Description
Aiming at the problem of reverse auction which involves
one buyer and multiple sellers in procurement market,
this paper studies about online reverse auction via internet
during which different sellers arrive at different time and
bid, and the buyer makes decision whether to purchase
after receiving each bid. And then, the random pricing
strategy of online reverse auction is researched. After the
compare with single pricing strategy, it shows that the
random pricing strategy using the market information to
make a procurement price can avoid the waste of cost and
incomplete procurement, and a case test is provided in
the end.
71
Copyright © Canadian Research & Development Center of Sciences and Cultures
ISSN 1923-841X [Print]
ISSN 1923-8428 [Online]
www.cscanada.net
www.cscanada.org
International Business and Management
Vol. 6, No. 2, 2013, pp. 71-76
DOI:10.3968/j.ibm.1923842820130602.1180
Research on Pricing Strategy of Online Reverse Auction Based on Complete
Information
LIU Zhongcheng
[a],*
; LI Hongyu
[a]
[a]
Finance & Economics Department, Shandong University of Science &
Technology, Jinan City, Shandong Province, China.
*Corresponding author.
Supported by National Natural Science Foundation Program (China) of
2013, NO.71240003.
Received 17 March 2013; accepted 12 May 2013
Abstract
Aiming at the problem of reverse auction which involves
one buyer and multiple sellers in procurement market,
this paper studies about online reverse auction via internet
during which different sellers arrive at different time and
bid, and the buyer makes decision whether to purchase
after receiving each bid. And then, the random pricing
strategy of online reverse auction is researched. After the
compare with single pricing strategy, it shows that the
random pricing strategy using the market information to
make a procurement price can avoid the waste of cost and
incomplete procurement, and a case test is provided in
the end.
Key words:
Online reverse auction; Random pricing
strategy; Competitive analysis
LIU Zhongcheng, LI Hongyu (2013). Research on Pricing Strategy of
Online Reverse Auction Based on Complete Information. International
Business and Management, 6(2), 71-76. Available from:http://www.
cscanada.net/index.php/ibm/article/view/j.ibm.1923842820130602.1180
DOI:http://dx.doi.org/10.3968/j.ibm.1923842820130602.1180
INTRODUCTION
How to use the new procurement technology and
operational mode to transform and manage the supply
chain and procurement processes, then reduce the
procurement costs and improve efficiency is becoming
more and more concerned and paid attention. The
FreeMarkets Company which was established in 1995 by
Glen Meakem is the earliest one who used online reverse
auction, which is innovative for traditional procurement
mode. Reverse auction is one kind of procurement which
makes a decision after the end of bidding. With the
intensification of the time effect on the procurement cost,
reverse auction participants are not willing to wait for
the results for a long time. Waiting means that the time
cost increases, as well as loss new purchases and sales
opportunities, so online reverse auction was proposed.
Online reverse auction is that sellers arrive at different
time and bid, the decision whether to buy the bidders’
goods needs to be made immediately after the buyer
receives each bid. Reverse auction in application process
gradually gets into transparent equalization. Buyers make
public supplier’s information and bidding to change the
incomplete information into complete information. The
supplier’s competition is more intense under the complete
information, which will bring lower prices, higher quality
suppliers, and reduce the procurement costs. In practice,
the online reverse auction becomes prevalent in Europe
and the U.S. since 2000, which has a reverse bid process
via internet. Compared with traditional negotiation, this
kind of auction can save costs up to 11%-12% for buyers.
In this paper, we will mainly study the random pricing
strategy of online reverse auction, with comparative
analysis to the single pricing strategy.
1. LITERATURE REVIEW
With the development of E-business, it is common to
buy and sell goods via internet. The researches on online
reverse auctions began from auction research in the first
deriving from McAfee, R. P. and J. McMillan’s (1986)
agent competitive strategy analysis and government
procurement mathematical model in the commissioned
agency theory. Subsequently, Dasgupta. S and D. F.
Spulber (1989) analyze the reverse auction strategy
problem of the procurement management. CHEN (1999)
Research on Pricing Strategy of Online Reverse
Auction Based on Complete Information
72
Copyright © Canadian Research & Development Center of Sciences and Cultures
summarizes the quantities of the reverse auction and
strategic equilibrium of price auction on the basis of the
aforementioned studies, and comparatively analyzes
the efficiency of the different auction mechanisms. The
research of online reverse auction model and algorithm
mostly focus on the online algorithms and competitive
analysis methods growing up in computer science.
Ron Lavi and Noam Nisan (2000) study the online
auctions that after bidders arriving at different time the
auction mechanism must make decision immediately
after receipt of each bid, they also take advantage of
the competition analysis in the worst case to identify
the auctioneer optimal supply curve, based on which
the online auction mechanism is very competitive. Alan
Smart and Alan Harrison (2003) study the role in buyer-
supplier relationships of online reverse auctions. Avrim
Blum, Tuomas Sandholm and Martin Zinkevich (2006)
put online learning applications in digital goods online
auction, get a new digital goods auction model and a
constant competition ratio on the optimal auction revenue
under fixed price, and apply the technology applications
in the design of online auction mechanism.
The goods purchased through reverse auction are
generally standardized goods, of which the true valuation
of the supplier is generally converge, so the majority of
the bids usually fluctuate within a relatively small range.
Buyers provide complete information to suppliers, and
then a phenomenon appear that all bids of suppliers are
concentrated in a range because of the fierce competition
to get the object with smaller advantage. Because buyers
can not understand this small range, their valuations
of the commodity usually belong to a large range, in
which a single pricing is likely to be too high to cause
waste of cost, or be set so low that reverse auction
comes to nothing, so that the procurement tasks can not
be completed. With the help of researches on online
algorithms and competitive analysis methods by many
other scholars (XU, XU, & LU, 2005; DING & XU,
2007; XIN, XU, & YI, 2007; XU & XU; 2008), this
paper studies the random pricing strategy of online
reverse auction in which all bids in competition are more
concentrated, and comparative analysis with a single
pricing proves that when a random pricing strategy of
online reverse auction takes advantage of the market price
information, the disadvantages of single pricing caused
such as the waste of cost or unable to complete the task of
procurement can be overcome.
2. PROBLEM DESCRIPTION
Assumi ng buyers want t o buy a cert ai n t ype of
standardized non-market exclusive products, and select a
purchase items from a number of suppliers, and suppliers
can meet the number of purchasing items of buyers.
According to the complete information provided by the
buyer, in each stage of the bidding process of online
reverse auction, suppliers give different bids in different
time, and change the bids in accordance with the changes
of other suppliers. Suppliers bid on the one hand are based
on their own reservation price, on the other hand are
based on the bids of other suppliers at any time to adjust,
and maximize their expected utility with lower prices.
When the expected utility falls to the minimum margin,
the price will no longer be reduced. According to the pre-
determined procurement strategy, the buyer can analysis
the bids of suppliers, determine the most suitable purchase
price, and close a deal with a supplier. Overall, in this
process, the buyer always expects that the price is more
and more lower to achieve the maximum expected utility
by reducing procurement costs.
