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c 1. 2 2011 2012 0.248 0.252 1 Data Envelopment Analysis DEA 4 2 180 8633 3 3 1 IT DHARMA Ltd. 272 0122 1 14 12 13.10.7 14.5.27 DEA-AR (Assurance Region) 1 DEA 1 1 [1] 2011 2012 220 446 [2] 2. [2] 1 1 9 (RF : Range factor) 47240Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.

1 2012 20 RF 0 0 3 0 8 1 1 0 4 4 6 2 0 5 3 8 5 3 0 8 0 1 0 0 7 1 7 1 19 0 9 0 0 RF 0 3 8 0 8 1 2 0 4 6 6 2 0 5 0 5 5 3 0 5 0 2 0 0 7 0 7 1 18 0 8 0 0 9 RF 1 UZR (Ultimate Zone Rating) Defensive Runs Saved : DRS 2011 2012 60 1 144 1 2012 20 20 1 1 2 2011 2 2011 2012 7 (1/5) 1 (1/7) 1 6 (1/10) 36 (6/7) 2 5 (1/8) 13 (2/13) 3 3 (1/6) 30 (3/7) 4 (1/7) 2 (1/4) 1 (1/19) 4 (2/21) 2 (2/19) 3 (1/21) 8 (3/19) 14 (7/21) 2011 2012 55 (6/6) 24 (2/4) 1 19 (1/11) 14 (4/11) 2 7 (2/9) 7 (1/7) 3 21 (3/7) 44 (7/8) 8 (1/5) 2 (1/7) 2 (2/21) 4 (2/19) 1 (1/21) 5 (3/19) 5 (4/21) 1 (1/19) 34 18 (a/b): 220 b a 3. 2011 2012 220 446 (DEA) DEA / 9 1 1. / 2. / 3. / 4. / 5. / 6. / 7. / 8. / 2014 8 Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.41473

9. / 1 0 2012 0.312 0.194 x (x 0.194)/(0.312 0.194) DEA CCR [3] o F 1 n M 9G 1 x gh (=1): h g y jh: h j θ =max M u jy jo u jy jh G v gx gh 0 g=1 (h =1,...,n; h o ) G v gx go =1, u 2 2u j (j 2) g=1 v g 0(g =1,...,G), u j 0(j =1,...,M) 1 h o 1 3 (u 2 2 u j (j 2)) 2 1 (G =1) 1 4 5 u jy jh 1 (h =1,...,n; h o), u j 0(j =1,...,M) v g i k S(i, k) DEA-AR SS I(i, k, j)= 1 : i k j 0: 6 6 Ce Pa 1: 2 :13 :24 :3 5: 6 :7 : A(i, j) =1: i j 0: A(i, j) S(i, k) [ DEA-AR ] I(i, k, j) k F 1 max I(i, k, j) S(i, k) i,k,j SS I(i, k, j) A(i, j) =c j; i,k c j =1(j 6),c 6 =3 3 1 I(i, k, j) =Q [Q =8,Q=9] i,k,j I(i, k, j) 1, I(i, k, j) {0, 1} k,j 4 I(i, k, j) A(i, j) =1; k 6 6 1 i,j I(i, 6,j) A(i, j) =P [P =3,P =4] i,j 6 3 best9 DEA (DEA best9) Ce11 2011 2012 2 θ hih u j[j =1,...,M] i 4 h i 47442Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.

3 4 θ hi 2012 Ce11 best9 DEA best9 437 437 1 596 596 2 615 615 3 518 518 590 590 578 578 606 583 643 276 Ce12 best9 DEA best9 556 556 1 359 359 2 593 224 3 575 394 619 619 653 229 631 631 422 246 Pa11 best9 DEA best9 264 397 1 372 498 2 633 633 2 622 582 633 633 578 578 463 463 653 304 577 622 Pa12 best9 DEA best9 328 316 1 601 290 2 505 505 3 498 390 567 567 597 597 567 567 525 595 507 290 θ =0.611 u j[j =1,...,M] θ hh<θ hi h i θ hh>θ hi h i best9 DEA best9 θ hh>θ hi h i 3 224 5 i h 0.980 0.611 0.594 0.898 350 DEA best9 () Ce11 Ce12 437 556 1 596 359 2 615 593 3 518 394 590 619 578 653 583 631 515 422 6 350 DEA best9 Pa11 Pa12 397 439 1 498 601 2 633 505 3 582 390 633 567 578 597 463 567 653 595 622 584 best9 DEA best9 best9 359 350 DEA best9 5 6 7 3 best9 5 6 DEA 2011 best9 8 8 5 DEA best9 (u 2 2u j (j 2)) 2 best9 6 2011 DEA best9 3 2014 8 Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.43475

