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1 2001 3

2 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 43 i

3 5.4 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 79 2 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 121 ii

4 1 1.1, [34] ( 12 ) ( ) [30][31][32][33][34] 3 2 ( ) 3 2 [23] [35] (2 2.1 )

5 1.1: ( ) ( ) ( ) : 2 2

6 1.2: = N / Nn 2 3 [35] 2 1 3

7 1.2: 3 (-:,=:,N:,/:,+: ) / - = N = = / N N / / / - - / - / - - N N / - / / / / = = / / / / / = / - N N / / - / = = = / N N / / N N / / / - = = = / - - N N / / - / / / = = / - - N / = = N N / / - - / = = / - - / / - = N N / / / - - / N / - / = = / - - N N / - - / - = = / - / / - N N / - = = / / - / N N / / - / = = = / - / = = N N / / / / / / / = = / - - / N N / - - = / - - / / = = N N / / / - - / = / - N N / / - - = / / / - / = / - / = = N N / / = = / N / = = = / N N / / / / - - = / - = = = / - / / N / / - = = / - - / = = = / = N N / - - / / = = N N / / = = / - - / + - / = = / / - / N N / = N N / + - / - / / / = N N / / / / = = / - - = / / - / = = / / - - N N / - = / - - N N / / - - / / / / - - / - - / - = = N N / - = = / / / = = N N / / / N / = = / - - = = / / - - N N / / = / / N N / - / - = / / - / / = = N N / - - / / - / - = / N N / / + = = N = / / - N N / / - - = = / - / / = = / / - = / N N / / / = N N / / - = = / / - - / - = = N N / - / / / - = = N N / / / = = / / - / - = = N N / - - / - - / / N N / - - / / / / = = / / - N N / = / - = = / = = / - - / / / - / - - N N / = = / - - / - N N / = = / - = / - N N / - = = / - = / / - + / N N / - - = = = / - - / - / : =: N:

8 1.3: 2 (-:,Nn:,/:,+: ) / - Nn + 1 N n / / - - / - N n / + - / - N n N n / N n / / / N n N n / / / N n N n / / / - - N n N n / / / N / - - N n / - - / N n / / - - N n / - / / / N n N n / / / / / / / - / - / / / n / / - N n N n / / - N n N n / - / - N n N n / / - / / - - / / N n N n / - / - N n N n / N n / / / / N n N n / - - / N n / / / N n / / N n / N n / - / N n / / - - N n / N n / / / / N n N n / N n / / - N n N n / / / - / / N n N n / - / / N N n / / / N n / / + N n / - - / N n / - / - - N n / / - N n N n / / - - / N n / - / / / - / - N n / n / / - / / N n N n / / / N n / / - - / N n N n N n / / / - - N n / - - / - N n / - - N n / - - / - - / / N n / / - N n / - / / N n / + + N n / - / N n / - / N n / / - - / / - - / N n / / / N n / - / N n n / - / / / - - N n / - - / / - N n / / / N n N / N n / / + N n / / / N n / - - N n / / N n / N n / N n / - - N n / / / N n N n / / - / / / / / / / - N n / - - N n / - - / N n / / - N n / / - N n / - - / - - / N n / - / - - N n N n / / / - - N n N n / / / N n / / - N n / - - N n / - / - - N n / / / / - N n / / N n N n / / / N n N n / / / - - N n N n / - + N n / - - N n / - - / - N n / - + / / n N n / N n / / / / N n / / / / N n N N n / / / - - / N n N n / / / - - N n / + - N n / N n / N n / / - - N n / - - N n / / - / / / N n N n / / N n / / N n / / - N n / N n / / / / / N n N n / - - / / N n N n / - / - - / N / / / - N n / - - N n / / / - / N n N n / N n / / - - N n / - / - N n N n / - / / N n / - - N n / / / - N n / / - - / - N n N n / - - / N n N n / / / N n N n / / - + N n / - - N n / / / / N n / N n N n / - + / N n / - - N n / - - N n / / / / / / N n N n / / N n N n / / / / / N n / N n N n / / / N n N n / + / / / + + / + N n / / N n / / / / / N n N n / - / / N n N n n / / / / - + / N n N n / N n / - - / N n N n / / - / / / - - / - / / / - - / - / / / - - / - / / / - - / : Nn:

9 j Φ ΦΦß i ρ ρ ρ= 1.3: ( ) [29][35][36][37][38][39] 6

10 [39] [36] [36][38] 1.4 Smith-Daniels,Schweikhert and Smith-Daniels[14] Siferd and Benton[13],Li and Benton[5] Miller[8] 1 Warner[16] 3 (3 ) Warner Miller Warner Musa and Saxena[9], Rosenbloom and Goertzen[12], Venkataraman and Brusco[15] Arther and Ravindran[1] 3 1 7

11 1 1 [2][6] 7 [7][12] 7 [11] 7 14 [3][4][8][15][16] [2][10][11][16] 3 [1][4][6][10][11][16] 2 [2][3] Millar and Kiragu[7] [28] , [20] 22 [34] [23]

12 ( ) ( )

13 [19] A 6.8 (40 ) 1 30 (

14 4 4 2 (85.2 ) B ( ) ( ) ( ) (2 ) 12

15 2.1: ( ) (1) (2) (3) 2.2: ( ) (1) (2) (3) 13

16 2.3: (1) 4 (2) (3) C ( ) ( )

17 2.4: (1) (2) 15

18 2.5: (3 ) (1) (2) (3) 4 2.6: (2 ) (1) (2) 2 7 (3)

19 : (1) (2) (3) D (3) (1)(2)(4) E (2 )

20 2.8: (1) (2) (3) (4) ( ) 2 4 ( 8 ) (1) 6 (2) 24 (3) 22 (4)

21 [23] ( 8 ) (34 ) 16 (43 ) 2 (2.1 ) 8 2 ( 3 ) A ( ) 3 ( 6 ) [34]

22 ( ) B ( ) ( )

23 2.9: (1 ) ( ) 2.10:

24 (a) (b) (a) (b) ( ) 22

25 ( ) ( ) (float nurse) [4][7][15] 2 ( ) 23

26 ( ) ( 1) ( 2) ( 3) ( 4) ( 5)

27 [21][22][26] m n w M = f 1, 2,:::, mg : N = f1,2,:::,ng : W = f 1, 2,:::, wg : R = frjr g G r = fiji r g, r 2 R F 1 = f(i; j; k);i2 M; j 2 N; k 2 W j i j k g F 0 = f(i; j; k);i2 M; j 2 N; k 2 W j i j k g P h = f(k 1 ;k 2 ;:::;k h );k 1 ;k 2 ;:::;k h 2 W j k 1 ;k 2 ;:::;k h g, h 2f2; 3;:::g Q h = f(k; u; v);k2 W;u;v 2f0; 1; 2;:::gj k, h u v g, h 2f2; 3;:::g d jk ;j 2 N; k 2 W : j k a rjk ;r 2 R; j 2 N; k 2 W : j k r b rjk ;r 2 R; j 2 N; k 2 W : j k r c ik ;i2 M; k 2 W : i k e ik ;i2 M; k 2 W : i k x ijk ;i2 M; j 2 N; k 2 W : i j k 1, S = fsjs g f s (x ijk ; i 2 M ; j 2 N ; k 2 W );s2 S : x ijk s ( ) 25