3. MODELING AND ANALYSIS
A buyer usually determines his own pricing strategy
independently, but as a seller, the supplier can refer to
the bids of other multiple suppliers to determine his own
bidding strategy, whose goal of participating in the auction
is to maximize expected utility (DING & XU, 2007). In
general, it should be set up in advance when the bid of
online reverse auction begins. In this article, it is assumed
that the buyer can end the auction at any time based on the
price situation during the online reverse auction process,
also he can end the auction if his bid price is higher
enough for the supplier to win the bidding, or end the
auction because one buyer of urgent demand for the goods
is willing to purchase at the bid price of the time.
Given an online reverse auction A, in which there are
n suppliers. Assume that the i -th bidder’s real valuation
of goods is v
i
(i = 1,2...,n), his quoted price is b
i
, and
the buyer pay the i-th bidder a price of p
i
. If pi ? b
i
,
transaction maybe occurred, then the i -th bidder’s utility
is U
i
= p
i
- v
i
. If p
i
< b
i
, transaction will not occur, the
bidder’s utility is 0.
Now let’s consider about an online reverse auction
problem with the objective of minimum cost. For any bid
sequence L, C
A
(L) is taken to be the cost that the online
reverse auction
A
makes an instant decision of bidding
sequence L, and C'
A
(L) indicates the decision-making cost
if the bidding sequence
L
is known in advance. If there is a
constant r independent of the bidding sequence L, which
meets C
A
(L) ? r·C'
A
(L), then the competitive ratio is ?,
which shows the better between the optimal procurement
costs in the two cases. This analysis process of the online
algorithms performance is called competitive analysis.
Therefore, before the analysis of random pricing
strategy of online reverse auction, it needs firstly to study
the single pricing condition, and thus to analyze the
competitive performance of random pricing strategy.
3.1 Optimal Single Pricing
If the buyer has determined a purchase price before online
LIU Zhongcheng; LI Hongyu (2013).
International Business and Management, 6(2), 71-76
73
Copyright © Canadian Research & Development Center of Sciences and Cultures
reverse auction, the first supplier whose bid price is less
than or equal to this purchase price will close a deal with
the buyer. This online reverse auction strategy is called
online single pricing strategy (abbreviated as the online
SP strategy).
If the buyer has an estimated range [B
1
, B
2
] of the
commodity price, then assumed that the single price is
set to B
3
, if the price is set too low, there is probably not
one supplier can win the bidding all the way, the buyer
has to purchase at the last-minute bid price because of the
procurement time limit, and if B
3
is set too high, the online
reverse auction may soon close a deal, but can not achieve
the goal of saving costs. From the competitive analysis
point of view:
If the bid price B
1
doesn’t appear in procurement time,
the cost ratio of online and offline is B
3
/B
1
.
If the bid price below the single fixed price doesn’t
appear all the way during the procurement time, and the
final bid price comes to the ceiling, then the cost ratio of
online and offline is B
2
/B
3
.
So given the single fixed price B
3
, the competition ratio
of this online reverse auction is r
SP
= sup{B
3
/B
1
, B
2
/B
3
},
and the optimal B
3
should be the solution of the equation
B
3
/B
1
=B
2
/B
3
because the price makes the r
sp
minimum
value, then
2 1 3
B B B ? = , so r
SP 1 2
/ B B r
SP
= .
3.2 Random Pricing Strategy and Competitive
Analysis
3.2.1 Random Pricing Strategy
With complete information, if the bid prices of suppliers
are more concentrated, the buyer needs to analyze all
the bid prices of small difference. Then, we will apply
the random pricing strategy of online reverse auction
(abbreviated online reverse auction RP strategy) to
analyze the supplier’s bids in competition.
Let the estimated range [B
1
, B
2
] of the buyer about
the commodity price be separated into m subintervals,
m ? ? ? , , 2 , 1 ? , whe r e ) , (
1 i i
c c i
?
= ? , i = 1, 2. . . , m.
Assuming the selected number of bid prices up to n (that
is, up to the n -th bid auction will end), now let the right
end point c
1
of the first subinterval (c
0
, c
1
) be the minimum
reserve price, and assuming the price making sequence is
p
1
, p
2
,..., p
n
that is to make the price p
i
for the commodity
of the i -th bidder, then the random pricing strategy of
online reverse auction is as follows:
? The probability of price p1 made for the
commodity of the first supplier meets Pr (p1 =
c1) = 1, if the first bid price b1 ? c1, the purchase
price is c
1
. Otherwise, the transaction will be
unsuccessful, and then look at the second bid.
? Assuming b
2
falls into the subinterval ) 1 ( ? ? k k ,
then the price p
2
made for the commodity of the
second supplier satisfies
n
n
c p P
r
1
) (
1 2
?
= = , P
r
(p
2
= c
k
) = 1/n, and if the second bid price b
2
? c
1
, then
the transaction will be successful, so the probability
of price c
1
in the successful deal is
n
n 1 ?
, as the
probability of price c
k
in the deal is 1/n. If c
1
c
k
, the transaction can not be
reached, then see the third bid.
? Usually, the probability of the price p
i
made for
the commodity of the i -th supplier satisfies:
) ) (
2
1
n
N n
c p P
m
j
j
i r
?
=
?
= =
,
) ) (
n
N
c p P
j
j i r
= =
, j=2,3,...m (1)
where N
j
represents the number of bid prices falling
into the j -th subinterval of the front i -1 suppliers.
3.2.2 Competitive Analysis
If bid prices of all suppliers concentrate in a subinterval
with a length of ? within the valuation interval [B
1
, B
2
]
of the buyer, then split [B
1
, B
2
] to several small intervals
with each length of ?/k, and suppose that there are nbid
prices concentrating in a small area [?, ?+?], then all bid
prices will fall into at most k+1 segmented subintervals.
According to the random pricing strategy of online reverse
auction, the worst case is that the transaction is concluded
at the price of ?+?+?/k with the probability of
n
n 1 ?
, and
no deal is closed with the probability of 1/n, then the buyer
has to purchase at the price ceiling B
2
. So the expected cost
( 1)( / )
( )
RP
n k
E C
n n
? ? ? ? ? + ? + +
? + , while the offline
optimal cost is
?
, then the ratio of expected cost ( )
RP
E C
and offline optimal cost ? is:
( 1)( / )
( )
RP
a n a k
E C
n n
a a
? ? ? + ? + +
+
=
1 1
1 1
1
a n n
a n ka B n kB
? ? ? ? + ? ?
? + ? ? + + ?
(2)
When the interval is split up into much more
smal l er subi nt er val s, namel y, i f ? ? k , t hen:
1 1 1
( ) 1
lim lim(1 ) 1
RP
k k
E C n
B n kB B
? ? ?
? ?? ??
?
= + + ? = +
, a n d
( )
sup
RP
RP
E C
r
?
