the

market,

m a n y E - c o m m e r c e c o m p a n i e s closed almost overnight. This fact cautions us that we have to know not just

[1,4,5]

" how to do it" but how to do it best and how to do it in

problems E-commerce

impacts

almost

all

commercial

a c t i v i t i e s , i n c l u d i n g information g a t h e r i n g , trading,

brokerage ,

finance ,

auction,

marketing,

material

banking,

accounting,

negotiation, supply,

scheduling, manufacturing,

shopping, auditing,

collaboration,

partnering,

training,

d i s t r i b u t i o n , service , and

by the

National

T h e optimization of resource allocation is the way

to

enhance

enterprise

[ 8 ]

.

the

Modeling

competitive and

Natural

Science

Foundation

of

The

main

functions

three

categories:

China ( N o . 7 0 4 3 1 0 0 3 ) and the National Textile Center of

visit web sites for t r a d i n g .

Tel: 8 6 - 2 4 - 8 3 6 8 0 6 6 2 ; E - m a i l

:

[email protected]

of

best an

approaches

auctioning,

optimal

trading,

resource in one of

and

analysis.

are used to attract customers to

web page and link d e s i g n , Selling,

to

can be p l a c e d

attraction,

the United States of America ( N o .

* * To whom correspondence should be a d d r e s s e d .

optimization

related

Attraction functions

101-sOl)

ability

are the tools for realizing optimal resource allocation. allocation for E - c o m m e r c e

Received: 2005-11-09 * Support

face of serious competition.

They i n c l u d e

advertising,

and competitive

and brokering are m a i n

pricing. trading

Tsinghua

762

functions.

T h e trading functions are supported by their

Science

and Technology,

December

2005, 10(SI)

761 - 7 7 1

:

supply c h a i n . T h e key analysis functions are customer

1

behavior analysis a n d logistics situation analysis.

T h e first important issue of Ε - c o m m e r c e is advertising.

There

are

problems

many

related

new

to

modeling

these

and

functions.

optimization There

are

n u m b e r of pioneering works on m a t h e m a t i c a l

a

models

and optimization a p p r o a c h e s . T h e s e works covered the m a i n Ε - c o m m e r c e functions m e n t i o n e d above.

Because

Electronic Advertising

No matter w h e t h e r B-To-B or B - T o - C ,

advertising is

absolutely n e c e s s a r y . 1. 1

L i n e a r p r o g r a m m i n g m o d e l for a d v e r t i s i n g

Ε - c o m m e r c e w e b site owners often play d u a l roles in E -

of t h e limitation of s p a c e , we focus on the following

advertising.

eighteen m o d e l s / a l g o r i t h m s r e p r e s e n t i n g t h e six main

products

research directions:

advertisers to sell advertising s p a c e on their own w e b

•

L a n g h e i n r i c h ' s linear

•

;

[ 1 0 ]

b e c a m e t h e earliest r e s e a r c h t o p i c

Rafiei

[ 1 1]

and

approach

Mendelzon's

Markov

;

Sung

and

Lee' s

based

pricing

;

[ 1 5 ]

;

[ 1 6 ]

and

Tennenholtz' s

combinatorial a u c t i o n

[ 1 9 ]

[ 1 8 ]

[ 1 7 ]

;

; for

;

on the click-through

rates

( click

advertisement-keyword

and

then

adjusts

its

display

s c h e d u l e so as to maximize the total n u m b e r of c l i c k s . weights

for

each

advertisement

with

each

display keyword

c o m m e r c e to customers Balachander' s

l

requiring

display

on

[2 0]

price

; [ 2 1 ]

;

to estimate the value of E -

2 2 ]

model

to 2 3]

modify

customer

;

customer

referral

Sun' s

fuzzy

reward

stochastic

a n d J o ' s constraint

2 5]

dynamic ;

satisfaction

( C S P ) model for internet b r o k e r a g e

[2 6 ]

2

,m,

ί = 1 ,2

···

2

we obtain ^

In

addition to p r e s e n t i n g a n d c o m m e n t i n g on t h e a u t h o r s ' possible

objective

extensions is

to

and

encourage

related more

r e s e a r c h e r s to pay more attention to this emerging a r e a .

n

, j = 1,

The

By n o r m a l i z i n g ,

h - 1.