7 best9 DEAbest9 Ce11 Ce12 Pa11 Pa12 606 579 60 180 25 6 76 1 1 25 13 0.31 6 643 583 44 170 23 8 55 0 0 60 4 0.29 6 515 477 73 133 13 2 72 0 5 33 23 0.28 6 583 494 85 133 25 1 94 1 4 84 23 0.27 6(62 ) 575 516 58 130 27 1 85 2 6 54 12 0.25 4 394 356 23 95 5 1 38 16 1 23 3 0.27 4 372 342 48 92 21 0 72 0 2 28 10 0.27 2 498 437 45 117 20 7 52 18 3 40 9 0.27 2 577 529 81 137 21 3 84 0 7 41 17 0.26 622 525 116 141 30 4 134 0 6 91 48 0.27 4 582 525 83 148 38 27 128 3 3 51 25 0.28 4 498 432 79 100 17 2 125 0 1 66 27 0.23 4 390 360 56 108 35 16 63 0 2 33 9 0.3 4 525 477 61 149 35 8 68 1 4 43 3 0.31 6 595 523 45 141 17 54 104 12 4 56 4 0.27 6 507 461 76 129 32 2 130 0 3 45 21 0.28 584 512 41 143 29 6 98 40 0 32 9 0.28 5 6 2012 DEA best9 7 10 DEA best9 8 6 2011 DEA best9 2011 2012 202 4. 4.1 DEA u j o 220 (u 2 2u j (j 2))2 8 350 DEA best9 10 Pa11 Pa12 397 439 1 498 601 2 633 505 3 622 390 633 567 578 597 559 595 653 567 463 583 3 (a, b) u a/u b L ab U ab 2 L ab U ab DEA-AR (a, b) u a/u b L ab U ab DEA-AR M 47644Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.

n (DEA-AR) θ o =max M u jy jo u jy jh 1 (h =1,...,n; h o) u kl jk u j u ku jk ( j k) u j 0(j =1, 2,...,[M =9]) 4.2 4.1 o θ o 3 F 1 350 60 10 (1) 9 350 DEA best9 2011 best9 54 35 best9 15 1 (2) 7 10 6 4 c 7 =1, I(i, 6,j) A(i, j) =4, I(i, k, j) =9 i,j i,k,j 10 350 DEA best9 10 2011 2012 2 9 DEA best9 best9 2011 [243] 2012 [252] (3) 108 (6) 250 1 (6) 157 (5)* 75 2 (2)* 15 (6) 206 3 (6) 184 (6)* 68 (1) 216 (3) 239 (6) 238 (1) 248 (4)* 54 (2) 231 (5)* 35 (4) 112 * 3 best9 () [] 10 DEA best9 best9 2011 [207] 2012 [204] (6)* 3 (6)* 14 1 (3)* 26 (4) 135 2 (2) 175 (6)* 5 3 (4) 142 (3)* 34 (6) 187 (6) 201 (6) 194 (6) 192 (1)* 7 (5) 101 (6) 129 (2)* 27 (5)* 187 + (1)* 54 + * 3 best 9 () [] + 2011 2012 3 best9 3 1 best9 best9 best9 3 54 24 DEA best9 best9 5. 4 (DEA best9) (1) 220 2014 8 Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.45477

11 best9 SS0 3 3DEA 5, 6 8 9, 10 Ce11 8.680 8.992 8.767 8.611 Ce12 7.984 8.277 8.132 8.125 Pa11 8.858 9.336 9.280 9.198 9.154 Pa12 9.213 10.005 9.530 9.445 9.407 3 (2) 350 5 6 (3) 350 10 8 (4) 350 10 9 10 (1) (2) DEA best9 best9 (4) 220 350 SS 220 best9 SS0 11 4 best9 best9 220 350 1 0.95 UZR DRS [1] T. Ueda and H. Amatatsu, Determination of bounds in DEA assurance region method: Its application to evaluation of baseball players and chemical companies, Journal of the Operations Research Society of Japan, 52, 453 467, 2009. [2] http://bis.npb.or.jp/2011/stats/ http://bis.npb.or.jp/2012/stats/ [3] DEA 1993. 1. 1 Ce11 2011 32 (5/6) 32 6 5 1 1 1 1 2011 2012 RF 1 1 2 1 2. DEA-AR (a, b) 47846Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.