28 1 X min f s (x ijk ;i2 M; j 2 N; k 2 W ) (3.0) s2s subject to X i2m x ijk d jk j 2 N; k 2 W (3.1) X a rjk» x ijk» b rjk i2g r r 2 R; j 2 N; k 2 W (3.2) X c ik» x ijk» e ik j2n i 2 M; k 2 W (3.3) x ijk = fi (i; j; k) 2 F fi ; fi 2f0; 1g (3.4) hx ff=1 u» X k2w x i j+ff 1 kff» h 1 i 2 M; j 2f1;:::;n h +1g; (3.5) hx ff=1 (k 1 ;k 2 ;:::;k h ) 2 P h ; h 2f2; 3;:::g x i j+ff 1 k» v i 2 M; j 2f1;:::;n h +1g; (3.6) (k; u; v) 2 Q h ; h 2f2; 3;:::g x ijk =1 i 2 M; j 2 N (3.7) x ijk =0or 1 i 2 M; j 2 N; k 2 W (3.8) (3.0) (3.1) j k (3.2) j k r (3.3) i k (3.4) i j k (fi =1) k (fi =0) (3.5) j h (3.6) j h k (3.7) i j 1 (3.8) x ijk (3.1) 2 (3.2) 3 (3.3) 4 (3.4) 5 (3.5) (3.7) (3.1) (3.2) (3.3) (3.7) 26

29 3.1 i x ijk i x ijk (3.3) (3.7)... x ijk... (3.1)(3.2) HY H H@ H@ H Ψ... x ijk : i j k 0-1 (3.3)(3.4)(3.5)(3.6)(3.7) 3.1: 1 5 ( 6 ) ( 3 ) ( 4 ) ( ) 4 ( +1) 1 (3.6) (3.6) (3.5) ( ) (3.5) (3.6) (3.5) k x ijk k P k 0 2W;k6=k 0 x ijk 0 (3.5) 27

30 (3.1) (3.8) A = f(r 1 ;r 2 ;j;k;g);r 1 ;r 2 2 R; j 2 N; k 2 W j j k r 1 r 2 g g X i2g r 1 x ijk X i2g r 2 x ijk» g (r 1 ;r 2 ;j;k;g) 2 A (3.9) (3.1) ( ) G r = M r (3.2) 2 [25] n ( 1 (3.3) (3.4) (3.5) (3.6) (3.7) ) i 2 M P i q 2 P i ffi iqjk (j k 1 0) 1 x ijk i q iq ( q 1 0) x ijk = X q2p i ffi iqjk iq i 2 M; j 2 N; k 2 W (3.10) X q2p i iq =1 i 2 M (3.11) 1 (3.0) (3.2) 2 f 0 s iq s 2 S 0 ( ) 28

31 2 X min fs( 0 iq ;q 2 P i ;i2 M) (3.12) s2s subject to X X ffi iqjk iq d jk i2m q2p i j 2 N; k 2 W (3.13) X X a rjk» ffi iqjk iq» b rjk q2p i r 2 R; j 2 N; k 2 W (3.14) X i2g r iq =1 q2p i i 2 M (3.15) iq =0or 1 i 2 M; q 2 P i (3.16) (3.12) (3.13) j k (3.14) j k r (3.15) i 1 (3.16) iq ( ) ( 1 (3.3) (3.7) ) 2 P i d jk a rjk b rjk 29

32 ... iq... iq : i q 0-1 (3.13)(3.14)» = Z} Z Z Z = 1 Z (3.15) 1 3.2:

33 2 [24] 1 (3.5) (3.6) (3.5) (3.6) (1) 7 1 (2) ( ) (3)1 ( 3 4 ) 3 1 ( 1 ) 1 2 (1)(2)(3) 3 4 (3.5) (3.6) (3.3) (3.4) ( ) (3.13) (3.14) A B (1)(2)(3) (8+4+3) 2=30 AB (2+1+1) 2= (8+4+3) 30 Ξ 21 = 21: (2+1+1) 30 Ξ 21 = 5:

34 (3.14) (3.14) 2 (3.14) d jk a rjk m ( ) ( ) 2 32

35 [21] 33

36 ( ) [26] q 2 P i ;i 2 M ( 2 (3.13) (3.14) ) ( 1 (3.3) (3.7) ) 1 (3.1) (3.8) i 2 M : i i i ( ) ( ) 2 (3.13) (3.14) w jk ;u rjk ;v rjk 0 ff jk ;ff+ jk ;fi rjk ;fi+ rjk ;fl rjk ;fl+ rjk 0 i i0 q;q 2 P i 0;i 0 2 M; i 0 6= i 0 1 i 2 M