{

i

/=i

problem

is

to

set

of W for Α., t

engine so as to maximize through

y

i

k - 1 and ^

(probability) x rate.

max s.t.

n a t u r e , t h e s e authors are the p i o n e e r s of this area.

,W

i

V a l u e s for k a n d c. , V i, j ,

,n.

can b e obtained from past statistics.

problem

.

Although some of the work a p p e a r s preliminary in

Our

desired

t

The

Y^^iXij

the

display

weights

V i, j for the selection

the expected

problem

following linear program

p r o g r a m m i n g model of customer a c q u i r i n g

,

2

The

is i n p u t . T h e input probability of keyword W is k a n d

tj

;

discuss

website.

T h e actual display of t h e a d v e r t i s e m e n t s d e p e n d s on

i=ι

;

ι i[24]

and

a

t

expectations of d u r a b l e p r o d u c t Biyalogorsky' s

S u p p o s e that there are m a d v e r t i s e m e n t s , A ,A ,

the click-through rate of A. on keyword W is ( Μ + 1 ) -th

K e e n e y ' s method

problems.

statistics

1

method

•

we

advertising

which of a n u m b e r of search keywords W ,W ,

determination

M e n a s c e ' s customer behavior analysis m o d e l

work,

of their

]r

•

Jung

engine

display rate for a d v e r t i s e m e n t j is h , j = 1 , 2 , ··· , m.

partition-constrained

W u r m a n ' s M - t h price a n d

rules for double a u c t i o n s

•

learning

advertisement

m

S a n d h o l m ' s winner

Weber

the

pair,

A,

multi-object auction m o d e l

•

for

s e a r c h . T h e model is as follows.

Penn

model

.

[ 9 1 0 ]

n u m b e r p e r d i s p l a y s ) for e a c h

S a i r a m e s h a n d K e p h a r t ' s price a n d quality joint

•

•

as

Therefore,

T h e m o d e l e d objective is to find t h e optimal

knowledge

K a o ' s multi-object auction m o d e l

•

also

system. T h e basic idea of the learning engine is that it gathers

prediction

;

1 4]

•

•

[12]

based

;

decision m e t h o d

•

chain

A b e a n d K a m b a ' s automatic pricing method to

method •

and

their

L a n g h e i n r i c h et al. p r e s e n t e d a linear p r o g r a m m i n g model

S a r u k k a i ' s Markov c h a i n b a s e d link [ 13]

for

;

maximize the total sale profit •

advertising,

sell

m a i n income source for web site owners.

K l e i n b e r g ' s m u t u a l reinforcement

approach •

to

the models on how to arrange web pages for advertising

a p p r o a c h to evaluate w e b page r e p u t a t i o n •

via

merchants

T o m l i n ' s entropy optimization model to modify

web link a n a l y s i s •

service

as

pages to other m e r c h a n t s . Initially, advertising was t h e

;

[ 9 ]

Langheinrich ' s m o d e l •

model

or

play

for

advertising d e s i g n

programming

They

is

total

formulated

clickas

the

:

^

^

y=i

y=i

= h

j9

Ay:..*..

( 1)

j = 1,2,••·,τη

(2)

i=1

Σ χ ~ ^ 0 ,

= 1,

^ = 1 , 2 , · · · ,τι

(3)

i = 1 , 2 , · · · , 7 i , j = 1 , 2 , · · · ,77i

(4)

T h e above formulations are recognized as a classical Hitchcock-type

transportation

problem

2 7

.

The

WANG Dingwei

et a l Survey

of E-Commerce

:

Modeling

for ease of b r o w s i n g

E n t r o p y o p t i m i z a t i o n m o d e l for a d v e r t i s i n g

Tomlin points out that with this model there will always be nm

( η + m )

-

solution

[ 10 ]

.

zero

elements

This m e a n s that e a c h

in

the

optimal

keyword

will

be

c o n n e c t e d with only a few of a d v e r t i s e m e n t s , which is both

undesirable

and

unrealistic.

To

avoid

But

ijm

most

variables

to be

at their

lower

b o u n d s , which is still unsatisfactory. proposed an entropy optimization m o d e l i

the

success

( analogous

'

2 8 ]

Tomlin

.