= , that is, when the valuation range is
split up infinitely, r
RP
approximates to
1
1
B
?
+
.
If ? ? k , then:
When ?=0, rRP?1..
When ?=B
2
-B
1,
2
1
RP
B
r
B
?
.
Research on Pricing Strategy of Online Reverse
Auction Based on Complete Information
74
Copyright © Canadian Research & Development Center of Sciences and Cultures
When
1
1
B
?
+
<
2 1
/ B B
, i.e. when
1 2 1
[0, ] B B B ? ? ?
, r
RP
< r
SP
, now the competitive performance of random pricing
strategy is better than that of optimal single pricing strategy.
Therefore, the smaller the ? is, the smaller r
RP
is too.
That is, the more concentrated the bid prices are, the
closer the expected cost of random pricing strategy is to
the offline optimal cost. So, even if the buyer does not
know the fluctuant cost range of suppliers, he can also
adjust gradually the probability of bid price making by
random pricing strategy, so that the expected cost of the
online close offline optimal cost.
4. CASE TEST
4.1 Case Description
An assembly production enterprise wants to procure
a number of parts from multiple suppliers. Because
assembled commodities parts has the characteristics such
as purchasing large quantities and high standardization,
the enterprise decides to use multi-stage online reverse
auction by using bulk procurement of multi-channel.
During online reverse auction, the buyer will firstly audit
and evaluate the suppliers who applied online to determine
their participation eligibility, then get price information of
each supplier and eliminate weaker competitive suppliers
to determine those outright ones. Finally, the buyer can
distribute the order form to complete the procurement for
the minimum purchase cost.
The detailed procurement process of this enterprise is
described as follows:
(1) The number attributes of supplier
Because of bulk purchasing, the buyer needs to
divide an order into multi orders to respectively procure.
According to the number attributes of the procurement
goods and each batch procurement number range, in this
case, 3 suppliers are needed, and at most one supplier
is selected in each procurement stage, so at least there
are 3 stages of the bidding. For the simplicity of test,
assuming that one supplier is chosen in each stage and the
procurement needs 3 stages to be finished.
(2) Assuming that that buyers’ understanding of this
product price is limited to a certain price range [48, 72],
the initial price is set at b
0
=60, because the supplier’s bid
would be more concentrated in the less bid interval, the
buyer will put every 10 bids into a stage.
To easily establish the model, we assume that
the bidding sequence number is the serial number of
suppliers, which is shown in Table 1, 2, 3.
Table 1
Price List 1 of Online Reverse Auction
Series number 1 2 3 4 5 6 7 8 9 10
Competitive tender 63 64 65 63 61 62 61 60 62 60
Supplier 1 2 3 4 5 6 7 8 9 10
Table 2
Price List 2 of Online Reverse Auction
Series number 1 2 3 4 5 6 7 8 9 10
Competitive tender 56 59 58 58 57 55 56 54 55 54
Supplier 11 12 13 14 15 16 17 18 19 20
Table 3
Price List 3 of Online Reverse Auction
Series number 1 2 3 4 5 6 7 8 9 10
Competitive tender 53 53 54 52 53 54 52 51 52 52
Supplier 21 22 23 24 25 26 27 28 29 30
4.2 Pricing
As we can see the bidding sequence from Table 1, 2, 3, in
this transaction period if we consider the optimal offline
purchasing transaction price that it is clearly 59. The optimal
single price is
1 2
48 72 58.8 B B ? = × = , and the ratios
of the optimal single pricing strategy to the optimal offline
purchases is
2 1
/ 1.22
SP
r B B = = . Obviously, 59
?
58.8
×
1.22, that is to say that applying single pricing strategy
to procure is better than offline purchases. But according
to single pricing strategy to procure, apparently it can not
quickly make deal. Because the previous bidding prices are
not lower than 59, the buyer may lose the opportunity after
waiting for a long time. Even the procurement can not be
completed during the limited time of online reverse auction.
(1) Using the RP strategy of online reverse auction to
price the first phase bids, the analysis is as follows:
Divide [48, 72] into 8 small pieces [48, 51], [51, 54],
[54, 57], [57, 60], [60, 63], [63, 66],[66, 69], [69, 72], the
pricing and probability sequence is as follows:
1) P
r
(p
1
=51)=1, and b
1
=63, So the transaction can not
be reached.
2) P
r
(P
2
=51)=9/10, P
r
(p
2
=63)=1/10, and b
2
=64, So
LIU Zhongcheng; LI Hongyu (2013).
International Business and Management, 6(2), 71-76
75
Copyright © Canadian Research & Development Center of Sciences and Cultures
the transaction can not be reached.
3 ) P
r
( P
3
= 5 1 ) = 8 / 1 0 , P
r
( p
3
= 6 3 ) = 1 / 1 0 ,
P
r
(p
3
=66)=1/10, and b
3
=65, So the probability of the
deal is 1/10, the transaction value is 66.
4 ) P
r
( p
4
= 5 1 ) = 7 / 1 0 , P
r
( p
4
= 6 3 ) = 1 / 1 0 , P
r
(p
4
=66)=2/10, and b
4
=63, So the probability of the deal
is 1/10, the transaction value is 63.
5) P
r
(p
5
=51)=6/10,P
r
(p
5
=63)=2/10,P
r
(p
5
=60)=2/10,
and b
5
=61 , So the probability of the deal is 2/10, the
transaction value is 63.
6) P
r
(p
6
=51)=5/10,P
r
(p
6
=63)=3/10,P
r
(p
6
=66)=2/10,
and b
6
=62, So the probability of the deal is 3/15, the
transaction value is 63.
7) P
r
(p
7
=51)=4/10,P
r
(p
7
=63)=4/10,P
r
(p7=66)=2/10,
and b
7
=61, So the probability of the deal is 4/10, the
transaction value is 63.
8) P
r
(p
8
=51)=3/10,P
r
(p
8
=63)=5/10,P
r
(p
8
=66)=2/10,
and b
8
=60, So the probability of the deal is 5/10, the
transaction value is 63.
9) P
r
(p
9
=51)=2/10 ,P
r
(p
9
=63)=6/10,P
r
(p
9
=60)=2/10,
and b
9
=62, So the probability of the deal is 6/10, the
transaction value is 63.
10) P
r
( p
10
=51) =1/ 10 , P
r
( p
1 0
= 6 3 ) = 7 / 1 0 , P
r
(p
10
=66)=2/10 , and b
10
=60, So the probability of the
deal is 9/10, the probability of the transaction value which
equals 63 is 7/10, the probability of the transaction value
which equals 66 is 2/10.
The ratio of the expected cost in this procurement
stage to the optimal offline cost is competitive ratio:
( )
1
sup 1.06
rp
RP
E C
a n ka k
r
a na n ka
? ? ? + ? + +
= = + ? =
(2) Using the RP strategy of online reverse auction to
price the second phase bids, the analysis is as follows:
Divide [48, 72] into 8 small pieces [48, 51], [51, 54],
[54, 57], [57, 60], [60, 63], [63, 66], [66, 69], [69, 72] ,
the pricing and probability sequence is as follows:
1) P
r
(p
1
=51)=1, and b
1
=56, So the transaction can not
be reached.
