A Location-Price-Based Buyer Coalition

Santit Narabin1

1Software Systems Engineering Laboratory, Department of Computer Science, King Mongkut’s Institute

of Technology Ladkrabang, Bangkok, Thailand E-mail: S9062901@kmitl.ac.th

Veera Boonjing1,2

2National Centre of Excellence in Mathematics PERDO, Bangkok,

Thailand E-mail: Kbveera@kmitl.ac.th

Abstract— A buyer coalition is a group of buyers who join together to negotiate with sellers to purchase items for a larger discount. In this article, a novel buyer coalition scheme, called the "GroupSimilarBuyer Scheme," is introduced. The new idea focuses on buyer coalition formation based on similarity of buyers. The mechanism of approach begins to prepare data for driving the next step. Then, a k-mean clustering algorithm is used to form the coalition of buyers which are very similar in both reservation price and location of buyer. In addition, the utility of each buyer coalition is calculated. Based on the simulation result, the GroupSimilarBuyer showed that the average standard deviation of the coalition was nearly the optimum result.

Keywords-GroupSimilarBuyer, electronic commerce, group- buying, coalition formation, buyer coalition.

I. INTRODUCTION

A buyer coalition is a group of buyers who join for purchasing any items at a larger discount [9]. Varieties of buyer coalition formation schemes already exist in the buyer coalition literatures which are based on price such as [2], [3], [4], [5], and [8]. Currently, only the price is insufficient for getting the best benefit. Therefore, the buyer coalition principle needs to find the best factor for consideration. Existing schemes do not consider the forming of buyer coalition with the location of buyers.

Currently, the K-mean clustering algorithm is the best method for this, especially the algorithm of Jain and Dubes [1], which is a simply and fast clustering technique. Therefore, it is natural to ask if we can add the distance to these schemes. Furthermore, the benefit will be increased when using this factor to join with the traditional factors. In addition, it challenges us to combine the k-mean technique to create the most efficient buyer coalition.

We propose a new buyer coalition formation scheme using many attributes of the buyer by using a similarity base, called the "GroupSimilarBuyer" scheme. This solution aims at buyers who can buy items within a reasonable price and distance. There are three steps in our method of the scheme: (1) The preprocessing phase, (2) The formation of the coalition of buyers and (3) The calculation the utility of each buyer coalition. A prototype system, which uses a theater ticket purchasing case as an example, is created to demonstrate the idea and show how the model works. In the experimental result, the simulation showed that the GroupSimilarBuyer took the average standard deviation of the coalition which was almost the optimum result. Our

proposed solution creates both an optimal coalition group, in terms of the location of the members of the coalition.

The article is organized as follows: Section 2 provides related works. Section 3 describes the GroupSimilarBuyer scheme. Section 4 presents the GroupSimilarBuyer scheme simulation setup and the experimental attributes of the scheme. Section 5 analyzes the result of the simulation. The conclusions are in Section 6.

II. RELATED WORKS

Many existing buyer coalition schemes already exist in the literature (e.g., [2], [3], [4], [5], [6], [7], [8], [9], [10]). Some buyer coalition research (i.e.,[7], [8], [9] and [10]) form a buyer coalition with bundles of items. They propose the same optimal purchasing approaches that maximize the discount to buyers. In addition, J. Yamamoto and K. Sycara [2] propose a buyer coalition formation scheme, called GroupBuyAuction. This scheme, buyers form a group based on category of items. Matsuo et al. [6] addressed decision support systems for buyers in group buying. They integrate buyers with multi-attribute preferences (utility) into a coalition. The system uses an analytic hierarchy process to support the buyer’s decision-making. These schemes consider forming a buyer coalition with price of items and the reservation price of buyers. There is a lack of research on how buyers form a coalition with regards to the location of buyers. These issues lead to buyers being able to purchase items within a reasonable price and distance between them. These are the main issues addressed in this paper.

III. GROUPSIMILARBUYER SCHEME

In this section, we present a new approach for forming buyer coalitions using the location of buyers as an important attribute. The following scenario is used to demonstrate the process of GroupSimilarBuyer scheme.

A. Description of the scenario As previously mentioned, in this research, the buyer

coalition is re-defined, using the location of buyers as a central attribute. Our assumptions are goods (items), buyers, third-parties, distances, and mobile phones, which are used as the mechanism for driving the solution. We describe the scenario of the buyer coalition formation through the following examples.

For example, there is a group of movie theatres and they have available seats prior to movies being shown. A

2012 IEEE 12th International Conference on Computer and Information Technology

978-0-7695-4858-6/12 $26.00 © 2012 IEEE

DOI 10.1109/CIT.2012.97

416

2012 IEEE 12th International Conference on Computer and Information Technology

978-0-7695-4858-6/12 $26.00 © 2012 IEEE

DOI 10.1109/CIT.2012.97

416

2012 IEEE 12th International Conference on Computer and Information Technology

978-0-7695-4858-6/12 $26.00 © 2012 IEEE

DOI 10.1109/CIT.2012.97

416

2012 IEEE 12th International Conference on Computer and Information Technology

978-0-7695-4858-6/12 $26.00 © 2012 IEEE

DOI 10.1109/CIT.2012.97

416

manager of each theatre will send the price schedule of available seats to the third-party shown in Table I.