First,

users from W to A-

tj

with

[ 1 0

V i, j , the problem can be viewed as

ij

one involving the transport of y to

of

cost )

t

transportation The

c~.

probability

objective

r e p r e s e n t s the total n u m b e r of successfully

[ 2 9

'

3 0

]

.

Link analysis models

T h e first

model

on

the

proposed by K l e i n b e r g

link-structure

in 1 9 9 8 .

analysis

Kleinberg' s

method

is

called

reinforcement a p p r o a c h ( M R A )

[ U ]

function

transported

.

1 3

' ' 2 9

the

for

a

system

in

equilibrium

under

conditions of constant volume and t e m p e r a t u r e . function is F - Ε - Κ\ηω,

has

3 1

]

.

mutual

H e distinguishes

b e t w e e n two types of web sites related to a

specific

of sites is h u b .

H u b s are simply resource lists.

do not directly contain information topic,

but

rather

point to m a n y

The

where Κ is a c o n s t a n t , Ε is

They

p e r t a i n i n g to the authoritative

sites.

A c c o r d i n g to this m o d e l , h u b s and authorities exhibit a mutually reinforcing r e l a t i o n s h i p : good h u b s point to m a n y good a u t h o r i t i e s , and good authorities are pointed to by many good h u b s . Consider a collection C of η web sites ( i . e . ,

R e c a l l the Helmholtz free-energy function which is at minimum

was

This p a p e r

b e e n cited by a n u m b e r of other r e s e a r c h e r s

users. a

763

t o p i c . T h e first are authoritative sites. T h e second type

As an alternative to L a n g h e i n r i c h ' s m o d e l , letting γ~ =k x ,

2. 1

this

p r o b l e m , we could set lower b o u n d s on the x this will force

Strategies

page reputation analysis and design of linkage structure

formulations can be solved by the Simplex m e t h o d . 1. 2

and Optimization

η ) ,

which

contains

communities

of

IC I =

hubs

and

C and

authorities pertaining to a given topic T.

its

links can be r e p r e s e n t e d by a directed bipartite graph Its n o d e s are the sites in C , and for all i j e C the

G.

the internal e n e r g y , and ω is the n u m b e r of states. For

directed edge i—>j a p p e a r s in G if and only if site i

the above p r o b l e m , we are interested in maximizing the

contains a hyperlink to site j . Let W denote the η Χ η

click-through, or,

equivalently,

click-through probability. Cy = [ m a x c

] - c

minimizing the

By defining " c o s t "

nonvalues

and treating t h e s e cost values as

ij9

pq

adjacency matrix of G.

E a c h site s e C is now assigned a pair of w e i g h t s , a h u b weight h(s)

the analogue of e n e r g y , we o b t a i n :

Let S be the set of root sites

which can be found by t e r m - b a s e d search e n g i n e s . and an authority weight a(s)

, based

on the following two p r i n c i p l e s : F = constant + ^

^

i = l

v ,

:

/

+

rW )

(5)

y

j=l

T h e n , we obtain the entropy optimization model in

a

site's

weights of the sites it points to.

Σ

x

Σ

" r

l n

r )

( ) 6

y

Authority lies in the eyes of the b e h o l d e r : a site

is authoritative only if good h u b s d e e m it as

such.

H e n c e , a sites authority weight is proportional to the i=\

s.t.

j=i

sum of the h u b weights of the sites pointing to it.

= H

j9

j =

1

,

2

,

(

7

)

i = 1

Σ

J,, = K,,

£ = l,2,-,n

(8)

j=i y : Ξξ= 0 , i}

i = 1 , 2 , · · · ,τι,

It is clear that the model

j = 1 , 2 , ··· ,m

( Eqs.

(6)-(9))

is set to zero.

This model can be solved by

In order to assign s u c h w e i g h t s , Kleinberg proposed the following iterative a l g o r i t h m Step 1

will

sites s e C.

an

efficient iterative ( s c a l i n g ) p r o c e d u r e without resorting

Step 2

An E - c o m m e r c e web site consists of linked web p a g e s . Two important issues related to page linkage are web

'

2 9 ]

.

Initialize a ( s ) < — 1 , a i ( s ) < — 1 $

for all root

R e p e a t the following three operations until

c o n v e r g e n c e is o b t a i n e d : •

general n o n l i n e a r p r o g r a m m i n g m e t h o d s .