2) P
r
(p
2
=51)=9/10, P
r
(p
2
=57)=1/10, and b
2
=59, So
the transaction can not be reached.
3) P
r
(p
3
=51)=8/10, P
r
(p
3
=57)=1/10, P
r
(p
3
=60)=1/10,
and b
3
=58, So the probability of the deal is 1/10, the
transaction value is 60.
4) P
r
(p
4
=51)=7/10, P
r
(p
4
=57)=1/10, P
r
(p
4
=60)=2/10,
and b
4
=58, So the probability of the deal is 2/10, the
transaction value is 60.
5) P
r
(p
5
=51)=6/10,P
r
(p
5
=57)=2/10, P
r
(p5=60)=2/10,
and b
5
=56, So the probability of the deal is 1/10, the
transaction value is 57.
6) P
r
(p
6
=51)=5/10, P
r
(p
6
=57)=3/10, P
r
(p
6
=60)=2/10,
and b
6
=55, So the probability of the deal is 2/15, the
transaction value is 57.
7) P
r
(p
7
=51)=4/10, P
r
(p
6
=57)=3/10, P
r
(p
6
=60)=3/10,
and b
7
=56, So the probability of the deal is 3/10, the
transaction value is 57.
8) P
r
(p
8
=51)=3/10, P
r
(p
8
=57)=4/10, P
r
(p
8
=60)=3/10,
and b
8
=54, So the probability of the deal is 4/10, the
transaction value is 57.
9) P
r
(p
9
=51)=2/10, P
r
(p
9
=57)=5/10, P
r
(p
9
=60)=3/10,
and b
9
=55, So the probability of the deal is 5/10, the
transaction value is 57.
1 0 ) P
r
( p
1 0
= 5 1 ) = 1 / 1 0 , P
r
( p
1 0
= 5 7 ) = 6 / 1 0 ,
P
r
(p
10
=60)=3/10, and b
10
=54, So the probability of the
deal is 9/10, the probability of the transaction value which
equals 57 is 6/10, the probability of the transaction value
which equals 60 is 3/10.
The ratio of the expected cost in this procurement
stage to the optimal offline cost is competitive ratio:
( )
1
sup 1.06
rp
RP
E C
a n ka k
r
a na n ka
? ? ? + ? + +
= = + ? =
(3) Using the RP strategy of online reverse auction to
price the third phase bids, the analysis is as follows:
Divide [48, 72] into 8 small pieces [48, 51], [51, 54],
[54, 57], [57, 60], [60, 63], [63, 66], [66, 69], [69, 72] ,
the pricing and probability sequence is as follows:
1) P
r
(p
1
=51)=1, and b
1
=53, So the transaction can not
be reached.
2) P
r
(p
2
=51)=9/10, P
r
(p
2
=54)=1/10, and b
2
=53, So the
probability of the deal is 1/10, the transaction value is 54.
3) P
r
(p
3
=51)=8/10, P
r
(p
3
=54)=2/10, and b
3
=54, So the
probability of the deal is 2/10, the transaction value is 54.
4) P
r
(p
4
=54)=7/10, P
r
(p
4
=54)=3/10, and b
4
=52, So the
probability of the deal is 3/10, the transaction value is 54.
5) P
r
(p
5
=51)=6/10, P
r
(p
5
=54), and , So the probability
of the deal is 4/10, the transaction value is 54.
6) P
r
(p
6
=51)=5/10, P
r
(p
6
=54)=5/10, and b
6
=54, So the
probability of the deal is 5/15, the transaction value is 54.
7) P
r
(p
7
=51)=4/10, P
r
(p
7
)=54=6/10, and b
7
=52, So the
probability of the deal is 6/10, the transaction value is 54.
8) P
r
(p
8
=51)=3/10, P
r
(p
8
=54)=7/10, and b
8
=51, So the
probability of the deal is 7/10, the transaction value is 54.
9) P
r
(p
9
=51)=2/10, P
r
(p
9
=54)=8/10, and b
9
=52, So the
probability of the deal is 8/10, the transaction value is 54.
10) P
r
(p
10
=51)=1/10, P
r
(p
10
=54)=9/10, and b
10
=52, So
the probability of the deal is 9/10, the transaction value is 54.
The ratio of the expected cost in this procurement
stage to the optimal offline cost is competitive ratio:
( )
1
sup 1.07
rp
RP
E C
a n ka k
r
a na n ka
? ? ? + ? + +
= = + ? =
Obviously, it is better than the cost of offline
purchasing by using online reverse auction RP strategy.
Although using the RP strategy can not make a deal
soon, it is able to reflect the supplier's bidding information
from the prices, and the probability of which the transaction
price closes to the bidding prices of most suppliers is the
largest. The buyer can conduct the transaction price and
decide whether or not to choose the supplier.
From the bidding information of the three stages,
according to the principle of highest probability, the price
Research on Pricing Strategy of Online Reverse
Auction Based on Complete Information
76
Copyright © Canadian Research & Development Center of Sciences and Cultures
in the first stage is 63, and the second phase of the price
is set at 57, and the price of the third stage is 54. At this
time, due to the supplier's bids are intensive, it may appear
that several suppliers bid the same price, so the buyer can
make the decision based on the evaluation of other aspects
of the suppliers.
CONCLUSION
Aiming at the procurement problem that using online
reverse auction to select a supplier, this paper studies
the optimal single pricing strategy and random pricing
strategy, using which the price made for the supplier
is independent of has bid price. The latter can take
advantage of market price information, correct the defects
caused by static single pricing, besides, it has many other
advantages such as full market information, low cost of
transaction management, and excellent operability, etc.
However, this strategy is applicable to the online reverse
auction for standard commodities with bid prices more
concentrated. It still needs further studies on the problem
of more dispersive bid prices and big competitive ratio.
REFERENCES
Avrim Blum, Tuomas Sandholm, Martin Zinkevich (2006).
Online Algorithms for Market Clearing. Journal of The
ACM - JACM , 53(5), 845-879.
Chen F. R. (1999). Market Segmentation, Advanced Demand
Information and Supply Chain Performance. Columbia
University, Columbia Business School.
Dasgupta S., D. F. Spulber (1989). Managing Procurement
Auctions. Information Economics and Policy, 4, 5-29.
Ding L. L., & Xu Y. F. (2007). The Problem of Busy Line
Preferential Card and Competition Assay Based on
Variable Price. Planning and Management, 10, 23-28.
LAN Smart, Alan Harrison (2003). Online Reverse Auctions and
Their Role in Buyer-Supplier Relationships. Journal of
Purchasing & Supply Management, 9, 257-268.