TABLE I. THE PRICE SCHEDULE OF THE THEATRE

Volume (unit) - 1 2 3 �4

Price ($) 100 95 90 85 80

Table I illustrates the price schedule of one theatre where the price per ticket when multiple tickets are sold together. The third-party will invite their members to form a coalition.

For instance, if there are fifty buyers as members of the third-party and if the members are interested in buying tickets to see the movies, then they will send the acceptance message and their reservation price to the third-party. The details of buyers who want to form a coalition are shown in Table II.

Afterwards, the third-party can detect any positions of the buyers by using locations of their mobile phones. The locations of buyers are shown in Table III. To achieve the optimum selection of buyers, the third-party will do as follows:

1) Forming a coalition or selecting the buyers into a coalition, called "winners,"

2) Dividing a surplus in the coalition to winner based on their reservation prices and their locations, and

3) Sending the final prices back to the winners and send rejected messages back to buyers who are not selected to be members of the coalition.

TABLE II. THE EXAMPLE OF BUYERS WHO WANT TO FORM ACOALITION.

Reservation price ($) Buyers Theatre 1 Theatre 2 Theatre 3

b1 88 94 82 b2 84 81 92 b3 97 81 84 b4 81 83 94 b5 85 97 93

TABLE III. THE LOCATION OF BUYERS.

Distance to the theatre (unit) Buyers Theatre 1 Theatre 2 Theatre 3

b1 4 3 19 b2 6 12 10 b3 14 10 3 b4 7 6 9 b5 18 18 13

B. Problem formulation We recall the necessary basic notions used for

representing a buyer coalition formation scheme, as described below.

Let },...,,{ 21 KtttT � is a set of K theatres where kt is a

theatre thk , and Kk ��1 .

The manager of theatre send a price schedule of the available seats P , where a descending function

numberrealaP �: and )( tktk aP is a unit price that

the theatre would expect from selling a bundle of size ‘ tka ’ of the movie tickets to the third-party.

The third-party will invite a set of his members },...,,{ 21 gmmmM � to form a coalition C .

Each member xm who wants to purchase the ticket is

called buyer }...,,,{ 21 nbbbB � , and each xm will send the

reservation price ir back to the third-party.

The third-party detects the locations of all buyers },...,,{ 21 knkkkLB ���� where ki� is the location

thi buyer, and thence The third-party selects the buyers into the coalition C .

The winner coalition of the theatre kt is called

},...,,{ 21*

kpkkkk wwwWC �� where 0)( * �kCv .

Afterwards, the third-party divides the surplus },...,,{ 21 kpkkk dddD � among the members of the

coalition. The main attributes of the members of the coalition are the offer price and the location of the coalition member.

Finally, the third-party sends the final prices },...,,{ 21 kpkkk fffF � back to the winners from

klklkl drf �� where klr is a reservation price of the thkl winner.

Moreover, the reject messages will be sent to buyers without the coalition.

C. Scheme Implementation This subsection shows the GroupSimilarBuyer process:

The preparation data, the formation of the buyer coalition, and the calculation of the coalition value. The preparation method uses all tables mentioned in the previous section for arranging the data. The group data then allows us to form a buyer coalition using a k-mean algorithm, and then the buyer coalition value is created. The three major steps are described as follows.

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Step 1: Preparation data

In this step, the reservation price data and the distance data of all buyers are assumptions to preparation. Then, we transform these data into the suitable rank. As a result, the priority of each attribute as well.

Next, we normalize the rank into value [0,1]. Illustrated the example mentioned in previous section, Table IV and Table V show the normalized details of all buyers.

TABLE IV. THE NORMALIZE RESERVATION PRICE OF ALL BUYERS.

Reservation price ($) Buyers Theatre 1 Theatre 2 Theatre 3

b1 0.56 0.89 0.11 b2 0.33 0.00 0.67 b3 1.00 0.00 0.33 b4 0.00 0.22 0.89 b5 0.44 1.00 0.78

TABLE V. THE NORMALIZED LOCATION OF ALL BUYERS.

Distance to the theatre (unit) Buyers Theatre 1 Theatre 2 Theatre 3

b1 0.10 0.00 1.00 b2 0.20 0.60 0.50 b3 0.80 0.50 0.00 b4 0.30 0.20 0.40 b5 0.90 0.90 0.70

Step 2: Forming Buyer Coalition

As previous mentioned, K-mean clustering method is a simply and fast clustering technique. The main steps of K-mean algorithm are modified from Jain and Dubes [6] using cosine similarity function. We apply this K-mean clustering algorithm [6] to form the buyer coalition steps, based on their reservation prices and their locations. These steps are as follows.