Web Link Design

[ 11

Procedure M R A

(9)

r e d u c e to L a n g h e i n r i c h ' s LP model w h e n the constant

2

a

:

y

γ

Specifically,

h u b weight is proportional to the sum of the authority •

m

T h e quality of a h u b is d e t e r m i n e d by the quality

of the authorities it points to.

where γ is a constant. Ref. [ 1 0 ]

•

U p d a t e the authority weight of e a c h a

( )

hub

)

site s by

;

weight

of

each

site

s

by

Tsinghua

764

•

Normalize

the

authority

weights

and

the

hub

weights. Thus,

we

Science

obtain

the

weights

of all

sites

C.

in

fact,

the coordinates of the normalized p r i n c i p a l eigen-vector while

normalized

the

resulting

principal

hub

weights

eigen-vector

are

WW

of

(see

T

pages are preferred by the surfers Sarukkai

proposed

a

[ 13

]

.

Markov

prediction a p p r o a c h as follows

[ 13 ]

chain-based

.

the tuple (Ξ,Α,λ) A

is

a

matrix

representing

transition

and A is the

initial probability distribution of the states in S.

to evaluate web page r e p u t a t i o n

[ 12 ]

.

They

case,

there

is one

state

for

each

If the vector S ( t)

interest.

of the

denotes

In this

pages

probabilities that a surfer will visit e a c h i at time

probability that a r a n d o m surfer looking for topic t will

t h e n , S(t)

as follows

[ 12 ]

The r a n d o m walk model can be formulated .

The

maximum

the surfer

principle

selects

an

c u r r e n t p a g e . Let N

t

outgoing

link

and

leaves

Intuitively,

the

probability at e a c h step that the surfer visits page ρ in a r a n d o m j u m p is d/N

t

if page ρ contains term t and it is

zero otherwise. Let q^p and 0(q)

denote a link from page q to

denote the n u m b e r of outgoing links

Intuitively, the probability that the

surfer

of the matrix A

cqj)

the

to

where C ( i)

Vk

visited page i, and C(i,j)

is the n u m b e r of times that

they have visited page j immediately following page i in the walk history. Given the

" link

history" ,

i.e.,

the

is [ ( 1 - d)/0

L(t

R

n

, where R

(q,t)

l

n

(q,t)

l

denotes the probability that the surfer visits page q for topic

t at step

of the

η

walk [12]

can

,···,

- 1 ) , the estimate of the vector of probabilities of S(t)

+ aE _ A

= αΕ _ Α γ

ι{ι

+ ··· +

2

γ)

2

L(t

2)

aE _ A

(12)

k

be

k

where E

:

previously

- k + 1)

b e i n g in e a c h state at time t i s :

topic t at step η - 1. T h u s , the probability of visiting c a l c u l a t e d by following iterative f o r m u l a

by

[13]

is the n u m b e r of times that surfers have

visits page ρ at step η via link q—>p after visiting page q (q)]

( denoted

£c(ä)

Vk

e n t e r e d s t a t e s , denoted by L ( ί - A;) ,L(t

for

applied

C(i)

and A ( i )

£c(i,*)

denote the total n u m b e r of pages

on the web that contain the term t.

page ρ

is

) can be estimated by following formulas

that contain the term t, and with probability ( 1 - d) ,

of page q.

likelihood

row and j - t h column

j u m p s to a page randomly selected from the set of pages

page ρ,

t,

=S(t-l)A.

estimate the e l e m e n t s of A and A . T h e e l e m e n t of i-th

Suppose at e a c h s t e p , with probability d,

he or she

of

the vector of

define the reputation of a page ρ on topic t to be the visit page p.

by

, where S c o r r e s p o n d s to the state

probabilities from one state to a n o t h e r ,

Rafiei and Mendelzon proposed a Markov c h a i n b a s e d

link

A discrete Markov c h a i n model can be defined space,

Page reputation evaluation

approach

761 - 7 7 1

:

this process is to use the walk history to predict which

the

Refs. [ 1 1 , 2 9 ] ) . 2. 2

2005, 10(SI)

link a " c u r r e n t p a g e " to those web pages preferred by

c o n v e r g e , and that the resulting authority weights are T

December

surfers b a s e d on their " w a l k h i s t o r y " . T h e first step in

K l e i n b e r g showed that p r o c e d u r e MRA does in

of W W

and Technology,

L{t

k)

stands for the A;-th row of identity m a t r i x , and

k

a- is a weight r e p r e s e n t i n g our trust in the information N,

+ (1

0(q)

of the j - t h previous s t e p .