McAfee, R. P., J. McMillan (1986). Incentives in Government
Contracting. University of Toronto Press.
Ron Lavi, Noam Nisan (2000). Competitive Analysis of Incentive
Compatible On-Line Auctions. EC 2000: 2nd ACM
Conference on Electronic Commerce, 233-241.
Xin C. L., Xu Y. F., Yi F. L. (2007). The Problem of Busy Line
Particular Preferential Card and Competition Assay Based
on Expectant. Journal of Systems Engineering, 4, 14-17.
Xu J. H., Xu W. J. (2008). The Pricing Strategy and Competitive
Assay in Reverse Auctions. Systems Engineering Theory
and practice, 5, 47-54.
Xu W. J., Xu Y. F., & Lu Z. J. (2005). Online Decision Problem
and Competitive Assay Method. Systems Engineering, 5,
106-110.
doc_297914958.pdf
Aiming at the problem of reverse auction which involves
one buyer and multiple sellers in procurement market,
this paper studies about online reverse auction via internet
during which different sellers arrive at different time and
bid, and the buyer makes decision whether to purchase
after receiving each bid. And then, the random pricing
strategy of online reverse auction is researched. After the
compare with single pricing strategy, it shows that the
random pricing strategy using the market information to
make a procurement price can avoid the waste of cost and
incomplete procurement, and a case test is provided in
the end.
71
Copyright © Canadian Research & Development Center of Sciences and Cultures
ISSN 1923-841X [Print]
ISSN 1923-8428 [Online]
www.cscanada.net
www.cscanada.org
International Business and Management
Vol. 6, No. 2, 2013, pp. 71-76
DOI:10.3968/j.ibm.1923842820130602.1180
Research on Pricing Strategy of Online Reverse Auction Based on Complete
Information
LIU Zhongcheng
[a],*
; LI Hongyu
[a]
[a]
Finance & Economics Department, Shandong University of Science &
Technology, Jinan City, Shandong Province, China.
*Corresponding author.
Supported by National Natural Science Foundation Program (China) of
2013, NO.71240003.
Received 17 March 2013; accepted 12 May 2013
Abstract
Aiming at the problem of reverse auction which involves
one buyer and multiple sellers in procurement market,
this paper studies about online reverse auction via internet
during which different sellers arrive at different time and
bid, and the buyer makes decision whether to purchase
after receiving each bid. And then, the random pricing
strategy of online reverse auction is researched. After the
compare with single pricing strategy, it shows that the
random pricing strategy using the market information to
make a procurement price can avoid the waste of cost and
incomplete procurement, and a case test is provided in
the end.
Key words:
Online reverse auction; Random pricing
strategy; Competitive analysis
LIU Zhongcheng, LI Hongyu (2013). Research on Pricing Strategy of
Online Reverse Auction Based on Complete Information. International
Business and Management, 6(2), 71-76. Available from:http://www.
cscanada.net/index.php/ibm/article/view/j.ibm.1923842820130602.1180
DOI:http://dx.doi.org/10.3968/j.ibm.1923842820130602.1180
INTRODUCTION
How to use the new procurement technology and
operational mode to transform and manage the supply
chain and procurement processes, then reduce the
procurement costs and improve efficiency is becoming
more and more concerned and paid attention. The
FreeMarkets Company which was established in 1995 by
Glen Meakem is the earliest one who used online reverse
auction, which is innovative for traditional procurement
mode. Reverse auction is one kind of procurement which
makes a decision after the end of bidding. With the
intensification of the time effect on the procurement cost,
reverse auction participants are not willing to wait for
the results for a long time. Waiting means that the time
cost increases, as well as loss new purchases and sales
opportunities, so online reverse auction was proposed.
Online reverse auction is that sellers arrive at different
time and bid, the decision whether to buy the bidders’
goods needs to be made immediately after the buyer
receives each bid. Reverse auction in application process
gradually gets into transparent equalization. Buyers make
public supplier’s information and bidding to change the
incomplete information into complete information. The
supplier’s competition is more intense under the complete
information, which will bring lower prices, higher quality
suppliers, and reduce the procurement costs. In practice,
the online reverse auction becomes prevalent in Europe
and the U.S. since 2000, which has a reverse bid process
via internet. Compared with traditional negotiation, this
kind of auction can save costs up to 11%-12% for buyers.
In this paper, we will mainly study the random pricing
strategy of online reverse auction, with comparative
analysis to the single pricing strategy.
1. LITERATURE REVIEW
With the development of E-business, it is common to
buy and sell goods via internet. The researches on online
reverse auctions began from auction research in the first
deriving from McAfee, R. P. and J. McMillan’s (1986)
agent competitive strategy analysis and government
procurement mathematical model in the commissioned
agency theory. Subsequently, Dasgupta. S and D. F.
Spulber (1989) analyze the reverse auction strategy
problem of the procurement management. CHEN (1999)
Research on Pricing Strategy of Online Reverse
Auction Based on Complete Information
72
Copyright © Canadian Research & Development Center of Sciences and Cultures
summarizes the quantities of the reverse auction and
strategic equilibrium of price auction on the basis of the
aforementioned studies, and comparatively analyzes
the efficiency of the different auction mechanisms. The
research of online reverse auction model and algorithm
mostly focus on the online algorithms and competitive
analysis methods growing up in computer science.
Ron Lavi and Noam Nisan (2000) study the online
auctions that after bidders arriving at different time the
auction mechanism must make decision immediately
after receipt of each bid, they also take advantage of
the competition analysis in the worst case to identify
the auctioneer optimal supply curve, based on which
the online auction mechanism is very competitive. Alan
Smart and Alan Harrison (2003) study the role in buyer-
supplier relationships of online reverse auctions. Avrim
Blum, Tuomas Sandholm and Martin Zinkevich (2006)
put online learning applications in digital goods online
auction, get a new digital goods auction model and a
constant competition ratio on the optimal auction revenue
under fixed price, and apply the technology applications
in the design of online auction mechanism.
The goods purchased through reverse auction are
generally standardized goods, of which the true valuation
of the supplier is generally converge, so the majority of
the bids usually fluctuate within a relatively small range.
Buyers provide complete information to suppliers, and
then a phenomenon appear that all bids of suppliers are
concentrated in a range because of the fierce competition
to get the object with smaller advantage. Because buyers
can not understand this small range, their valuations
of the commodity usually belong to a large range, in
which a single pricing is likely to be too high to cause
waste of cost, or be set so low that reverse auction
comes to nothing, so that the procurement tasks can not
be completed. With the help of researches on online
algorithms and competitive analysis methods by many
other scholars (XU, XU, & LU, 2005; DING & XU,
2007; XIN, XU, & YI, 2007; XU & XU; 2008), this
paper studies the random pricing strategy of online
reverse auction in which all bids in competition are more
concentrated, and comparative analysis with a single
pricing proves that when a random pricing strategy of
online reverse auction takes advantage of the market price
information, the disadvantages of single pricing caused
such as the waste of cost or unable to complete the task of
procurement can be overcome.
