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報告人：陳明山 學 號： 917803

Measuring the Efficiency of Decision-making Units : Applied Data Envelopment Analysis. 報告人：陳明山 學 號： 917803. 1. A. Boussofiane, R. G. Dyson, E. Thanassoulis, “Applied data envelopment analysis,” European Journal of Operations Research (1991) 1-15.

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報告人：陳明山 學 號： 917803

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  1. Measuring the Efficiency of Decision-making Units : Applied Data Envelopment Analysis 報告人：陳明山 學 號：917803

  2. 1. A. Boussofiane, R. G. Dyson, E. Thanassoulis, “Applied data envelopment analysis,” European Journal of Operations Research (1991) 1-15 A. Charnes, W. W. Cooper, E. Rhodes, “Measuring the efficiency of decision making,” European Journal of Operations Research (1978) 429-444 2. 3. Chiang Kao, Yong Chi Yang, “Reorganization of forest districts via efficiency measurement,” European Journal of Operations Research (1992) 356-362 4. 5. 高強, 黃旭男, Toshiyuki Sueyoshi “管理績效評估 -資料包絡分析法,” 華泰文化事業公司 (2003) 97-117 Toshiyuki Sueyoshi, “Stochastic DEA for restructure strategy: an application to a Japanese petroleum company,” The International Journal of Management Science (2000) 385-398 Reference

  3. Outline ■Deterministic & Stochastic DEA ■Introduction for DEA ■Deterministic Model ■Case Study on Deterministic Model ■Drawbacks for Deterministic Model ■Stochastic Model ■Illustration ■Case Study ■Conclusion

  4. Deterministic & Stochastic DEA o 一般傳統DEA模式僅將過去確定的資訊納入DEA的運算架構中，稱為Deterministic DEA。若將未來不確定性資訊納入DEA的運算架構中，並以隨機過程予以描述，則稱為Stochastic DEA o高強, 黃旭男, Toshiyuki Sueyoshi “管理績效評估 -資料包絡分析法,” 華泰文化事業公司 (2003) 97

  5. Introduction for DEA1 In the simplest case where a unit has a single input and a single output, efficiency is defined simply as: output Efficiency = input 1 A. Boussofiane, R. G. Dyson, E. Thanassoulis, “Applied data envelopment analysis,” European Journal of Operations Research (1991) 1-15

  6. Introduction for DEA2 More typically organizational units have multiple inputs and outputs, defining the efficiency as: weighted sum of output Efficiency = weighted sum of input 2 A. Boussofiane, R. G. Dyson, E. Thanassoulis, “Applied data envelopment analysis,” European Journal of Operations Research (1991) 1-15

  7. Deterministic Model 3 where n= the number of units s= the number of outputs m= the number of inputs subject to ur = the weight given to output r vi = the weight given to input i yrj = amount of output r from unit j xij = amount of input i from unit j ur, vi ε; r=1, 2, …, s; i=1, 2, …, m j=1, 2, …, n 3 A. Charnes, W. W. Cooper, E. Rhodes, “Measuring the efficiency of decision making,” European Journal of Operations Research (1978) 429-444

  8. Deterministic Model 4 where n= the number of units subject to s= the number of outputs m= the number of inputs ur = the weight given to output r vi = the weight given to input i yrj = amount of output r from unit j xij = amount of input i from unit j ur, vi ε; r=1, 2, …, s; i=1, 2, …, m j=1, 2, …, n 4 CS Sarrico, RG Dyson“Using DEA for planning in UK university,” Journal of the Operations Research Society (2000) 789-800