'

if term t a p p e a r s on page ρ;

R"(p,t)

/r'( ,o

(i - < * ) £

(10)

0(q)

'

of visiting page ρ for topic

t, i. e., ir

(11)

= UmR (p,t) n

Ptt

Rafiei and Mendelzon proved that the probabilities

tt

pj

iterative formulas N > 0 and d>0 t

2. 3

exist (10)

and

a

very

important

issue

to

E-commerce.

great detail in the economics l i t e r a t u r e , the n a t u r e of

Define the reputation of page ρ on topic t as the pJ

is

Although the pricing m e t h o d s have b e e n d i s c u s s e d in

otherwise e q u i l i b r i u m probability 7T

Pricing for E-Commerce

Pricing

g

„

3

are

unique,

are c o n v e r g e n t ,

equilibrium i.e.,

the

as long

as

( s e e Ref. [ 1 2 ] ) .

A u t o m a t i c link d e s i g n

T h e p r o b l e m of automatic link design deals with how to

E-commerce

markets

is

very

different

from

that

of

traditional m a r k e t s .

E - c o m m e r c e may c h a n g e not only

industrial

structure

but

compare

the

m a r k e t s and

cost

also

price

differences

Ε-markets

from

structure.

between

both

buyer

They

traditional and

seller

[31]

perspectives As K e p h a r t et al. pointed o u t , we are entering the time of " i n f o r m a t i o n e c o n o m y " , bustling with billions of

autonomous

software

agents

that

exchange

information on goods and services with h u m a n s

and

other

the

agents

[ 3 2 ]

.

In

the

information

economy,

WANG Dingwei

et a l

Survey

:

of E-Commerce

Modeling

and Optimization

Strategies

765

p l e n i t u d e a n d low cost of u p - t o - d a t e information will

profit that is not desirable from t h e perspective of t h e

e n a b l e c o n s u m e r s ( b o t h h u m a n a n d a g e n t ) to b e better

seller.

informed about p r o d u c t s a n d p r i c e s

[ 3 2 ]

.

Thus,

it is

necessary to study n e w pricing m e t h o d s for t h e n e w information e n v i r o n m e n t . 3. 1

Sung a n d L e e proposed

A b e a n d K a m b a proposed a n automatic pricing method to maximize t h e total profit from t h e sales of a single [ 1 4 ]

.

Suppose that t h e volume of sales S(p)

the product is a function production

of its price ρ,

of

while t h e

( or p u r c h a s e ) cost of t h e offering

is a

c o n s t a n t , C. T h e n , t h e total sale profit of t h e offering is: P(p)

= S(p)p

1 5]

.

Now t h e goal of a n automatic pricing method is to ; that i s , to

competitor's prices, into o n e formula.

= a r g max P(p)

p*

(14)

p

pricing

a n d price elasticity of d e m a n d

T h e resulting price consists of three

c o m p o n e n t s : a cost-plus p r i c e , a competitor-referenced price, and a demand-driven price. Retailers usually u s e a m a r k u p rate to set prices so as to ( h o p e f u l l y )

g u a r a n t e e a profit.

Using m a r k u p

rate t h e price c a n b e d e t e r m i n e d as follows: Pl

=

where ί, ί = I ,2 , - - ,m,

+«„)

(16)

denotes t h e i t e m , s is a store

in t h e r e t a i l e r ' s c h a i n , ρ denotes t h e p r i c e , c t h e c o s t , a the markup rate,

find ρ * such that

a knowledge-based

It integrates t h e r e t a i l e r ' s m a r k u p r a t e ,

(13)

- C

find quickly a price ρ that maximizes P(p)

a n d t h e superscript a indicates

price calculated by t h e cost-plus m o d e l . The competitor-referenced price takes into a c c o u n t

and set t h e price accordingly. Since t h e a m o u n t sold is usually quite sensitive to the p r i c e , S(p)

Knowledge-based pricing method

method

Automatic pricing method

product

3. 2

is u n k n o w n prior to t h e initiation of its

sale in t h e on-line w e b m a r k e t .