2. PROBLEM DESCRIPTION
Assumi ng buyers want t o buy a cert ai n t ype of
standardized non-market exclusive products, and select a
purchase items from a number of suppliers, and suppliers
can meet the number of purchasing items of buyers.
According to the complete information provided by the
buyer, in each stage of the bidding process of online
reverse auction, suppliers give different bids in different
time, and change the bids in accordance with the changes
of other suppliers. Suppliers bid on the one hand are based
on their own reservation price, on the other hand are
based on the bids of other suppliers at any time to adjust,
and maximize their expected utility with lower prices.
When the expected utility falls to the minimum margin,
the price will no longer be reduced. According to the pre-
determined procurement strategy, the buyer can analysis
the bids of suppliers, determine the most suitable purchase
price, and close a deal with a supplier. Overall, in this
process, the buyer always expects that the price is more
and more lower to achieve the maximum expected utility
by reducing procurement costs.
3. MODELING AND ANALYSIS
A buyer usually determines his own pricing strategy
independently, but as a seller, the supplier can refer to
the bids of other multiple suppliers to determine his own
bidding strategy, whose goal of participating in the auction
is to maximize expected utility (DING & XU, 2007). In
general, it should be set up in advance when the bid of
online reverse auction begins. In this article, it is assumed
that the buyer can end the auction at any time based on the
price situation during the online reverse auction process,
also he can end the auction if his bid price is higher
enough for the supplier to win the bidding, or end the
auction because one buyer of urgent demand for the goods
is willing to purchase at the bid price of the time.
Given an online reverse auction A, in which there are
n suppliers. Assume that the i -th bidder’s real valuation
of goods is v
i
(i = 1,2...,n), his quoted price is b
i
, and
the buyer pay the i-th bidder a price of p
i
. If pi ? b
i
,
transaction maybe occurred, then the i -th bidder’s utility
is U
i
= p
i
- v
i
. If p
i
< b
i
, transaction will not occur, the
bidder’s utility is 0.
Now let’s consider about an online reverse auction
problem with the objective of minimum cost. For any bid
sequence L, C
A
(L) is taken to be the cost that the online
reverse auction
A
makes an instant decision of bidding
sequence L, and C'
A
(L) indicates the decision-making cost
if the bidding sequence
L
is known in advance. If there is a
constant r independent of the bidding sequence L, which
meets C
A
(L) ? r·C'
A
(L), then the competitive ratio is ?,
which shows the better between the optimal procurement
costs in the two cases. This analysis process of the online
algorithms performance is called competitive analysis.
Therefore, before the analysis of random pricing
strategy of online reverse auction, it needs firstly to study
the single pricing condition, and thus to analyze the
competitive performance of random pricing strategy.
3.1 Optimal Single Pricing
If the buyer has determined a purchase price before online
LIU Zhongcheng; LI Hongyu (2013).
International Business and Management, 6(2), 71-76
73
Copyright © Canadian Research & Development Center of Sciences and Cultures
reverse auction, the first supplier whose bid price is less
than or equal to this purchase price will close a deal with
the buyer. This online reverse auction strategy is called
online single pricing strategy (abbreviated as the online
SP strategy).
If the buyer has an estimated range [B
1
, B
2
] of the
commodity price, then assumed that the single price is
set to B
3
, if the price is set too low, there is probably not
one supplier can win the bidding all the way, the buyer
has to purchase at the last-minute bid price because of the
procurement time limit, and if B
3
is set too high, the online
reverse auction may soon close a deal, but can not achieve
the goal of saving costs. From the competitive analysis
point of view:
If the bid price B
1
doesn’t appear in procurement time,
the cost ratio of online and offline is B
3
/B
1
.
If the bid price below the single fixed price doesn’t
appear all the way during the procurement time, and the
final bid price comes to the ceiling, then the cost ratio of
online and offline is B
2
/B
3
.
So given the single fixed price B
3
, the competition ratio
of this online reverse auction is r
SP
= sup{B
3
/B
1
, B
2
/B
3
},
and the optimal B
3
should be the solution of the equation
B
3
/B
1
=B
2
/B
3
because the price makes the r
sp
minimum
value, then
2 1 3
B B B ? = , so r
SP 1 2
/ B B r
SP
= .
3.2 Random Pricing Strategy and Competitive
Analysis
3.2.1 Random Pricing Strategy
With complete information, if the bid prices of suppliers
are more concentrated, the buyer needs to analyze all
the bid prices of small difference. Then, we will apply
the random pricing strategy of online reverse auction
(abbreviated online reverse auction RP strategy) to
analyze the supplier’s bids in competition.
Let the estimated range [B
1
, B
2
] of the buyer about
the commodity price be separated into m subintervals,
m ? ? ? , , 2 , 1 ? , whe r e ) , (
1 i i
c c i
?
= ? , i = 1, 2. . . , m.
Assuming the selected number of bid prices up to n (that
is, up to the n -th bid auction will end), now let the right
end point c
1
of the first subinterval (c
0
, c
1
) be the minimum
reserve price, and assuming the price making sequence is
p
1
, p
2
,..., p
n
that is to make the price p
i
for the commodity
of the i -th bidder, then the random pricing strategy of
online reverse auction is as follows:
? The probability of price p1 made for the
commodity of the first supplier meets Pr (p1 =
c1) = 1, if the first bid price b1 ? c1, the purchase
price is c
1
. Otherwise, the transaction will be
unsuccessful, and then look at the second bid.
? Assuming b
2
falls into the subinterval ) 1 ( ? ? k k ,
then the price p
2
made for the commodity of the
second supplier satisfies
n
n
c p P
r
1
) (
1 2
?
= = , P
r
(p
2
= c
k
) = 1/n, and if the second bid price b
2
? c
1
, then
the transaction will be successful, so the probability
of price c
1
in the successful deal is
n
n 1 ?
, as the
probability of price c
k
in the deal is 1/n. If c
1
c
k
, the transaction can not be
reached, then see the third bid.
? Usually, the probability of the price p
i
made for
the commodity of the i -th supplier satisfies:
) ) (
2
1
n
N n
c p P
m
j
j
i r
?
=
?
= =
,
) ) (
n
N
c p P
j
j i r
= =
, j=2,3,...m (1)
where N
j
represents the number of bid prices falling
into the j -th subinterval of the front i -1 suppliers.
3.2.2 Competitive Analysis
If bid prices of all suppliers concentrate in a subinterval
with a length of ? within the valuation interval [B
1
, B
2
]
of the buyer, then split [B
1
, B
2
] to several small intervals
with each length of ?/k, and suppose that there are nbid
prices concentrating in a small area [?, ?+?], then all bid
prices will fall into at most k+1 segmented subintervals.
According to the random pricing strategy of online reverse
auction, the worst case is that the transaction is concluded
at the price of ?+?+?/k with the probability of
n
n 1 ?
