| 摘要: | 資料包絡分析(Data Envelopment Analysis, DEA)係廣為使用的研究方法，能評估具多投入及多產出決策單位(Decision-making Units, DMUs)的相對效率。然而，資料包絡分析存有兩個主要缺陷。其一係未能提供足夠的績效資訊用以排序有效率單位；其二則為難以建構完善的卓越標準(standard of excellence)用以標竿評選新單位。本研究基於非輻射型(Non-radial)架構，嘗試發展兩個相應的資料包絡分析替代模式，以解決上述缺陷。針對排序有效率單位議題，本研究提出雙效率前緣模式，同時融入最優與最劣效率前緣進行效率測量。有效率單位規劃求解之效率值愈高，意味著其具備愈好的非劣水準。與超效率模式比較結果顯示，雙效率前緣模式能(1)避免無可行解問題、(2)提供更穩健效率值及(3)檢視有效率單位的非劣特性。本研究以2015年台灣固體廢棄物(Municipal Solid Waste, MSW)資源回收資料為例，應用雙效率前緣模式評估20縣市政府廢棄物資源回收績效。其中，原近半數(45%)難以區別的有效率縣市政府被依其非劣水準進行排序。而透過差額分析，研究發現有效率縣市政府的非劣水準主要源自於人均預算與設備剩餘所導致。有關標竿評選新單位議題，本研究擴充Zhu (2002)輻射型(Radial)標竿模式至非輻射型標竿模式。所提非輻射型標竿模式為一階混合0-1線性規劃問題，而非植基於差額為基礎模式(Slacks-based measure, SBM)與超效率差額為基礎模式(Super SBM)的二階段方法。研究發現非輻射型標竿模式具以下優勢:(1)考慮投入與產出差額、(2)當新單位凌駕標竿，避免無可行解問題、(3)求解之標竿與投影點具備柏瑞圖最適效率(Pareto efficiency)及(4)可評價新單位為強凌駕或弱凌駕特性。本研究以2015-2016美國職業籃球聯賽(National Basketball Association, NBA)自由球員標竿評選為例，檢視模式的應用性。研究結果除表明非輻射型標竿模式能揭露候選自由球員與既有球員間的績效差距，作為球隊聘僱球員的參酌依據，更實證本研究於運動科學領域之貢獻。;Data envelopment analysis (DEA) is a widely used approach to measure the relative efficiency of peer decision-making units (DMUs). However, when implementing DEA, two primary issues arise. One is lack of offering enough information for ranking the efficient DMUs, and the other is failure to build a proper standard of excellence for benchmarking the new DMUs. In order to overcome these two issues, this dissertation attempts to develop two alternative models based on the non-radial framework of DEA. For ranking the efficient DMUs, a dual frontiers model that considers not only the best frontier, but also the worst frontier is proposed. The higher the efficiency of efficient DMUs implies the better its non-inferior level. Differ from the well-known super-efficiency model, the dual frontiers model can:(1) avoid the problem of infeasibility, (2) provide more robust efficiency score, and (3) further examine the non-inferiority for efficient DMUs. The proposed model is applied to a Municipal Solid Waste (MSW) recycling data in Taiwan during the year 2015, where nine out of 20 administrative regions originally deemed as commensurate are ranked depending on their non-inferior levels. Furthermore, this study found that the main sources of non-inferiority arise from the per capita budget and equipment. On the side of benchmarking the new DMUs, this dissertation extends the Zhu’s (2002) work by developing a non-radial benchmarking model that is unified as a mixed 0-1 linear program instead of a cumbersome two-stage approach combining both slacks-based measure (SBM) and super SBM in sequence. The proposed model has following merits: (1) it takes slacks into assessment, (2) it overcomes the infeasibility problem, (3) it guarantees that the benchmarks and projections are strongly Pareto-efficient, and (4) it classifies outperformance status into strong and weak. We illustrate the proposed model with a National Basketball Association (NBA) player recruitment case in the 2015-2016 regular season. The results not only show that our model can provide new insights into gap between candidates and the team’s benchmark players for a NBA team, but also evidence the salient contributions of this dissertation in sport science domain. |