37 X X X X X X X min w jk ff jk + j2n k2w r2g subject to X X i 0 2M q2p i 0 X X i 0 2G r q2p i 0 X X i 0 2G r q2p i 0 X j2n k2w u rjk fi rjk + X r2g j2n k2w v rjk fl + rjk (4.1) ffi i0 qjk i0 q + ff jk ff + jk = d jk j 2 N; k 2 W (4.2) ffi i0 qjk i0 q + fi rjk fi + rjk = a rjk r 2 R; j 2 N; k 2 W (4.3) ffi i0 qjk i0 q + fl rjk fl + rjk = b rjk r 2 R; j 2 N; k 2 W (4.4) iq =1 q2p i (4.5) iq =0or1 q 2 P i (4.6) ff jk ;ff+ jk 0 j 2 N; k 2 W (4.7) fi rjk ;fi+ rjk ;fl rjk ;fl+ rjk 0 r 2 R; j 2 N; k 2 W (4.8) i i i i q 2 P i (3.13) (3.14) ( ) (ff jk ff+ jk fi rjk fi+ rjk fl rjk fl+ rjk ) 0 35

38 ( ) y Ω Ωffi : 2 n jrj n 2 jrj r j k jRj(j 1) + jrj(k 1) + r 36

39 4 ( ) ( ) ( ) S i2m P i 1 ( ) m ( ) 1 ( ), = P i ( ) = ,0,0,0,1,1,0,0 ( 29 )

40 v Q QQQ Q QQQ v v Qv A A A AA AA AA A A A AA AA AA v v v v v v v v v ΠE Π EE Π Π E EE Π Π Π ΠE EE E EE Π Π Π ΠE EE E EE Π Π Π ΠE EE E EE Π Π Π ΠE EE Π Π Π Π Π Π Π Π Π vvvvvvvvvvvvvvvvvvvvvvvvvvv Π Π Π Π Π Π Π Π Π 6 E EE Π Π Π ΠE EE E EE Π Π Π ΠE EE E EE Π Π Π ΠE EE E EE Π Π Π ΠE EE E EE 4.2: v Q QQQ Q QQQ v v Qv A A Q A AA AA AA A A A AA AA AA v v v v v v v v v Π E Π EE Π Π E EE Π E Π EE Π Π E EE Π E Π EE Π Π E EE ΠE Π EE Π Π E EE Π Π Π ΠE EE Π Π Π Π Π Π Π Π Π Π vvvvvvvvvvvvvvvvvvvvvvvvvvv yyyπ yπ Πy Π Π Πy Π Π E EE Π Π Π ΠE EE E EE Π E Π EE Π Π E EE 6 Π Π Π ΠE EE E EE Π Π Π ΠE EE E EE 4.3: 38

41 2 3 3 ( ) ( 4.3 ) ( ) ( ) 27 6 m m m ( ) 39

42 (1.1 )

43 5.2 2 ( 2 (3.13) (3.14) ) 3 2 P i ;i2 M w jk ;u rjk ;v rjk W = fnight; dayg 2 1 q 2 P i ;i 2 M (i; j; k) 2 F q 2 P i ;i2 M ffi iqjk j ffi iqj night 1 j 0 ffi iqj day j 1 j (3.7) (4.2)(4.3)(4.4) 5 ( P k2w ffi iqjk» 1;j 2 N; q 2 P i ;i2 M.) 41

44 5.1: N n N n / N n N n / N n / z } 4 z } 3 5.2: 3 Nn:,/:, : N n / N n / N n / N n / N n / z } 3 w jk ;u rjk ;v rjk v rj day q 2 P i ;i2 M 5 i : / N n / N n / / N n / / N n / N n / / q 2 P i ;i2 M ffi iqj night ;j 2 N j ffi iqj day =