Therefore,

t h e key

the competitors prices in conjunction with our s t o r e ' s " p r i c e i m a g e " of its competitors. It c a n b e expressed as:

problem is how to estimate p* from on-line sales d a t a , quickly.

P

ß ü

=f(Pi/jJ

=

l, ,'~,n)

P

= / ' ' 1 -ß

2

and

A b e a n d K a m b a proposed

a n iterative method to

(17)

>

approximate ρ *. Suppose that using step size A ( for

where j , j - 1 , 2 , · · · , η , denotes c o m p e t i t o r s , p . is t h e

example, A - I

suggested price of item i in light of competitor j ' s

1

, where / is t h e current t r i a l , i. e. ,

3

t/

iteration n u m b e r ) , we c o n d u c t on-line sales at both

price, ß

prices ρ + A a n d ρ - A for a certain fixed period of

price image of store s, a n d t h e superscript β indicates

t i m e , a n d b a s e d on t h e a m o u n t of sales obtained during

price calculated by t h e competitor-referenced m o d e l .

these p e r i o d s , S (ρ + A)

a n d S ( ρ - A ) , we c a n

calculate t h e profit f i g u r e s : P(p+A)

is t h e price image of competitor j m i n u s t h e

s j

The d e m a n d - d r i v e n price reflects t h e expected price sensitivity.

=

S(p+A)( +A)

=

S(p-A)(p-A).

T h e price

and P(P-A)

Ρ =P

A P(p + A)

+

A

p[ y

- P(p - A)

(15)

2T

where A is a n u p d a t e i n t e r v a l ,

set as a d e c r e a s i n g

function of the trial n u m b e r ( f o r e x a m p l e , A = cl~ ) in

;

and Τ is t h e duration of each trial. The s e q u e n c e

of prices given by E q . ( 15 )

= p,d +r„)

and

"

^(/)

Η

Any

Σ

2

_

will

„

Note that both of these conditions are m e t by setting A = c/~

1 / 3

and Α =

/~ . 13

A b e a n d K a m b a ' s automatic pricing method c a n get the best p r i c e ,

(is)

indicates

price

calculated

b u t it r e q u i r e s a n u m b e r of pricing

trials. T h e trials m a y , of c o u r s e , result in some loss of

by t h e d e m a n d - d r i v e n

model. Sung a n d L e e adopted a weighted linear

additive

model to integrate t h e three c o m p o n e n t prices d i s c u s s e d above as p

is

Γ15]

= ; . [ | > , ( 1 - β,)]

" I [/>, n - i °) (^ )Λ···Λμ ( u _ ) Λ Ε[μ η

u

u

Ι

λ

;

=

ΰ

max u ,-,u _ 0

21(3)

i n t r i n s i c motivations

.

to maximize the m e m b e r s h i p degree of

, ··· ,u

2

4 4 ]

*μΟ (χ) aggregation

Μ,

B h a t t a c h e r j e e A. A c c e p t a n c e of e - c o m m e r c e Systems,

* ···

D

T h e c a s e of e l e c t r o n i c

t h e n , the resultant decision is the fuzzy set D with the =μϋ(χ)

Gardner

o p p o r t u n i t i e s in e l e c t r o n i c c o m m e r c e . Decision

N

\μ 1

0

C°

N

C~ N

l

(x )]}.

x

N

G

N

Boyd Ε A , Ε-commerce. 1363 - 1 3 8 6 .

Bilegan

I C.

Management

Revenue Science,

management 2003,

and

49(10):

WANG Dingwei

[7]

et a l Survey

of E-Commerce

:

Modeling

Olson J R , Boyer Κ Κ. Factors influencing the utilization of Internet purchasing in small organizations. Journal

[8]

Operations

Management,

Kuechler

W

Jr.,

Supporting

and Optimization

[26]

:

Vaishnavi

V

K,

of

e-commerce relationships.

Kuechler

D.

[27]

Support

[28]

Systems,

:

Langheinrich

Μ,

Nakamura

A,

Abe N ,

Kamba

Computer

[29]

Tomlin

J

A n entropy

2000, 3 3 ( 1 - 6 )

approach

to u n i n t r u s i v e

161

:

In

Proc.

:

Computing

9 t h ACM SIAM

web

:

Symp.

on

:

reputations.

