考慮屬性關(guān)聯(lián)的兩階段獲勝者確定模型

摘要： 研究了多屬性逆向拍賣的獲勝者確定問題。考慮屬性之間的兩兩關(guān)聯(lián),以定義在2-可加模糊測度上的Choquet積分表達(dá)拍賣人的偏好,其中模糊測度的值由拍賣人提供的偏好信息推測得出。由于一般情況下與偏好信息一致的模糊測度取值并不唯一,考慮所有一致的評分函數(shù)提出了兩階段獲勝者確定方法。首先采用線性規(guī)劃挑選出在任意評分函數(shù)下可能獲勝的報價,再通過混合整數(shù)規(guī)劃確定一個與所有一致的評分函數(shù)的評價結(jié)果最為接近的報價排序,以得分最高者為穩(wěn)健獲勝報價。仿真實驗表明,大量的報價為不可能獲勝報價,說明了在第一階段進(jìn)行篩選的必要性。與現(xiàn)有方法的比較表明了該方法的有效性,且在拍賣輪數(shù)較大、報價數(shù)目較多時,該方法在計算效率上更有優(yōu)勢。
Winner determination problem(WDP)is one of the most important research issues in multi-attribute reverse auctions.Presently,the additive value function is commonly used as the scoring rule to solve WDP,which ignores the interactions among the attributes in reality.To deal with the interacting effects,the Choquet integral defined on 2-order additive fuzzy measures is used in this paper to represent an auctioneer's preference,where the n+C_n~2 parameters are inferred by a set of indirect preference information in accordance with the preference aggregation-disaggregation paradigm.Generally,the scoring functions which could restore the auctioneer's preference are not unique.A two stage winner determination model is then proposed,which aimes at utilizing all the compatible scoring functions to determine the winner.In each round of an iterative auction,all the potential winning bids are first selected via a linear programming model.Then,a mixed integer linear programming model is developed to determine a ranking which is most close to the evaluations of all the compatible scoring functions.The bid with the highest score in this ranking will be the robust winning bid,which will be recommended to the auctioneer.The auctioneer's final decision will generate a feedback information to further refine the elicitation.Finally,a simulation experiment is conducted to evince the practical applicability of the method.The simulation results show that in general a large amount of bids are impossible to win,and the percentage increases with the number of bids in each round,which illustrates the necessity of choosing the potential winning bids in the first stage.The comparison with an existing approach verifies the validity and efficiency of the method.According to the simulation,the proposed method can identify all the outranked bids determined by the existing approach as losing bids.Moreover,unlike the existing method which will generate a set of"unknown bids",the proposed one can distinguish the potential winning bids from the offers.In computation efficiency,the running time of the proposed method is always less than the existing one in the same auction setting.Although both two methods will cost more time with larger rounds or more bids,the running time of the existing method increases more sharply,which proves the advantage of the proposed method in computation efficiency.