在日益激烈的竞争中，决策和效率已成为组织获得竞争力的关键因素，但在管理实践中往往会出现以牺牲效率来达到决策优化的目的。为了在保证效率甚至提高效率的基础上优化组织的决策，本文首次从基于效率进行多属性决策的角度，将DEA方法和TOPSIS方法进行组合。DEA方法不仅可以对具有多种投入多种产出指标的组织的相对效率进行测算，还可求得决策单元（Decision Making Unit，DMU）各指标的松弛改进量，这使得DEA方法与TOPSIS方法进行组合在理论上是可行的。以首都医科大学为例，假设组织为了提高整体的效率竞争力，希望在2013年效率的基础上使有效DMU的个数增加，并在实现过程中使各指标松弛改进总量尽可能小（即使改变尽可能"容易"）。将首都医科大学附属的10所三甲综合医院作为DMUs，并运用DEA-TOPSIS组合方法，从提高技术效率的角度进行了研究。研究结果表明，DEA-TOPSIS组合方法不仅可以有效地对基于效率的决策备选方案进行排序，还可以通过选择不同的模型和指标处理方法以尽可能地反映实际情况，具有很强的实践价值。
In an increasingly competitive environment, decision making and efficiency have become to be the key factors. But in practice, managers usually appear to achieve the purpose of optimizing decision-making with the sacrifice efficiency. This practice is very easy to make managers in the dilemma of care for this and lose that.Therefore, ensuringor even improving efficiency is crucial during the process of optimization of decision making. However, no scholars have combined the data envelopment analysis(DEA) method with the decision method in existing researches, which is in order to solve the problem of optimizing the decision based on the current relative efficiency.From the perspective of multi criteria decision making,based on the current efficiency, the DEA method is firstly combined with technique for order preference by similarity to an ideal solution(TOPSIS) method. The DEA-TOPSIS integrated method can deal with the issue of multi criteria decision making on the base of efficiency assurance.DEA is a non-parametric method that measures therelative efficiencies of organizations, which is with multi inputs and outputs.This method also can calculate the inputs and outputs'slack improvements of ineffective decision making units(DMUs). These slack improvements provide a clear direction and goal for further decision making optimization based on the efficiency. TOPSIS method is widely used in multi criteriadecision making problems.As DEA method, TOPSIS method'sbasic idea is to sort alternatives according to the evaluation of ideal and negative ideal distance between the targets. So it is feasible in theory to integrate the DEA method and TOPSIS method.DEA-TOPSIS integrated method consists of two stages: the first stage is to measure theDMUs'relative efficiencyby DEA, and determine the decision alternatives set according to the efficiency values and decision goals. The second stage is to constructthe decision matrix according to the projections of inefficiency DMUs, then rank the alternatives using TOPSIS method. Taking Capital Medical University for example, the organization is assumed, in order to improve its efficiency, intend to increase the numbers of DEA efficient DMUs. Meanwhile the organization' objective is to minimize the slack improvements (i.e. let the revolution easier) during the efficiency improvement. The 10 class1, Grade 3 general affiliation hospitals as the DMUs, we study the technical efficiency by using the DEA-TOPSIS integrated method. 2008 ~ 2013 is taken as the observation period, and 3 inputs-including the number of employees(person), the purchase of medical equipment gross this year(million yuan) and the number of beds(zhang)-and 1 output-outpatients(person) are selected. The data are derived from the Beijing health Yearbook 2009~2014. The results show that DEA-TOPSIS method can not only rank the alternatives effectively, but also reflect the actual situation by choosing different models or index disposal methods. This research can provide some management ideas and references for similar organizations, such as administrations of hospital,education departments, group corporations, etc.
[1] Charnes A, Cooper W W, Rhodes E. Measuring the efficiency of decision making units[J]. European Journalof Operational Research, 1978, 2(6): 429-444.
[2] Liu J S, Lu L Y Y, Lu W M, et al. A survey of DEA applications[J]. Omega, 2013, 41(5): 893-902.
[3] Kawaguchi H, Tone K, Tsutsui M. Estimation of the efficiency of Japanese hospitals using a dynamic and network data envelopment analysis model[J]. Health Care Management Science, 2014, 17(2):101-112.
[4] Haelermans C, Ruggiero J. Estimating technical and allocative efficiency in the public sector: A nonparametric analysis of Dutch schools[J]. European Journal of Operational Research, 2013, 227(1): 174-181.