1) �Select an initial centroids with K clusters; repeat steps 2 and 3 until cluster membership stabilizes.

2) �Generate a new cluster by assigning each buyer to its closest cluster centroid.

3)�Compute new cluster centroids.

From example data in Table IV and Table V, we have b1and b5 which are members of coalition for theatre 1, b3 which is only one member for theatre 2 and b2, b4 which are member of theatre 3.

Step 3: Calculate Coalition Value

The value of all coalitions for each theatre is calculated in this step.

1) WHILE Kk ��1 2) Calculate )(Cv from

|||)(|)( kkCb

klk CCPrCvkkl

���

3) IF )( kCv < 0

- Eliminate the lowest reservation price klw - GOTO 2) 4) *

kC kC 5) GOTO 1) 6) END �If the price decreasing rate is 0.2, We have�

7)290()8588()( 1 ������Cv ,

149581)( 2 ����Cv and

6)290()9492()( 3 �����Cv . Therefore,� )( 3Cv is the winner coalition of theatre 3, when C1, C2, C3 is the coalition of buyer of theatre 1, theatre 2 and theatre 3 respectively.

IV. EVALUATION

In this section, we have used the simulation to show the performance of the presented GroupSimilarBuyer scheme.

A. Assumptions We make the following assumptions.

1) Sellers can supply unlimited tickets to buyers.

2) All theatres use the same price schedule.

B. Experiment Setup We performed 100 sets of experiments for 20 buyers

with the different of criteria used in the experiment. Table VI summarizes the simulation parameters in our evaluation when the number of buyers is 20. We assigned the price schedules to all tickets as the market price equal to 100, the lowest price is set at 80, and the price have declined by 5 in proportion to the number of buyers.

We used various price decreasing rate (PDR) determining the amount of discount. PDR is the ratio of the least number of buyers getting the lowest discount price to the number of buyers in a group [2]. For example, if PDR = 0.6, no discount will be given to the first two units purchased. Fig. 1 shows the sample price schedule with PDR = 0.6. Finally, the average result of the experiment is shown in Figure 2.

TABLE VI. SIMULATION PARAMETERS

Parameters Value The number of buyer 20 Distance between buyer to each theatre [0,1] Reservation price of each buyer [80,99] Price decreasing rate (PDR) 0.2,0.4, 0.6, 0.8, 1.0

418418418418

Figure 1. Price schedules, PDR = 0.6

V. RESULT AND ANALYSIS

This simulation compares the average standard deviation of GroupSimilarBuyer scheme with the conditions where price only, distance only and both price and distance. Table VII show that the mean of standard deviation of Price’s column is the best, when GroupSimilarBuyer scheme rely on only reservation price. The standard deviation of Distance’s column is highest and the mean of standard deviation in Price & Distance’s column is much closed to Price’s column.

TABLE VII. THE STANDARD DEVIATION WHEN PRICE-BASE CLUSTERING

Standard Deviation (SD)

Price Distance Price & Distance

Theater 1 0.20 0.30 0.23�Theater 2 0.20 0.30 0.27 Theater 3 0.27 0.29 0.30

Table VIII shows the observed average of standard deviation of Distance’s column which is lowest when GroupSimilarBuyer scheme rely on only distance. The standard deviation of Price’s column is highest and the mean of standard deviation of Price & Distance’s column closed to Distance’s column.

TABLE VIII. THE STANDARD DEVIATION WHEN DISTANCE-BASE CLUSTERING

Standard Deviation (SD)

Price Distance Price & Distance

Theater 1 0.28 0.18 0.22 Theater 2 0.27 020 0.25 Theater 3 0.27 0.25 0.29

Fig. 2 shows the simulation result of GroupSimilarBuyer scheme. The results of the simulation are divided into: a) group’s total utility is and b) the number of buyers who got the items.

a) Group’s total utility b) The number of buyer who got items

Figure 2. The average simulation result of GroupSimilarBuyer scheme

The group’s total utility is the sum of coalition value of all coalition. From Figure 2, (a) and (b), shows the average simulation result of GroupSimilarBuyer scheme. It is observed that both group’s total utility and the number of buyer who got items are similar to the experimental result of J. Yamamoto and K. Sycara [2].

VI. CONCLUSION

In this article, a new buyer coalition formation scheme, called GroupSimilarBuyer scheme, is proposed. Our new scheme consists of three steps. The first step is the preparation data. Then, a k-mean clustering algorithm is used for forming the coalition of buyers which are very similar in both reservation price and location of buyer in the second step. In final step, calculation the utility of each buyer coalition is done. The simulation result showed that the average of standard deviation of coalition are generated from GroupSimilarBuyer is nearly the best result where the K-mean algorithm rely on reservation price only, and distance of buyers only. Moreover, the buyers, in the winner coalition of new approach, do not pay more to subsidize other buyers; especially, the buyers who may make a buyer would hesitate to join the coalition, because we have the similarly coalition both reservation price and location of buyers.

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