[32]

[33]

Sung Ν Η ,

L e e J Κ.

Knowledge

assisted

dynamic

large-scale

retailers.

Decision

Support

, 2000 , 28 347 - 3 6 3 .

Systems [16]

:

Support

Systems,

Kao Μ Y , Qi J , T a n L. O p t i m a l b i d d i n g

algorithms

a g a i n s t c h e a t i n g in m u l t i - o b j e c t e d a u c t i o n s . [18]

Penn

M,

[19]

and

[20]

:

Processing

auctions.

Decision

Support

Systems,

Wurman Ρ R , Walsh W E , Wellman Μ P.

24(1)

[23]

Support

[37]

[38]

[40]

[41]

Biyalogorsky referral Marketing

[25]

Weber

E,

Gerstner

Science, K,

Sun

:

K.

Modifying

Ε,

:

customer

[42]

Rothkopf

Μ

Teich J ,

Systems,

S,

Carter

Reverse buyer

Research

Β.

reward

Ρ L,

auctions—

and Part

supplier 2004,

E,

Η,

[43]

Fuzzy

stochastic

2000, 1 5 ( 8 ) 763 - 7 8 3 . :

A,

Harstad

1998, 4 4 ( 8 )

Science,

H,

R

combinatorial :

M.

auctions.

1131 - 1 1 4 7 .

W a l l e n i u s J.

Multiple-issue

Support

1 9 9 9 , 2 6 ( 1 ) 49 - 6 6 .

Systems,

:

P a t e l A , Blinov M , Bessonov M. R e f e r e n c e m o d e l a n d architecture Standards

for

information

availability.

1 9 9 9 , 2 1 273—285.

& Interfaces,

:

H a n d s J , Bessonov M , Blinov M , Patel A , Smith R. An and

extensible

architecture

for

electronic

2000, 2 9 : 305 — 321.

A l m e i d a V A F , Meira W Jr. , R i b e i r o V F , Ziviani N. analysis

of

Computer

brokers Networks,

in

the

electronic

1999, 3 1 ( 6 — 11) :

Gupta A , Su Β C , Walter Z. Risk profile and consumer shopping behavior in electronic a n d traditional c h a n n e l s .

82-95.

:

Pekec

manageable

Bell

402-417.

:

1 0 7 9 - 1090.

Customer programs.

, 1 9 8 2 , 13

Wallenius

marketplace.

Decision

dynamic

p r o g r a m m i n g for m a r k e t i n g d e c i s i o n s u p p o r t . Int. J. of Intelligent

the

Transportation

of Economics

Efficiency

776-786.

Libai

Optimal

2001,20(1) Z.

from

Beall

Κ J.

brokerage. Decision Support Systems,

1999, 4 5 ( 4 ) 533 — 543.

1998, 4 4 ( 6 )

management:

L,

R a s s e n t i S J , Smith V L , Bulfin R L. A c o m b i n a t o r i a l

inclusive

Keeney R L. The value of internet commerce to the

Science,

2004,

Science,

a u c t i o n a n d m a r k e t a l g o r i t h m s for t h e world wide w e b .

2000,

Evaluation,

223 - 2 3 9 .

Management

with

Science,

J u m p b i d d i n g s t r a t e g i e s in

Petersen

theory

Management [39]

1998,

Systems,

Performance

Srinivasan

Elserier

Management

Kaufmann

Τ Ε,

Computer

S,

Aumann

:

of G a m e Theory

229-254.

:

Journal

e x p e c t a t i o n s of p r i c e d e c r e a s e s for a d u r a b l e p r o d u c t . [24]

Carter C R ,

functional

Balachander

2000,

1407 - 1 4 1 9 .

:

A. B u s i n e s s - o r i e n t e d r e s o u r c e m a n a g e m e n t p o l i c i e s for

Science,

Dynamic

Networks,

New Y o r k :

auctions.

Decision

customer. Management

Computer

Hart S, eds. Handbook

e-commerce :

1287 - 1 3 0 9 .

:

W i l s o n R. Strategic a n a l y s i s of a u c t i o n s . I n

40(2)

17 - 2 7 .

servers.

directions.

731 - 7 5 2 .