1 (a/b) 1 2 3 Ce11 32 (5/6) 29 (7/7) 37 (4/6) 45 (1/5) 44 (5/6) 6 (6/20) 7 (7/20) 10 (10/20) 19 (2/6) 21 (1/7) 14 (3/6) 3 (3/5) 6 (1/6) 42 (12/20) 45 (15/20) 40 (10/20) 11 (3/6) 17 (4/7) 32 (4/6) 15 (1/5) 27 (2/6) 30 (12/20) 33 (14/20) 31 (13/20) 27 (1/6) 20 (7/7) 9 (3/6) 19 (1/5) 4 (4/6) 39 (10/20) 43 (14/20) 42 (13/20) RF 14 (5/6) 1 (1/7) 22 (6/6) 30 (4/5) 25 (6/6) 29 (1/20) 35 (5/20) 32 (2/20) (2/6) Ce12 34 (4/9) 30 (6/7) 41 (1/8) 60 (6/8) 56 (7/7) 17 (16/24) 19 (18/24) 13 (13/24) 28 (5/9) 32 (2/7) 23 (8/8) 3 (3/8) 7 (1/7) 47 (8/24) 44 (5/24) 51 (12/24) 9 (1/9) 21 (5/7) 14 (2/8) 49 (2/8) 20 (1/7) 42 (16/24) 31 (12/24) 36 (14/24) 32 (2/9) 16 (2/7) 7 (2/8) 23 (2/8) 1 (1/7) 43 (5/24) 37 (1/24) 47 (8/24) RF 11 (5/9) 1 (1/7) 12 (1/8) 35 (3/8) 23 (3/7) 34 (1/24) 45 (7/24) 37 (2/24) (6/9) Pa11 21 (1/9) 18 (2/7) 41 (3/7) 55 (4/6) 47 (2/6) 6 (6/22) 20 (18/22) 9 (9/22) 32 (8/9) 36 (6/7) 17 (5/7) 1 (1/6) 10 (4/6) 48 (13/22) 40 (5/22) 45 (10/22) 1 (1/9) 10 (1/7) 22 (1/7) 52 (2/6) 40 (2/6) 1 (1/22) 48 (22/22) 1 (1/22) 40 (7/9) 13 (1/7) 7 (3/7) 17 (1/6) 1 (1/6) 49 (15/22) 48 (14/22) 34 (5/22) RF 9 (3/9) 5 (5/7) 17 (3/7) 30 (1/6) 21 (1/6) 31 (1/22) 37 (3/22) 40 (6/22) (3/9) Pa12 34 (8/9) 19 (2/6) 36 (1/5) 50 (3/5) 40 (1/7) 7 (7/20) 16 (16/20) 2 (2/20) 19 (2/9) 32 (5/6) 17 (5/5) 2 (2/5) 13 (7/7) 46 (14/20) 40 (8/20) 50 (18/20) 7 (3/9) 5 (1/6) 22 (1/5) 48 (2/5) 47 (6/7) 21 (9/20) 40 (16/20) 20 (8/20) 26 (2/9) 13 (1/6) 9 (5/5) 21 (3/5) 4 (3/7) 44 (12/20) 46 (14/20) 45 (13/20) RF 9 (3/9) 3 (3/6) 13 (1/5) 31 (3/5) 21 (2/7) 27 (2/20) 35 (5/20) 33 (4/20) (6/9) (a/b) : 60 b a u a/u b L ab U ab 1 2 3 4 5 6789 6 6 10 9 1. 2. 3. 4. 5. 6. 7. 8. 9. (m =)6 6 1 2 9 3 2 1 1 8 3 1 8 1 2 1 139 3 2014 8 Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.47479

1 139 7 k t k 7 t 7 1 t k t k i j k t k i j f ij =log e t k ln t k [1] N M j μ j μ N N μ j = f ij/n, μ = f ij/(nm) i=1 i=1 D B D W D T D B = μ j μ /M N D W = { f ij μ j /N }/M i=1 N D T = f ij μ /(NM) i=1 = D B + D W D T t k =10 kd B + D W C 2 D B + D W = C 2 D B D W t k v v +(s 1 s 2)=0,s 1 0, s 2 0 (A1) C(1 b) s 1 0, C b s 2 0, b {0, 1} (A2) C: (A3) (s 1 + s 2) v (A2) s 1 s 2 =0s 1 s 2b D B + D W = C 2 D B t k F 2 t k F 2 max (s 1j + s 2j)/M D B N N : μ = f ij/(nm), μ j = f ij/n i=1 i=1 μ j μ + s 1j s 2j =0; j =1, 2,...,M μ j μ = s 1j + s 2j[ (A1)] (s 1j + s 2j)/M D B =0 D B M C 2(1 b j) s 1j 0, M C 2 b j s 2j 0, b j {0, 1} [ (A2) MC 2 (A3) C ] f ij μ j + t (1) ij t (2) ij =0 f ij μ j = t (1) ij + t (2) ij N i=1 (t (1) ij + t (2) ij )/(NM) D W =0 D W t (1) ij 0, t (2) ij 0: i =1,...,N; j =1,...,M D B + D W = C 2 : ln(t k) ln(t k+1) C 0 : k =1,...,m; t m+1 =1 s 1j,s 2j,t (1) ij,t (2) ij (i =1,...,N; j =1,...,M), t k(k =1,...,m+1),D W,D B N =10, M =9, m =6, C 0 = (ln 9)/20 ln t 1 =ln9 ln t 7 =0 (ln 9)/6 C 0 k t k 4 j μ j = 10 fij/10 5 i=1 3 1 1 (t 1) 5 2 (t 2) 4 3 (t 3) 1 48048Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.