[5] Ebrahimnejad A, Tavana M, Lotfi F H, et al. A three-stage data envelopment analysis model with application to banking industry[J]. Measurement, 2014, 49: 308-319.
[6] 杜娟, 霍佳震. 基于数据包络分析的中国城市创新能力评价[J]. 中国管理科学, 2014, 22(6): 85-93.
[7] 陈聚祥, 曾培培, 陈亚运, 等. 基于 DEA 的全国中医类医疗卫生资源配置效率评价[J]. 中国卫生统计, 2016, 33(2): 271-273.
[8] 薛晖, 郑中华, 谢启伟. 基于多种 DEA 模型和 Gini 准则的效率评价方法——兼对我国高校运营绩效的评价[J]. 中国管理科学, 2014, 22(4): 98-104.
[9] Fuentes R, Lillo-Banuls A. Smoothed bootstrap Malmquist index based on DEA model to compute productivity of tax offices [J]. Expert Systems with Applications, 2015, 42(5): 2442-2450.
[10] Sueyoshi T, Goto M. DEA environmental assessment in time horizon: Radial approach formalmquist index measurement on petroleum companies[J]. Energy Economics, 2015, 51: 329-345.
[11] 王晓东. 产业升级和转移背景下广东工业行业效率变化实证研究——基于Malmquist 指数的分析[J]. 预测, 2010,(4): 75-80.
[12] 徐建中, 曲小瑜. 装备制造业环境技术创新效率及其影响因素研究——基于 DEA-Malmquist和Tobit的实证分析[J]. 运筹与管理, 2015, 24(1): 246-254.
[13] McDonald J. Using least squares and tobit in second stage DEA efficiency analyses[J]. European Journal of Operational Research, 2009, 197(2): 792-798.
[14] Samut P K, Cafri R. Analysis of the efficiency determinants of health systems in OECD countries by DEA and panel tobit [J]. Social Indicators Research, 2016, 129(1): 113-132.
[15] 曾薇, 陈收, 周忠宝, 等.金融监管对商业银行产品创新影响——基于两阶段 DEA 模型的研究[J]. 中国管理科学, 2016, 24(5): 1-7.
[16] 王有森, 许皓, 卞亦文. 工业用水系统效率评价: 考虑污染物可处理特性的两阶段 DEA[J]. 中国管理科学, 2016, 24(3): 169-176.
[17] Zeydan M, Çolpan C. A new decision support system for performance measurement using combined fuzzy TOPSIS/DEA approach[J]. International Journal of Production Research, 2009, 47(15): 4327-4349.
[18] Shafii M, Hosseini S M, Arab M, et al. Performance analysis of hospital managers using fuzzy AHP and fuzzy TOPSIS: Iranian Experience [J]. GlobalJournal of Health Science, 2016, 8(2): 137-155.
[19] 卞亦文, 许皓. 基于虚拟包络面和 TOPSIS 的 DEA 排序方法[J]. 系统工程理论与实践, 2013, 33(2): 482-488.
[20] 朱卫东, 吴鹏. 引入TOPSIS法的风险预警模型能提高模型的预警准确度吗?——来自我国制造业上市公司的经验证据[J]. 中国管理科学, 2015, 23(11): 96-104.
[21] 魏权龄, 评价相对有效性的数据包络分析模型: DEA和网络 DEA[M]. 北京:中国人民大学出版社, 2012.
[22] Banker R D, Charnes A, Cooper W W. Some models for estimating technical and scale inefficiencies in data envelopment analysis[J]. Management Science, 1984, 30(9): 1078-1092.
[23] Tone K. A slacks-based measure of efficiency in data envelopment analysis[J]. European Journal of Operational Research, 2001, 130(3): 498-509.
[24] Hwang C L, Yoon K. Multiple attribute decision making[M]. New York: Springer Verlag, 1981.
[25] 李美娟, 陈国宏, 林志炳, 等. 基于理想解法的动态评价方法研究[J]. 中国管理科学, 2015, 23(10): 156-161.
[26] 岳超源.决策理论与方法[M].北京:科学出版社,2003.
[27] 李刚, 迟国泰, 程砚秋. 基于熵权 TOPSIS 的人的全面发展评价模型及实证[J]. 系统工程学报, 2011, 26(3): 400-407.