:

Grounded

Flexible

Menasce D A , Almeida V A F , Fonseca R , Mendes Μ

42 [22]

:

Research

a n d future

2003, 49(10)

Science,

Computationally

Decision

considerations:

practices,

a u c t i o n m e c h a n i s m for airport time slot a l l o c a t i o n .

d o u b l e a u c t i o n s for e l e c t r o n i c c o m m e r c e : Theory a n d

[21]

inventory

K e p h a r t J 0 , H a n s o n J E , G r e e n w a l d A R.

Hendrick

165 - 1 7 6 .

implementation.

eBay

:

2001,

Management,

E a s l e y R F , Tenorio R.

A p p r o a c h e s to w i n n e r d e t e r m i n a t i o n in

combinatorial 2000, 2 8

Information

of

[ 35 ]

29-34.

:

387 - 4 0 1 .

:

and e-commerce

Journal

of

perspective. multi-object

for

1 9 9 2 : 227 - 2 7 9 .

J.

Constrained

b-matching.

2000, 7 5 ( 1 )

S a n d h o l m Τ.

M.

approach

E b a y w e b site. h t t p : / / w w w . e b a y . c o m / .

:

Tennenholtz

auctions Letters,

SIAM

:

a n d t h e TKC effect.

[34]

1 9 9 8 , 2 8 ( 3 ) 955 - 9 6 9 .

on Computing,

The stochastic

Economic Application.

[36]

:

ratings.

current

50(10)

Decision

S.

Reputation

overview,

in

markets.

S S.

presence

Internet

2 0 0 0 , 2 8 ( 1 ) 35 - 4 7 . [17]

Entropy Boston

279-295.

:

Sairamesh J , Kephart J 0 . Price dynamics and quality information

Tsao Η S J.

E l m a g h r a b y W , K e s k i n o c a k P . D y n a m i c p r i c i n g in t h e

R J,

2000, 3 3 ( 1 —6) : 755 — 788.

Networks,

pricing

for

and Extensions.

2000, 3 3 ( l - 6 )

Networks,

33(1 - 6 )

2 0 0 0 , 3 3 ( 1 —6) :

Abe N , Kamba T. A web marketing system with automatic pricing. Computer

J R,

p r i c i n g by software agent.

S a r u k k a i R R. Link p r e d i c t i o n a n d p a t h a n a l y s i s u s i n g Networks,

Moran

Management

Computer

823 - 8 3 5 .

377 - 3 8 6 .

[15]

[31]

W h a t is this page known

page

Markov c h a i n s . Computer [14]

Programming

Rajasekera

R,

Standifird

27(2)

668 - 6 7 7 .

2000, 3 3 ( 1 - 6 )

Networks,

Lempel

negative

Rafiei D , M e n d e l z o n A 0 . for?

Linear

models.

a u c t i o n s a n d t h e a s y m m e t r i c a l i m p a c t of positive a n d

Networks,

-IIA.

D i s c r e t e A l g o r i t h m s , 1998

[13]

[30]

K l e i n b e r g J Μ. A u t h o r i t a t i v e s o u r c e s in a h y p e r l i n k e d environment.

[12]

Fang S C ,

Computer

A.

t a r g e t e d a d v e r t i s i n g on t h e w e b . Computer [11]

G B.

problem

2 0 0 0 , 2 8 : 2 9 3 —304.

link-structure analysis ( S A L S A )

1999, 3 1 ( 1 1 — 1 6 ) :

Networks,

1259 - 1272. [10]

Dantzig

satisfaction

Systems,

Kluwer A c a d e m i c P u b l i s h e r s , 1 9 9 7 .

T,

Koseki Y. U n i n t r u s i v e customization t e c h n i q u e s for w e b advertising.

Support

Optimization and Mathematical Programming.

2 0 0 1 , 3 1 ( 3 ) 363 - 3 7 7 . [9]

Decision

P r i n c e t o n : P r i n c e t o n University P r e s s , 1 9 6 3 .

business-to-business

Decision

J u n g J J , Jo G S. B r o k e r a g e b e t w e e n b u y e r a n d seller agents using constraint

of

2003 , 2 1 ( 2 ) 225 — 245.

optimization

111

Strategies

[44]

Support Systems,

2004, 3 8 ( 3 ) : 347 — 367.

Bellman R E , Zadeh L A. Decision-making in a fuzzy environment. Management

Science,

1970, 1 7 ( 1 )

:

141 — 164.