kes amsta 2009, june 5, 2009 1 forming buyer coalitions with bundles of items laor boongasame,...
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KES AMSTA 2009, June 5, 20091
Forming Buyer Coalitions with Bundles of Items
Laor Boongasame, Department of Computer Engineering, Bangkok University, Bangkok, Thailand
Ho-fung Leung, Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong, P.R. China
Veera Boonjing, Department of Mathematics and Computer Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok,
ThailandDickson K. W. Chiu, Dickson Computer Systems, 7 Victory Avenue,
Kowloon, Hong Kong, P.R. China
KES AMSTA 2009, June 5, 20092
Outline of Presentation
I. Motivation for the research
II. Forming Buyer Coalitions with Bundles of ItemsI. Example and Problem Formulation
II. Algorithm and Example Revisited
III. SimulationI. Setup of Experiments
II. Results and Analysis
IV. Discussion and Conclusion
KES AMSTA 2009, June 5, 20093
I. Motivation for the Research
KES AMSTA 2009, June 5, 20094
I. Motivation for the Research
A buyer coalition is a group of buyers who join together to negotiate with sellers for a bulk purchasing of items at a larger discount (Tsvetovat, M., Sycara, K. P., Chen, Y., 2001).
There are several existing buyer coalition schemes (He, L., Ioerger T., 2005; Anand, K.S., Aron, R., 2003; Tsvetovat, M., Sycara, K. P., Chen, Y., Ying, 2001, Hyodo, M., Matsuo, T., Ito, T., 2003). However, these schemes do not consider forming a buyer coalition with bundles of items.
KES AMSTA 2009, June 5, 20095
I. Motivation for the Research (Cont.)
This practice can be observed very often in the real world such as restaurants (e.g., McDonald's Happy Meal), durable consumer goods (e.g., personal computer options), and non-durable consumer goods (e.g., dishwasher detergent and rinse aid packages).
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II. Forming Buyer Coalitions with Bundles of Items
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II. Forming Buyer Coalitions with Bundles of Items: Example and Problem Formulation
Item Package/Item Unit Price ($)
1 (pk1) Printer, CPU, Monitor 2700
2 (pk2) Printer, CPU, RAM 2700
3 … Printer 1000
4 CPU 1000
5 Monitor 1000
6 RAM 1000
Pk
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II. Forming Buyer Coalitions with Bundles of Items: Example and Problem Formulation (Cont.)
Table 2 shows the subsidiaries' required computer equipment and their reservation prices, i.e., the maximum price that the buyer bk is willing to pay for a unit of each item. For instance, subsidiary Bangkok-B wants to purchase a unit of CPU at $900 or lower and a unit of monitor at $900 or lower.
KES AMSTA 2009, June 5, 20099
II. Forming Buyer Coalitions with Bundles of Items: Example and Problem Formulation (Cont.)
subsidiaries Rsi Of Printer
Rsi Of CPU
Rsi Of Monitor
Rsi Of RAM
Bkk-A 1000
Bkk-B 900 900
Bkk-C 800 1000 800
Bkk-D 900 1000 900
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II. Forming Buyer Coalitions with Bundles of Items: Example and Problem Formulation (Cont.)
The problem that we solve is forming buyer coalitions for purchasing item packages ,such that can purchase required items and is maximal, where is the joint utility that members of Ci can reach by cooperating via coalitional activity for purchasing a specic bundles of items.
PkPk l BCi Bbi i iV
iV
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II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited
Step 1: Calculate all the permutations that include up to k buyers. This is the set of all potential coalitions PC.
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II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited (Cont.)
The number of members in any buyer coalitions
The set of potential coalitions PC
1 {Bkk-A}, {Bkk-B}, {Bkk-C}, {Bkk-D}
2 {Bkk-A, Bkk-B}, {Bkk-A, Bkk-C}, {Bkk-A, Bkk-D}, {Bkk-B, Bkk-C}, {Bkk-B, Bkk-D}, {Bkk-C, Bkk-D}
3 {Bkk-A, Bkk-B, Bkk-C},{Bkk-A, Bkk-B, Bkk-D}, {Bkk-A, Bkk-C, Bkk-D}, {Bkk-B, Bkk-C, Bkk-D}
4 {Bkk-A, Bkk-B, Bkk-C, Bkk-D}
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II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited (Cont.)