μ 2 = {5ln(t 1)+4ln(t 2)+ln(t 3)} /10 = 2.10 μ j 1 μ j 2 2 2 3 2 1 2 3 2 3 1 h j k t k =exp(f hj) [ln t k = f hj] 6 3 1 2 2 4 t 2 7.78 6 1 2 7.78 a b r ab L ab U ab 1 h 2 4 r 24 7 1 r 24 =7.78 2/6.97 4= 1.12 1 7 L 24 =0.90 U 24 =1.55 (a, b) L abu ab 0.4 (max k μ k) >μ j j 1 0.4 (max k μ k)=0.4 2.10 = 0.84 5 1 0.84 1 79 [] 0.4 L abu ab DEA-AR 2 1 1 2 3 4 5 6 1 8 2 4 5 6 7 2 2 4 5 8 6 3 3 8 4 2 3 5 6 4 8 2 5 4 6 3 5 2 8 4 3 6 5 6 2 5 8 4 6 3 7 2 8 5 6 4 3 8 5 2 8 3 4 6 9 2 8 3 4 5 6 10 8 2 4 6 5 3 3 1 1 2 3 4 5 6 7 8 9 1 7 2 7 3 4 5 6 1 7 2 7 1 6 2 3 5 7 4 7 3 7 3 4 2 5 6 7 1 7 4 7 2 6 4 3 5 7 1 7 5 7 1 4 3 6 5 7 2 7 6 7 1 6 4 2 5 7 3 7 7 7 1 6 5 3 4 7 2 7 8 7 2 4 5 1 6 7 3 7 9 7 1 3 4 5 6 7 2 7 10 7 2 6 3 5 4 7 1 7 7 4 F 2 t k t 1 t 2 t 3 t 4 t 5 t 6 1 8.687 7.783 6.973 6.248 5.598 5.015 2 8.887 7.962 5.953 5.333 4.778 1.116 3 8.641 7.742 6.936 6.215 5.568 4.989 4 8.719 7.812 6.999 6.271 5.619 5.034 5 8.825 7.907 7.085 6.347 5.687 5.095 6 8.112 7.268 6.512 5.834 1.246 1.116 5 j μ j 1 2 3 4 5 6 7 8 9 1 0 2.10 1.55 1.89 1.87 1.71 0.16 2.05 0 2 0.03 1.75 0.36 1.63 1.78 2.15 0.17 1.51 0 3 1.41 1.95 1.89 0 1.97 0.19 1.61 0.70 1.58 4 2.14 1.38 1.96 0 1.63 0 1.94 0.49 1.81 5 1.64 2.01 1.88 0 1.93 0.16 1.87 0.33 1.60 6 0.07 1.91 0.11 0.21 1.79 0.85 1.30 1.82 0 2014 8 Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.49481

6 1 h j exp(f hj) 1 2 3 4 5 6 7 8 9 1 1 7.78 1 6.97 6.25 5.60 5.02 8.69 1 2 1 8.69 5.02 7.78 6.97 5.60 1 6.25 1 3 1 6.97 6.25 7.78 5.60 5.02 1 8.69 1 4 1 7.78 5.02 6.25 6.97 5.60 1 8.69 1 5 1 8.69 6.25 6.97 5.02 5.60 1 7.78 1 6 1 8.69 5.02 6.25 7.78 5.60 1 6.97 1 7 1 8.69 5.02 5.60 6.97 6.25 1 7.78 1 8 1 7.78 6.25 5.60 8.69 5.02 1 6.97 1 9 1 8.69 6.97 6.25 5.60 5.02 1 7.78 1 10 1 7.78 5.02 6.97 5.60 6.25 1 8.69 1 7 1 h 2 4 r 24 1 2 3 4 5 6 7 8 9 10 h r 24 1.12 1.12 0.90 1.25 1.25 1.39 1.55 1.39 1.39 1.12 48250Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.

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