45 w j night, u rj night, v rj night P 8i 2 M; P i P P i ;i2 M q 0 ( ) ( ) q 0 P i P i Big i Big Pk2W maxf0;c ik P j2n ffi iq0 jkg iq0 X X X min w jk ff jk + j2n k2w r2g X j2n X k2w u rjk fi rjk + X r2g 43 X X j2n k2w v rjk fl + rjk

46 +Big X k2w maxf0;c ik X j2n ffi iq0 jkg iq0 (5.1) 1 TL i z i z Λ i q (counter ) exchanged iq ( 6) TL ( 5) ( ) exchanged iq 1 ( 1 8) 0. P P 1. P P i 2 M P i exchanged iq = 1;q 2 P i 2. i 2 M q 0 P i = P i [fq 0 g 3. i 2 M q 0 q i = q 0 4. counter =1 5. i 2 M TABU i = fqjexchanged iq counter TLg[fq i g q i q 2 (P i n TABU i ) z i i iq =0;q 2 TABU i 6. z Λ = min i2m z i i q Λ q i q 0 = q i ;q i = q Λ q 0 = q 0 P i = P i nfq 0 g exchanged iq 0 = counter counter = counter z Λ =0 q i ;i2 M 5 8. i 2 M P i exchanged iq = 1;q 2 P i 9. i 2 M q 0 P i = P i [fq 0 g 10. i 2 M q 0 q i = q 0 44

47 11. counter =1 12. z Λ = ABC B 1 ( 19) 2 3 C 1 ( 28) P i P ffi iqj night ;j 2 N ffi iqj day ;j 2 N ( 19 8 ) (3.0) (3.8) P i 45

48 N n / N n / N n / N n / N n /? N n / N n / / N n / N n / N n / z } N n / N n / N n / N n / / / N n / z } 2 5.1: Nn:,/:, : 46

49 : / / / N n / + / 2 / / / / * / / * 3 N n / / / / 4 N n / / N n / / A 5 N n / 6 n / N n / 7 + N n / + / / 8 / / N n / + + / / x 9 N n / + + N n / / 10 / + + / 11 / / / N n / + / / 12 N n / / / / 13 / / N n / / / N n / 14 N n / / / B 15 n / N n / + / N n / 16 N n / N n / N n / 17 / / N n / / / N n / / / 21 / / 22 / / N n / / 23 N n / + / x C 24 n / + N n / + 25 / + N n / N n / N n / 26 / / / / N n / N n + 27 / N n / / + / + 28 N n / + (Nn:, :,+:,/:,*:,x: ) 47

50 5.5: A B C

51 w jk ;u rjk ;v rjk v rj day ;r 2 R; j 2 N TL z Λ = P 4.9 P Sun SS

52 5.6: / Nn + 1 n / / + N n / N n / N n / / N n / / N n / N n / / N n / N n / N n / / / N n / / N n / N n / / / N n / N / N n / N n / N n / / N n / / N n / N n / N n / N n / / / N n / / / / N n / N n / N n / N n / / + N n / / N n / / / N n / N n N n / N n / / N n / / / N n / N n / N n / / / + N n / N n / / N n / / / N n / / N n / N n / N n / N n / N n / + N n / N n / / / / / N n / / N n / N n / N n / N n / N / N n / N n / / N n / N n / N n / N n / / / / / N n / N n / N n / + N n / N n / / N n / / N n / N n / N n / N n / / / N n / N n / N n / + N n / / / N n / N n / / N n / N n / + N n / N n / / N n / / / N n / / N n / N n / N n / / N n / N n / N n / N n / / N n / N n / N n / N n / / N n / N n / / N n / N n / / + N n / N n / / N n / N n N n / + / / N n / N n / N n / n / / N n / N n / N n / N n / N / N n + / N n / / / N n / N n / n / / / N n / + / N n / + N n / N n / / / N n / N n / : Nn:

53 5.7: A B C

54 5.8: / Nn + 1 n / / / / + N n / N n / N n / / N n / / N n / N n / / N n / N n / / N n / / / N n / / N n / / N n / / / / N n / / N / N n / N n / N n / / N n / / N n / / / N n / / / N n / / / N n / / / N n / / / / N n / N n / N n / / / N n / / / / + N n / / N n / / / N n / / / N n / / / + + N n / N n / / N n / / / N n / N n / N n / / / + N n / / N n / / N n / / / / N n / / N n / / / N n / / / N n / N n / N n / + / N n / N n / / / / / N n / / / N n / / N n / N n / / / N n / N / N n / N n / / N n / / N n / / N n / / N n / / / / / / N n / / N n / / N n / / + N n / / N n / / N n / / N n / N n / N n / N n / / / / N n / N n / / / N n / / + N n / / / N n / / N n / / / N n / / N n / / + N n / N n / / N n / / / / / / / / + + / / / / N n / / N n / / N n / N n / / N n / / N n / / N n / N n / / / N n / / / N n / N n / N n / / N n / / N n / / N n / / / N n / / / + N n / / N n / / / N n / N n / N n / + / / N n / / / N n / N n / n / / N n / / N n / N n / / N n / / N / N n + / N n / / / / / N n / N n / / n / / / N n / + / N n / + / N n / N n / / / / / / N n / / N n / / / : Nn:

55

56 6 [27] ( ) q 2 P i ;i2 M (5 5.1 ) ,4,5,6,8,9,11,12,18,

57 N n / N n / N n / N n / N n /? N n / N n / / N n / N n / N n / z } N n / N n / N n / N n / / / N n / z } N n / N n / / N n / N n / N n / z }? ( ) N n / N n / / N n / N n / N n / 6.1: Nn:,/:, : 55

58 6.1: ( ) / Nn + 1 n / / N n / + N n / N n / N n / / N n / / N n / N n / / N n / N n / N n / / / N n / / N n / N n / / N n / N / / / N n / N n / / N n / N n / N n / N n / N n / N n / / / N n / / N n / N n / N n / / / N n / / + N n / / N n / / / N n / N n N n / + + N n / N n / N n / / / N n / / / N n / + N n / N n / / N n / N n / / N n / / / N n / N n / N n / N n / + N n / N n / / / / / N n N n / / N n / N n / N n / / N n / N n / / N n / N n / N n / N n / / / / / N n / N n / N n / / / + N n / N n / / N n / N n / N n / N n / N n / / / N n / N n / N n / / / + N n / N n / N n / / N n / + N n / N n / / N n / / / / N n / / N n / N n / N n / / N n / N n / N n / N n / / N n / N n / N n / N n / / N n / N n / / N n / N n / / + N n / N n / / N n / N n N n / + / / N n / N n / N n / n / / N n / N n / N n / N n / N / N n + / N n / / / N n / N n / n / / / N n / + / N n / + N n / N n / / / N n / N n / N : Nn: ( : Nn:2 +: /: ) 56

59 q 2 P i 1 P i2m jp i j q i q 5.4 ( 6.1) 97% ( ) 1 1 ( ) : Nn / / N n / N n / N n / N n / (1) / / N n / N n / N n / N n / N n / (2) N n / N n / N n / N n / / / N n / 4 1 (9 ) ( ) (1) (2) 1 (9 ) 57

60 q i q Λ 2 ( ) q q 0 nx j=1 jffi iqj night ffi iq0 j nightj (6.1) (0,2,4,...) 1 1 (1,3,5,...) 2 (2,4,8,...) 6.2 (1) (2) 1 (1) (2) ( 6.1) ( ) 1 47, w jk ;u rjk ;v rjk 5.4 v rj day 0 1 TL =