Step 2: In each coalition, the coalitional potential items vector is calculated by summing up the unused items of the numbers of the coalition. Formally,
Cb i
PCC
iGdGd
PCCGd
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II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited (Cont.)
The set of potential coalitions PC
printer CPU Monitor Memory
{Bkk-A} √
{Bkk-B} √ √
{Bkk-C} √ √ √
{Bkk-D} √ √ √
{Bkk-A, Bkk-B} √ √ √
{Bkk-B, Bkk-C} √ √√ √ √
…
PCCGd
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II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited (Cont.)
Step 3: For each bundle of items ,perform: Step 3.1: Check what items are wanted for the satisfaction of
Pkpk l
lGd
lpk
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II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited (Cont.)
packages Gdl
printer CPU Monitor Memory
pk1√ √ √
pk2√ √ √
pk3√
pk4√
pk5√
pk6√
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II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited (Cont.)
Step 3.2: Compare to the sum of the unused items of the members of the coalition , thus finding the packages that can be satisfied by coalition C. The coalition C will be formed to purchase the package if there is at least one member of coalition C wants to purchase any items in the package or when and .
lGd
PCCGd
lpk
lpk
lpk
lih Gdgd Cbi lh Gdgd
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II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited (Cont.)
The set of potential coalitions PC
packages
printer CPU Monitor Memory pk1 pk2 pk3 pk4 pk5 pk6
{Bkk-A} √ √ √ √{Bkk-B} √ √ √ √ √ √{Bkk-C} √ √ √ √ √ √ √ √{Bkk-D} √ √ √ √ √ √ √ √{Bkk-A, Bkk-B}
√ √ √ √ √ √ √ √
{Bkk-B, Bkk-C}
√ √√ √ √ √ √ √ √ √ √
…
PCCGd
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II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited (Cont.)
Step 3.3: , a discount that the coalition C get from forming to purchase the packages , will be calculated. Formally, when condition1) for and and condition2)
ClV
lpk
lihCl rsV Pr
jh
ih rsrs Cb j lh pkgd
Cbi
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II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited (Cont.)
The set of potential coalitions PC
Vcl
v1 v2 v3 v4 v5 v6
{Bkk-A} 1000-2700 = -1700 -1700 0
{Bkk-B} -900 -1800 -100 -100
{Bkk-C} -900 -100 -200 0 -200
{Bkk-D} -800 -900 -100 0 -100
{Bkk-A, Bkk-B} 1000+900+900-2700=100
-800
{Bkk-B, Bkk-C} 800+1000+900-2700=0
…
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II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited (Cont.)
Step 4: which give the maximum will be chosen.
clV
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II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited (Cont.)
The set of potential coalitions PC vcl
Bkk-A 0
…
Bkk-A, Bkk-B 100
…
Bkk-A, Bkk-B, Bkk-C 200
Bkk-A, Bkk-B, Bkk-D 200
Bkk-A, Bkk-C, Bkk-D 300
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II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited (Cont.)
Step 5: Update the items-vectors of all of the members of C” according to their contribution to the package-execution.
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II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited (Cont.)
Buyer-Items
rs of Printer
rs of CPU rs of Monitor
rs of RAM
Bkk-A 1000
Bkk-B 900 900
Bkk-C 800 1000 800
Bkk-D 900 1000 900
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II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited (Cont.)
Total discount . We repeat this process until all buyers in the group of buyers can purchase items that they require, like Table in next slide.
)(300 1pkVtot
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II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited (Cont.)
Buyer-Items
rs of Printer
rs of CPU rs of Monitor
rs of RAM
Bkk-A 1000
Bkk-B 900 900
Bkk-C 800 1000 800
Bkk-D 900 1000 900
KES AMSTA 2009, June 5, 200927
II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited (Cont.)
))(200())(200())(100()(0)(300 63611 pkpkpkpkpkVtot
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III. Simulation
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III. Simulation: Setup of Experiments
Table 3: summarizes the simulation parameters.
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III. Simulation: Setup of Experiments (Cont.)
