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Forming Buyer Coalitions with Bundles of Items

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

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Forming Buyer Coalitions with Bundles of Items

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  1. 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, Thailand Dickson K. W. Chiu, Dickson Computer Systems, 7 Victory Avenue, Kowloon, Hong Kong, P.R. China KES AMSTA 2009, June 5, 2009

  2. Outline of Presentation • Motivation for the research • Forming Buyer Coalitions with Bundles of Items • Example and Problem Formulation • Algorithm and Example Revisited • Simulation • Setup of Experiments • Results and Analysis • Discussion and Conclusion KES AMSTA 2009, June 5, 2009

  3. I. Motivation for the Research KES AMSTA 2009, June 5, 2009

  4. 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, 2009

  5. 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). KES AMSTA 2009, June 5, 2009

  6. II. Forming Buyer Coalitions with Bundles of Items KES AMSTA 2009, June 5, 2009

  7. II. Forming Buyer Coalitions with Bundles of Items: Example and Problem Formulation Pk KES AMSTA 2009, June 5, 2009

  8. 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, 2009

  9. II. Forming Buyer Coalitions with Bundles of Items: Example and Problem Formulation(Cont.) KES AMSTA 2009, June 5, 2009

  10. 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. KES AMSTA 2009, June 5, 2009

  11. 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. KES AMSTA 2009, June 5, 2009

  12. II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited(Cont.) KES AMSTA 2009, June 5, 2009

  13. 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, KES AMSTA 2009, June 5, 2009

  14. II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited(Cont.) KES AMSTA 2009, June 5, 2009

  15. 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 KES AMSTA 2009, June 5, 2009

  16. II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited(Cont.) KES AMSTA 2009, June 5, 2009

  17. 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 Cwill be formed to purchase the package if there is at least one member of coalition C wants to purchase any items in the package orwhen and. KES AMSTA 2009, June 5, 2009

  18. II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited(Cont.) KES AMSTA 2009, June 5, 2009

  19. 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, whencondition1) for andand condition2) KES AMSTA 2009, June 5, 2009

  20. II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited(Cont.) KES AMSTA 2009, June 5, 2009

  21. II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited(Cont.) • Step 4: which give the maximum will be chosen. KES AMSTA 2009, June 5, 2009

  22. II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited(Cont.) KES AMSTA 2009, June 5, 2009

  23. 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. KES AMSTA 2009, June 5, 2009

  24. II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited(Cont.) KES AMSTA 2009, June 5, 2009

  25. 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. KES AMSTA 2009, June 5, 2009

  26. II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited(Cont.) KES AMSTA 2009, June 5, 2009

  27. II. Forming Buyer Coalitions with Bundles of Items: Algorithm and Example Revisited(Cont.) KES AMSTA 2009, June 5, 2009

  28. III. Simulation KES AMSTA 2009, June 5, 2009

  29. III. Simulation: Setup of Experiments Table 3: summarizes the simulation parameters. KES AMSTA 2009, June 5, 2009

  30. III. Simulation: Setup of Experiments(Cont.) KES AMSTA 2009, June 5, 2009

  31. III. Simulation: Results and Analysis • The results of the simulation are divided into three categories: • 1) the numberof 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. KES AMSTA 2009, June 5, 2009

  32. III. Simulation: Results and Analysis: Fig. 1 KES AMSTA 2009, June 5, 2009

  33. 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. KES AMSTA 2009, June 5, 2009

  34. III. Simulation: Results and Analysis: Fig. 2 KES AMSTA 2009, June 5, 2009

  35. 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, 2009

  36. 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. KES AMSTA 2009, June 5, 2009

  37. 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. KES AMSTA 2009, June 5, 2009

  38. III. Simulation: Results and Analysis : Fig 3 (Cont.) KES AMSTA 2009, June 5, 2009

  39. 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. KES AMSTA 2009, June 5, 2009

  40. IV. Discussion and Conclusion KES AMSTA 2009, June 5, 2009

  41. 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. KES AMSTA 2009, June 5, 2009

  42. 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. KES AMSTA 2009, June 5, 2009

  43. 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. KES AMSTA 2009, June 5, 2009

  44. Thank you for your participation KES AMSTA 2009, June 5, 2009

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