61 6.2: 1 6.3: 2 59

62 (P i ) : ( 1) : ( 2) , % 98% 60

63 6.5: 1 2 ( ) : 61

64 6.3 DIFF i P i q i DIFF ~ Pi k = night ~ Pi ~P i = fqj nx j=1 jffi iqjk ffi iq i jkj»diff; q 2 P i g (6.2) q 2 P i q i DIFF ~ Pi ITE ITE= P P 1. P P i 2 M P i exchanged iq = 1;q 2 P i 2. i 2 M q 0 q i = q 0 3. i 2 M ~ Pi = P i counter =1 4. i 2 M TABU i = fqjexchanged iq counter TLg[fq i g q i q 2 ( ~ Pi n TABU i ) z i 5. z Λ = min i2m z i i q Λ q i q 0 = q i ;q i = q Λ Pi ~ ( Pi ~ = fqj P n j=1 jffi iqjk ffi iqi jkj» DIFF; q 2 P i g) exchanged iq 0 = counter counter = counter z Λ =0 q i ;i2 M counter ITE 4 62

65 DIFF DIFF = 10 DIFF =1; 2; 3; DIFF = GATEWAY G6-266(OS:FreeBSD2.2.2) 6.6: (DIFF =1; 2; 3; 10) ( ) DIF F (78) (34) 18.0 (972) (47) 31.4 (972) 10( ) 71.3 (47) (972) 6.5: (DIFF =1 10) 1 DIFF 3 2 DIFF 2 DIFF

66 DIFF DIFF =1 1 2 DIFF = (ITE = z Λ =7) 1 ( 1 ) ( 6.4 ) DIFF DIFF 1 2 DIFF DIFF 2 1 DIFF ~ Pi q i q 2 P i q i DIFF ~ Pi DIF F DIF F 64

67 TL w jk ;u rjk ;v rjk DIFF TL ( ) w jk ;u rjk ;v rjk (w j day = u rj day = 1;v rj day = 0 w j night = u rj night = v rj night 1 5 ) TL TL TL ( 1 ) 65

68 6.6: TL 30 ( 1) 6.7: TL 30 ( 2) 66

69 6.8: ( 1 TL 30) 6.9: ( 1 TL 50) 67

70 6.10: ( 2 TL 30) 6.11: ( 2 TL 50) 68

71 2 3.5 ( )

72 70

73 OR NEC USA, NEC America SVP OR 71

74 72

75 [1] Jeffrey L. Arther and A. Ravindran. A multiple objective nurse scheduling model. AIIE transactions, Vol. 13, No. 1, pp , [2] Peter C. Bell, Genevieve Hay, and Y. Liang. A visual interactive decision support system for workforce (nurse) scheduling. INFOR, Vol. 24, No. 2, pp , [3] Kathryn A. Dowsland. Nurse scheduling with tabu search and strategic oscillation. European Journal of Operational Research, Vol. 106, No. 2 3, pp , [4] Brigitte Jaumard, Fr ed eric Semet, and Tsevi Vovor. A generalized linear programming model for nurse scheduling. European Journal of Operational Research, Vol. 107, No. 2, pp. 1 18, [5] L. X. Li and W. C. Benton. Performance measurement criteria in health care organization: Review and future research directions. European Journal of Operational Research, Vol. 93, No. 3, pp , [6] Joe D. Megeath. Successful hospital personnel scheduling. Interfaces, Vol. 8, No. 2, pp , [7] Harvey H. Millar and Mona Kiragu. Cyclic and non-cyclic scheduling of 12 h shift nurses by network programming. European Journal of Operational Research, Vol. 104, No. 3, pp , [8] Holmen E. Miller, William P. Pierskalla, and Gustave J. Rath. Nurse scheduling using mathematical programming. Operations Research, Vol. 24, No. 5, pp , [9] A. A. Musa and U.Saxena. Scheduling nurses using goal-programming techniques. IIE transactions, Vol. 16, No. 3, pp , [10] Irem Ozkarahan and James Bailey. Goal programming model subsystem of a flexible nurse scheduling support system. IIE Transactions, Vol. 20, No. 3, pp , [11] Sabah U. Randhawa and Darwin Sitompul. A heuristic-based computerized nurse scheduling system. Computer & Operations Research, Vol. 20, No. 8, pp ,