, and
no deal is closed with the probability of 1/n, then the buyer
has to purchase at the price ceiling B
2
. So the expected cost
( 1)( / )
( )
RP
n k
E C
n n
? ? ? ? ? + ? + +
? + , while the offline
optimal cost is
?
, then the ratio of expected cost ( )
RP
E C
and offline optimal cost ? is:
( 1)( / )
( )
RP
a n a k
E C
n n
a a
? ? ? + ? + +
+
=
1 1
1 1
1
a n n
a n ka B n kB
? ? ? ? + ? ?
? + ? ? + + ?
(2)
When the interval is split up into much more
smal l er subi nt er val s, namel y, i f ? ? k , t hen:
1 1 1
( ) 1
lim lim(1 ) 1
RP
k k
E C n
B n kB B
? ? ?
? ?? ??
?
= + + ? = +
, a n d
( )
sup
RP
RP
E C
r
?
= , that is, when the valuation range is
split up infinitely, r
RP
approximates to
1
1
B
?
+
.
If ? ? k , then:
When ?=0, rRP?1..
When ?=B
2
-B
1,
2
1
RP
B
r
B
?
.
Research on Pricing Strategy of Online Reverse
Auction Based on Complete Information
74
Copyright © Canadian Research & Development Center of Sciences and Cultures
When
1
1
B
?
+
<
2 1
/ B B
, i.e. when
1 2 1
[0, ] B B B ? ? ?
, r
RP
< r
SP
, now the competitive performance of random pricing
strategy is better than that of optimal single pricing strategy.
Therefore, the smaller the ? is, the smaller r
RP
is too.
That is, the more concentrated the bid prices are, the
closer the expected cost of random pricing strategy is to
the offline optimal cost. So, even if the buyer does not
know the fluctuant cost range of suppliers, he can also
adjust gradually the probability of bid price making by
random pricing strategy, so that the expected cost of the
online close offline optimal cost.
4. CASE TEST
4.1 Case Description
An assembly production enterprise wants to procure
a number of parts from multiple suppliers. Because
assembled commodities parts has the characteristics such
as purchasing large quantities and high standardization,
the enterprise decides to use multi-stage online reverse
auction by using bulk procurement of multi-channel.
During online reverse auction, the buyer will firstly audit
and evaluate the suppliers who applied online to determine
their participation eligibility, then get price information of
each supplier and eliminate weaker competitive suppliers
to determine those outright ones. Finally, the buyer can
distribute the order form to complete the procurement for
the minimum purchase cost.
The detailed procurement process of this enterprise is
described as follows:
(1) The number attributes of supplier
Because of bulk purchasing, the buyer needs to
divide an order into multi orders to respectively procure.
According to the number attributes of the procurement
goods and each batch procurement number range, in this
case, 3 suppliers are needed, and at most one supplier
is selected in each procurement stage, so at least there
are 3 stages of the bidding. For the simplicity of test,
assuming that one supplier is chosen in each stage and the
procurement needs 3 stages to be finished.
(2) Assuming that that buyers’ understanding of this
product price is limited to a certain price range [48, 72],
the initial price is set at b
0
=60, because the supplier’s bid
would be more concentrated in the less bid interval, the
buyer will put every 10 bids into a stage.
To easily establish the model, we assume that
the bidding sequence number is the serial number of
suppliers, which is shown in Table 1, 2, 3.
Table 1
Price List 1 of Online Reverse Auction
Series number 1 2 3 4 5 6 7 8 9 10
Competitive tender 63 64 65 63 61 62 61 60 62 60
Supplier 1 2 3 4 5 6 7 8 9 10
Table 2
Price List 2 of Online Reverse Auction
Series number 1 2 3 4 5 6 7 8 9 10
Competitive tender 56 59 58 58 57 55 56 54 55 54
Supplier 11 12 13 14 15 16 17 18 19 20
Table 3
Price List 3 of Online Reverse Auction
Series number 1 2 3 4 5 6 7 8 9 10
Competitive tender 53 53 54 52 53 54 52 51 52 52
Supplier 21 22 23 24 25 26 27 28 29 30
4.2 Pricing
As we can see the bidding sequence from Table 1, 2, 3, in
this transaction period if we consider the optimal offline
purchasing transaction price that it is clearly 59. The optimal
single price is
1 2
48 72 58.8 B B ? = × = , and the ratios
of the optimal single pricing strategy to the optimal offline
purchases is
2 1
/ 1.22
SP
r B B = = . Obviously, 59
?
58.8
×
1.22, that is to say that applying single pricing strategy
to procure is better than offline purchases. But according
to single pricing strategy to procure, apparently it can not
quickly make deal. Because the previous bidding prices are
not lower than 59, the buyer may lose the opportunity after
waiting for a long time. Even the procurement can not be
completed during the limited time of online reverse auction.
(1) Using the RP strategy of online reverse auction to
price the first phase bids, the analysis is as follows:
Divide [48, 72] into 8 small pieces [48, 51], [51, 54],
[54, 57], [57, 60], [60, 63], [63, 66],[66, 69], [69, 72], the
pricing and probability sequence is as follows:
1) P
r
(p
1
=51)=1, and b
1
=63, So the transaction can not
be reached.
2) P
r
(P
2
=51)=9/10, P
r
(p
2
=63)=1/10, and b
2
=64, So
LIU Zhongcheng; LI Hongyu (2013).
International Business and Management, 6(2), 71-76
75
Copyright © Canadian Research & Development Center of Sciences and Cultures
the transaction can not be reached.
3 ) P
r
( P
3
= 5 1 ) = 8 / 1 0 , P
r
( p
3
= 6 3 ) = 1 / 1 0 ,
P
r
(p
3
=66)=1/10, and b
3
=65, So the probability of the
deal is 1/10, the transaction value is 66.
4 ) P
r
( p
4
= 5 1 ) = 7 / 1 0 , P
r
( p
4
= 6 3 ) = 1 / 1 0 , P
r
(p
4
=66)=2/10, and b
4
=63, So the probability of the deal
is 1/10, the transaction value is 63.
5) P
r
(p
5
=51)=6/10,P
r
(p
5
=63)=2/10,P
r
(p
5
=60)=2/10,
and b
5
=61 , So the probability of the deal is 2/10, the
transaction value is 63.
6) P
r
(p
6
=51)=5/10,P
r
(p
6
=63)=3/10,P
r
(p
6
=66)=2/10,
and b
6
=62, So the probability of the deal is 3/15, the
transaction value is 63.
7) P
r
(p
7
=51)=4/10,P
r
(p
7
=63)=4/10,P
r
(p7=66)=2/10,
and b
7
=61, So the probability of the deal is 4/10, the
transaction value is 63.
8) P
r
(p
8
=51)=3/10,P
r
(p
8
=63)=5/10,P
r
(p
8
=66)=2/10,
and b
8
=60, So the probability of the deal is 5/10, the
transaction value is 63.