  9. Case study5 on deterministic model Input Output 原始林 木蓄積 森林 遊樂 木材 生產 平均 蓄積 預算 勞力 面積 67.55 85.78 80.33 205.92 51.28 82.09 123.02 71.77 61.95 25.83 27.87 72.60 84.83 82.83 123.98 104.65 183.49 117.51 104.94 82.44 88.16 99.77 105.80 107.60 132.73 104.28 44.37 55.13 53.30 144.16 32.07 46.51 87.35 69.19 33.00 9.51 14.00 44.67 159.12 60.85 108.46 79.06 59.66 84.50 127.28 98.80 123.14 86.37 227.20 146.43 173.48 171.11 26.04 43.51 27.28 14.09 46.20 44.87 43.33 44.83 45.43 19.40 25.47 5.55 11.53 85.00 173.93 132.49 196.29 144.99 108.53 125.84 74.54 79.60 120.09 131.79 135.65 110.22 23.95 6.45 42.67 16.15 0.00 0.00 404.69 6.14 1252.62 0.00 0.00 24.13 49.09 文山 竹東 大甲 大雪山 埔里 巒大 玉山 楠濃 恆春 關山 玉里 木瓜 蘭陽 資料來源：1978~1988年林務局統計資料 5 Chiang Kao, Yong Chi Yang, “Reorganization of forest districts via efficiency measurement,” European Journal of Operations Research (1992) 356-362

  10. Drawbacks for Deterministic Model 傳統DEA模式將過去確定的資訊納入DEA的運算架構，作為未來決策考量，從現實觀點較不實際。然未來產出通常受外在經濟或其他變動因子影響，在未來績效進行預測時，將未來產出視為隨機性變數，較使用過去資料來預估為適切

  11. Case Study 6 日本連鎖便利商店實際投入與產出估計值 2004年 (產出預估值) 2003年 (投入) 投入及產出 估計值 資本 營業額(億日圓) 顧客數(人/時) 員工人數 分店數 便利商店 (萬日圓) 1720000 3350 7780 Seven-Eleven 1658500 1777 6531 Family Mart ？ 346295 322 664 HOTSPAR 2800 22 54 Apple Mart 6000 85 102 Everyone 7150 36 67 Caramel Mart 4000 162 866 Coco Store ‧ ‧ ‧ 6高強, 黃旭男, Toshiyuki Sueyoshi “管理績效評估 -資料包絡分析法,” 華泰文化事業公司 (2003) 112-117

  12. Case Study 6 日本連鎖便利商店實際投入與產出估計值 2004年 (產出預估值) 2003年 (投入) 投入及產出 估計值 資本 營業額(億日圓) 顧客數(人/時) 員工數 分店數 便利商店 (萬日圓) OP ML PE OP ML PE 1720000 3350 7780 Seven-Eleven 20341 19661 18981 411410 329128 246846 1658500 1777 6531 Family Mart 8978 8397 7816 203475 162378 119107 1058 883 708 21866 16839 11310 346295 322 664 HOTSPAR 73 64 55 1866 1409 933 2800 22 54 Apple Mart 235 175 114 5372 4263 3070 6000 85 102 Everyone 110 84 58 1968 1443 944 7150 36 67 Caramel Mart 1399 1288 1177 24245 18221 11673 4000 162 866 Coco Store ‧ ‧ ‧ OP:最樂觀估計值, ML:最可能估計值, PE:最悲觀估計值 6高強, 黃旭男, Toshiyuki Sueyoshi “管理績效評估 -資料包絡分析法,” 華泰文化事業公司 (2003) 112-117

  13. Case Study 6 根據經驗統計，樂觀估計值、最可能估計值與最悲觀估計值之機率分配為beta分配，可得到下列估計值： 6高強, 黃旭男, Toshiyuki Sueyoshi “管理績效評估 -資料包絡分析法,” 華泰文化事業公司 (2003) 112-117

  14. 表效率值之最大期望水準 表效率值大於 之可容忍誤差程度 ur, vi ε; r=1, 2, …, s; i=1, 2, …, m; j=1, 2, …, n Stochastic Model 7 where n= the number of units s= the number of outputs subject to m= the number of inputs ur = the weight given to output r vi = the weight given to input i yrj = amount of output r from unit j xij = amount of input i from unit j 7 Toshiyuki Sueyoshi, “Stochastic DEA for restructure strategy: an application to a Japanese petroleum company,” The International Journal of Management Science (2000) 385-398