Parameter Range Range
Seller The number of sellers 1
Packages The number of packages
6
The number of single item
4
The number of bundles of items
2
The number of items necessary for each bundle of item
3
The average number of both item necessary for bundles of items and single item of the seller (AIS)
2
Buyers The number of buyers 4, 6, 8
Required items for each buyer
The average number of required items for each buyer (IB)
1, 2, 4
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III. Simulation: Results and Analysis
The results of the simulation are divided into three categories:
1) the number of buyers is smaller than the number of packages
2) the number of buyers is equal to the number of packages, and
3) the number of buyers is greater than the number of packages.
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III. Simulation: Results and Analysis: Fig. 1
-120
-100
-80
-60
-40
-20
0
0.5 1 1.5
IB/AIS
Mea
n of
the
tota
l dis
coun
t of
any
coal
ition
s in
the
Gro
upB
uyP
acka
ge s
chem
e
1
2
3
KES AMSTA 2009, June 5, 200933
III. Simulation: Results and Analysis : Fig 1 (Cont.)
From Fig. 1, it is observed that the mean of the total discount of any coalition in the GroupBuyPackage scheme with the third category are higher than that in the GroupBuyPackage scheme with the first category and the second category.
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III. Simulation: Results and Analysis: Fig. 2
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.5 1 1.5
IB/AIS
The
ratio
of b
undl
e of
item
s on
e by
sin
gle
of it
em
1
2
3
KES AMSTA 2009, June 5, 200935
III. Simulation: Results and Analysis: Fig. 2 (Cont.)
From Fig. 2, it is observed that the ratio of the number of formed bundles of items to one by single of item in the GroupBuyPackage scheme with the third category is higher than that in the GroupBuyPackage scheme with the first category and the second category.
KES AMSTA 2009, June 5, 200936
III. Simulation: Results and Analysis (Cont.)
From both graphs, we conclude that the total discounts of any coalition in this schemes is high as the number of buyers were more than the number of packages (third category).
This is because the ratio of the number of formed bundles of items to one by single of item in the GroupBuyPackage scheme with the third category is higher than that in the GroupBuyPackage scheme with the first category and the second category.
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III. Simulation: Results and Analysis (Cont.)
We denote the mean of the total discount of any coalition as TD and the difference between TD of the GroupBuyPackage scheme and TD of the optimal scheme as DIFF. The performance ratio of TD of the GroupBuyPackage scheme to DIFF is illustrated in Fig. 3.
The horizontal axis represents IB/AIS, while the vertical axis represents the ratio of TD of the GroupBuyPackage scheme to that by DIFF.
The value 1 means that the two schemes have the same performance; a value below 1 indicates that the optimal scheme is better; and a value above 1 shows the opposite.
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III. Simulation: Results and Analysis : Fig 3 (Cont.)
0
0.2
0.4
0.6
0.8
1
1.2
0.5 1 1.5
IB/AIS
The
ratio
of T
D o
f the
G
roup
Buy
Pac
kage
sch
eme
one
by D
IFF 1
2
3
KES AMSTA 2009, June 5, 200939
III. Simulation: Results and Analysis : Fig 3 (Cont.)
From Fig. 3, it is observed that the ratio of TD of the GroupBuyPackage scheme to one by DIFF is close to one on all values of IB/AIS.
In other words, the mean of the total discount of any coalition of the GroupBuyPackage scheme is close to that of the optimal scheme.
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IV. Discussion and Conclusion
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IV. Discussion and Conclusion
This algorithm is suitable for cases where buyers cooperate in order to maximize a total discount, especially when individual buyers cannot buy a whole bundle of items by themselves.
Nevertheless, they may get more discounts (or utilities) when the discounts from buying the items individually is lower than the discounts from purchasing bundles of items.
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IV. Discussion and Conclusion (Cont.)
To guarantee the performance of this algorithm, we compare its results with those of the optimal algorithm.
In the simulation, main effective forming factors were IB, and AIS.
From Fig. 1-3, the total discount of any coalition in this algorithm is close to that in the optimal algorithm in almost all values of IB and AIS.
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IV. Discussion and Conclusion (Cont.)
In our future research, pure bundling, whereby only the item bundle is offered and the individual items in the bundle cannot be purchased on their own, is considered in forming the buyer coalition.
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