9) P
r
(p
9
=51)=2/10 ,P
r
(p
9
=63)=6/10,P
r
(p
9
=60)=2/10,
and b
9
=62, So the probability of the deal is 6/10, the
transaction value is 63.
10) P
r
( p
10
=51) =1/ 10 , P
r
( p
1 0
= 6 3 ) = 7 / 1 0 , P
r
(p
10
=66)=2/10 , and b
10
=60, So the probability of the
deal is 9/10, the probability of the transaction value which
equals 63 is 7/10, the probability of the transaction value
which equals 66 is 2/10.
The ratio of the expected cost in this procurement
stage to the optimal offline cost is competitive ratio:
( )
1
sup 1.06
rp
RP
E C
a n ka k
r
a na n ka
? ? ? + ? + +
= = + ? =
(2) Using the RP strategy of online reverse auction to
price the second phase bids, the analysis is as follows:
Divide [48, 72] into 8 small pieces [48, 51], [51, 54],
[54, 57], [57, 60], [60, 63], [63, 66], [66, 69], [69, 72] ,
the pricing and probability sequence is as follows:
1) P
r
(p
1
=51)=1, and b
1
=56, So the transaction can not
be reached.
2) P
r
(p
2
=51)=9/10, P
r
(p
2
=57)=1/10, and b
2
=59, So
the transaction can not be reached.
3) P
r
(p
3
=51)=8/10, P
r
(p
3
=57)=1/10, P
r
(p
3
=60)=1/10,
and b
3
=58, So the probability of the deal is 1/10, the
transaction value is 60.
4) P
r
(p
4
=51)=7/10, P
r
(p
4
=57)=1/10, P
r
(p
4
=60)=2/10,
and b
4
=58, So the probability of the deal is 2/10, the
transaction value is 60.
5) P
r
(p
5
=51)=6/10,P
r
(p
5
=57)=2/10, P
r
(p5=60)=2/10,
and b
5
=56, So the probability of the deal is 1/10, the
transaction value is 57.
6) P
r
(p
6
=51)=5/10, P
r
(p
6
=57)=3/10, P
r
(p
6
=60)=2/10,
and b
6
=55, So the probability of the deal is 2/15, the
transaction value is 57.
7) P
r
(p
7
=51)=4/10, P
r
(p
6
=57)=3/10, P
r
(p
6
=60)=3/10,
and b
7
=56, So the probability of the deal is 3/10, the
transaction value is 57.
8) P
r
(p
8
=51)=3/10, P
r
(p
8
=57)=4/10, P
r
(p
8
=60)=3/10,
and b
8
=54, So the probability of the deal is 4/10, the
transaction value is 57.
9) P
r
(p
9
=51)=2/10, P
r
(p
9
=57)=5/10, P
r
(p
9
=60)=3/10,
and b
9
=55, So the probability of the deal is 5/10, the
transaction value is 57.
1 0 ) P
r
( p
1 0
= 5 1 ) = 1 / 1 0 , P
r
( p
1 0
= 5 7 ) = 6 / 1 0 ,
P
r
(p
10
=60)=3/10, and b
10
=54, So the probability of the
deal is 9/10, the probability of the transaction value which
equals 57 is 6/10, the probability of the transaction value
which equals 60 is 3/10.
The ratio of the expected cost in this procurement
stage to the optimal offline cost is competitive ratio:
( )
1
sup 1.06
rp
RP
E C
a n ka k
r
a na n ka
? ? ? + ? + +
= = + ? =
(3) Using the RP strategy of online reverse auction to
price the third phase bids, the analysis is as follows:
Divide [48, 72] into 8 small pieces [48, 51], [51, 54],
[54, 57], [57, 60], [60, 63], [63, 66], [66, 69], [69, 72] ,
the pricing and probability sequence is as follows:
1) P
r
(p
1
=51)=1, and b
1
=53, So the transaction can not
be reached.
2) P
r
(p
2
=51)=9/10, P
r
(p
2
=54)=1/10, and b
2
=53, So the
probability of the deal is 1/10, the transaction value is 54.
3) P
r
(p
3
=51)=8/10, P
r
(p
3
=54)=2/10, and b
3
=54, So the
probability of the deal is 2/10, the transaction value is 54.
4) P
r
(p
4
=54)=7/10, P
r
(p
4
=54)=3/10, and b
4
=52, So the
probability of the deal is 3/10, the transaction value is 54.
5) P
r
(p
5
=51)=6/10, P
r
(p
5
=54), and , So the probability
of the deal is 4/10, the transaction value is 54.
6) P
r
(p
6
=51)=5/10, P
r
(p
6
=54)=5/10, and b
6
=54, So the
probability of the deal is 5/15, the transaction value is 54.
7) P
r
(p
7
=51)=4/10, P
r
(p
7
)=54=6/10, and b
7
=52, So the
probability of the deal is 6/10, the transaction value is 54.
8) P
r
(p
8
=51)=3/10, P
r
(p
8
=54)=7/10, and b
8
=51, So the
probability of the deal is 7/10, the transaction value is 54.
9) P
r
(p
9
=51)=2/10, P
r
(p
9
=54)=8/10, and b
9
=52, So the
probability of the deal is 8/10, the transaction value is 54.
10) P
r
(p
10
=51)=1/10, P
r
(p
10
=54)=9/10, and b
10
=52, So
the probability of the deal is 9/10, the transaction value is 54.
The ratio of the expected cost in this procurement
stage to the optimal offline cost is competitive ratio:
( )
1
sup 1.07
rp
RP
E C
a n ka k
r
a na n ka
? ? ? + ? + +
= = + ? =
Obviously, it is better than the cost of offline
purchasing by using online reverse auction RP strategy.
Although using the RP strategy can not make a deal
soon, it is able to reflect the supplier's bidding information
from the prices, and the probability of which the transaction
price closes to the bidding prices of most suppliers is the
largest. The buyer can conduct the transaction price and
decide whether or not to choose the supplier.
From the bidding information of the three stages,
according to the principle of highest probability, the price
Research on Pricing Strategy of Online Reverse
Auction Based on Complete Information
76
Copyright © Canadian Research & Development Center of Sciences and Cultures
in the first stage is 63, and the second phase of the price
is set at 57, and the price of the third stage is 54. At this
time, due to the supplier's bids are intensive, it may appear
that several suppliers bid the same price, so the buyer can
make the decision based on the evaluation of other aspects
of the suppliers.
CONCLUSION
Aiming at the procurement problem that using online
reverse auction to select a supplier, this paper studies
the optimal single pricing strategy and random pricing
strategy, using which the price made for the supplier
is independent of has bid price. The latter can take
advantage of market price information, correct the defects
caused by static single pricing, besides, it has many other
advantages such as full market information, low cost of
transaction management, and excellent operability, etc.
However, this strategy is applicable to the online reverse
auction for standard commodities with bid prices more
concentrated. It still needs further studies on the problem
of more dispersive bid prices and big competitive ratio.
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doc_297914958.pdf