  15. Stochastic Model Assume

  16. 表效率值之期望水準 表效率值大於 之可容忍誤差程度 ur, vi ε; r=1, 2, …, s; i=1, 2, …, m; j=1, 2, …, n Stochastic Model 7 where n= the number of units s= the number of outputs subject to m= the number of inputs ur = the weight given to output r vi = the weight given to input i yrj = amount of output r from unit j xij = amount of input i from unit j 7 Toshiyuki Sueyoshi, “Stochastic DEA for restructure strategy: an application to a Japanese petroleum company,” The International Journal of Management Science (2000) 385-398

  17. Illustration output inputs output y x1 x2 OP ML PE 2 6 1 2 3 2 U0 U1 2 5 1.5 2 2.5 2 當 → F-1(0.9)=1.282 Max hUO = 2u Subject to 2v1+6v2 = 1 hU0=0.06 u= 0.03 v1= 0.5 v2≒0 hU1=0.22 u= 0.11 v1= 0 v2≒0.2 1.6 v1+ 4.8 v2-{2u+ *1.282} 1.6 v1 - 4 v2 -{2u+ *1.282} u, v1, v2 10-4

  18. Case study 8 自第2次世界大戰以後，為確保供油穩定，日本石油產業一直受日本政府的保護，因此產油成本一直高居不下。日本政府立法通過自1997年4月開放民間營運石油產業，為因應市場開放及提高營運效率，是以日本石油公司於1997年委託進行本項研究，以作為未來營運策略參考 8 Toshiyuki Sueyoshi, “Stochastic DEA for restructure strategy: an application to a Japanese petroleum company,” The International Journal of Management Science (2000) 385-398

  19. Case study 8 INPUT (1998) OUTPUT ESTIMATE (1999) No of employees Size of station Operation cost Group Station Gasoline PE ML OP Petrol PE ML OP 420 480 530 . . . 500 540 600 170 200 220 . . . 120 140 155 10 . . . 9 958 . . . 1087 5203 . . . 1087 Large 1 . . . 20 Medium 21 . . . 40 5 . . . 7 513 . . . 628 3028 . . . 3634 140 180 210 . . . 230 250 280 45 60 70 . . . 100 115 135 Small 41 . . . 60 75 85 100 . . . 65 80 90 20 30 35 . . . 25 35 40 3 . . . 4 287 . . . 326 1307 . . . 1453 8 Toshiyuki Sueyoshi, “Stochastic DEA for restructure strategy: an application to a Japanese petroleum company,” The International Journal of Management Science (2000) 385-398

  20. Case study 8 β＝1.0 efficiency Group Station α=0.05 α=0.1 α=0.5 α=0.9 α=0.95 Large 1 . 20 mean S dev. 89.77 . 95.19 87.92 5.30 91.06 . 96.21 89.12 5.32 95.95 . 100.00 93.63 5.38 101.41 . 104.43 98.69 5.52 103.08 . 105.77 100.21 5.56 94.08 . 100.00 93.71 5.55 Med. 21 . 40 mean S dev. 60.51 . 70.77 67.61 8.60 59.68 . 69.65 66.64 8.45 63.61 . 75.02 71.28 9.17 67.02 . 79.82 75.39 9.85 68.03 . 81.29 76.64 10.05 65.35 . 73.62 70.89 8.90 Small 41 . 60 mean S dev. 62.17 . 53.57 54.40 8.41 63.01 . 54.34 55.21 8.53 66.17 . 57.30 58.31 8.99 69.68 . 60.62 61.80 9.51 70.74 . 61.63 62.87 9.67 69.88 . 61.40 59.61 8.09 8 Toshiyuki Sueyoshi, “Stochastic DEA for restructure strategy: an application to a Japanese petroleum company,” The International Journal of Management Science (2000) 385-398

  21. 4. 在隨機性模式假設隨機變數為常態分配( ，是否有其他分配更為合適，未來可進一步研究 Conclusion • 上述日本油業案例，隨機性模式與確定性模式結果相似，主要由於在隨機性模式之估計準確 2. 由敏感性分析結果可獲知各條件效率趨勢應為一致 3. 大型油站顯然較中小型油站有效率，而中型油站較小型油站有效率，建議中小型油站應著眼於進一步整併以提高營運績效

  22. Thanks for your attention

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