76 [12] E. S. Rosenbloom and N. F. Goertzen. Cyclic nurse scheduling. European Journal of Operational Research, Vol. 31, No. 1, pp , [13] Sue Perrott Siferd and W. C. Benton. Workforce staffing and scheduling: Hospital nursing specific models. European Journal of Operational Research, Vol. 60, No. 3, pp , [14] Vicki L. Smith-Daniels, Sharon B. Schweikhert, and Dwight E. Smith-Daniels. Capacity management in health care services:review and future research directions. Decision Sciences, Vol. 19, No. 4, pp , [15] R Venkataraman and Mj Brusco. An integrated analysis of nurse staffing and scheduling policies. Omega, Vol. 24, No. 1, pp , [16] D. Michael Warner. Scheduling nursing personnel according to nursing preferense : A mathematical programming approach. Operations Research, Vol. 24, No. 5, pp , [17],,.. 36, pp , [18],,.. 37, pp , [19],,,,,.., Vol. 71, No. 10, pp , [20], , pp , [21],,.., Vol. 41, No. 8, pp , [22], , pp , [23],.. ( ), [24] , pp , [25],.. OR, pp ,

77 [26],. 2. Journal of Operations Research Society of Japan, Vol. 41, No. 4, pp , [27]. 2. Journal of Operations Research Society of Japan, Vol. 43, No. 3, pp , [28].., Vol. 44, No. 11, pp , [29]. 5., Vol. 3, No. 5, pp , [30]. 59., [31]. 62., [32]. 2., [33]. 5., [34]. 8., [35].. Nursing Today, Vol. 12, No. 5, [36]. 4., Vol. 3, No. 4, pp , [37]. 3., Vol. 3, No. 3, pp , [38]. 1., Vol. 3, No. 1, pp , [39]. 2., Vol. 3, No. 2, pp ,

78 1 2.3 A : ( ) ( )

79 B. [17] [18] 7.1 (a) 1 (b) 5 (c) 7.1: 3 80

80 (a) 1 (b) 5 5 (c) 3 (1 ) 30 ( ) ( 10 2 ) (1) 5 1 (2) (3) (d) (e) (f) 1 1 (g) 5 7 ( ) 5 (h) (i) ( ) ( 24 ) ( 32 ) 81

81 4 5 5 ( 3 )

82 ( ) 1 C (1) (2) (3) (4) (5) (6) (7) (1)

83 (2) (3) (4) ( ) (5) (6) ( ) (7) ( ) 84

84 [19]

85 5 ( ) (12 42 ) : ( )

86 7.2: ( ) ( ) ( ) ( ) ( )

87 7.3:

88 7.4:

89 7.3: (1) (2) (3)

90

91 7.4: (1) (1 6 ) (3 11 ) ( ) (2) (3)

92 7.5: ( ) (1) (2) (3) ( ) 93

93 : ( ) (1) (2) (3) ( )

94 7.7: (1) (2) (3) 29 ( ) 7.8: (1) (2)

95 (2 )

96 7.9: (3 ) (1) (2) (3) ( ) 97

97 7.10: (2 ) (1) (2) 7 2 (3)

98 : (1) 31 (2) 1 1 (3)

99 : (1) ( ) (2) (3) (4)

100 : (1) ( ) (2) (3) (4)

101

102 7.14: (1) (2) (3) (4) ( ) (5)

103 27 ( ) (1) 6 (2) 24 (3) 22 (4)

104 [23] : (3 1 2 ) ( 8 ) ( ) ( ) ( )

105 7.16:

106 :

107 7.6:

108

109 (

110 [1,2,3]7 [1,2]4 [2,3]8 [1,3]5 [2,3,5]1 111

111

112 7.17:

113 7.18:

114 7.19:

115 :

116 7.21:

117 : ( ) : ( ) (3 ) (2 )

118 : ( )

119 7.25: ( ) 2 3 ( ) 21 ) ( ) ( ) ( ) 120

120 (DIF F = 1) 4 1 (DIF F = 2)

1 n 1 1 2 2 3 3 3.1............................ 3 3.2............................. 6 3.2.1.............. 6 3.2.2................. 7 3.2.3........................... 10 4 11 4.1..........................

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