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Unformatted text preview: 1. 1. ---- ---- ---- ---- ---- 30 50 7 25 8 10 8 24 WBS WBS(Work Breakdown Structure) WBS WBS WBS """""" WBS "" WBS 0 1 2 A B C D E F G H K 3 A B C D E F G H K WBS : WBS : 0 1 2 WBS WBS : 0 1 2 3 WBS : 0 1 2 WBS 1000 1100 1110 1111 1112 1113 1120 1121 1122 1123 1200 WBS 0 1000 1 1100 1200 1300 1400 2 1110 1120 1210 1220 1310 1320 1330 1410 1420 3 1321 1322 1323 0 1000 1 1100 1200 1300 1400 1500 1600 2 1410 1420 1430 1440 1610 1620 1630 3 1411 1412 1000 1100 1200 1x00 1x10 1x11 1x12 WBS 1) 2) 3) 4) 5) J K I 1 A 2 B 1 C 2 D 1 E 2 F 1 G 2 H 1 2 I J G' H' WBS . WBS . WBS -- 1 0 1 0 1 1 A 1.1.1 1.1.2 1 2 B 1 2 B 1 1 A 1.1.1 1.1.2 WBS 1 1.1 1.2 2 2.1 2.2 2.3 2.3.1 2.3.2 2.4 2.4.1 2.4.2 2.4.2.1 2.4.2.2 2.4.2.3 3 3.1 3.2 3.3 3.4CD/VCD ( ) D X X A WBS ( ) WBS WBS 1 1.1 1.2 1.3 2 2.1 2.2 2.3 P P P S P P Beth Jim Jack Rose Steve Jeff Tyler Cathy Sharon Hannah Joe Gerri Maggie Gene Greg S S S P P S S P P S S S S S S S S S S S S P S 1-- 2-- 3-- 4-- 5-- 6-- WBS 6 2 5 2 2 2 2 1 1 3 3 3 3 1 5 3 3 3 3 3 3 3 1 4 1 4 4 4 1 1 1 1 1 3 3 4 1 4 4 4 4 1 1 1 1 1 3 3 4 4 1 4 4 1 1 1 1 1 3 3 4 4 4 4 4 1 4 3 4 3 4 3 4 3 5 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 A B GERT/VERT . AON , ( ) A C E B D F 1 (Finish) (Start) FST( FTS) A FST SST( STS) A SST B B 2 FFT( FTF) A B FFT SFT( STF) A SFT B (1) ---- A B B A A B 1 5 2 1 (2) ---- C A B D E (3) -- B SS5 A FS10 FF4 C D (3 ) -- SS5 B A D FS10 C FF4 AOA, ( ) 2 C 4 A 1 E 6 B 3 D 5 F 1 ---- ---- b c a 1 a b 3 c 4 b 1 3 2 a 2 c d a b c 4 1 c a b a b 3 c d 4 2 5 1 5 2 1 3 2 ---- 1 a b c a 4 3 c 5 4 b 3 2 a b a b 1 a1 2 a2 3 a3 4 b1 5 b2 6 b3 7 1 a1 2 a2 b1 4 a3 b2 6 3 5 7 b3 8 2 ---- a b a c b c d a 1 2 c 4 d b 3 5 A C A B D A C B D GERT VERT P--07 110 120 130 140 150 160 110 120 130 140 150 120 130 140 150 160 20 20 15 90 30 30 -- 1 2 3 4 5 6 7 8 A B C D E F G H - E Steve 2 A Susan 3 B Susan 10 C Susan 20 D Susan 5 F Steve 10 I Steve 65 K Jim 7 L Jim 8 M Jim 10 G Andy 12 J Andy 5 H Susan 2 - E 2 6 F 10 A 3 B 10 C 20 D 5 7 I 65 K 7 L 8 M 10 1 2 3 4 5 G 12 J 5 10 11 12 13 9 H 2 8 -- 1 2 3 4 5 6 7 8 9 -- 1 1 3 2 4,5 6 4,5 7,8 ( ) "3. " 4 " 4. " "7. " 6 " 9. " -- 1 2 3 4 5 6 7 8 A B C D E F G H -- -- A A A BE DCF D 2 1 2 2 2 4 2 1 CPM a b m PERT t (a+4m+b)/6 15 9 18 t=(9+415+18)/6=14.5 100 110 111 112 120 121 122 123 130 131 132 133 134 140 141 142 143 144 150 151 152 1600 1600 1600 3200 800 2400 2000 4800 3200 1600 1600 3200 2400 1600 1600 20 20 10 20 10 20 10 40 20 10 10 20 20 20 20 ( ) A B C D E F G H G' H' J K -- A G C,H A B,E E F,G G H C,G',H' I D,J #1 5 #2 5 #1 #2 #1 #2 #1 #2 #1 #2 I 26 18 5 5 4 5 21 21 28 28 3 2. (1) CPM PERT PERT CPM CPM PERT a m b t PERT CPM ES EF LS LF TF FF ES ES MAX{ EF} EF EF ES t 38 40 E Steve 2 0 3 3 13 13 33 33 38 38 48 48 113 113 K Jim 120 7 120 L Jim 128 8 128 138 A Susan 3 B Susan 10 C Susan 20 D Susan 5 F Steve 10 I Steve 65 M Jim 10 38 50 50 55 G Andy 12 J Andy 5 38 H Susan 2 40 38 E 2 40 6 38 F 10 0 1 A 3 3 2 3 B 10 13 3 13 C 20 33 4 33 38 D 5 5 38 48 7 48 113 I 65 113 10 120 K 7 120 11 L 8 128 12 128 138 M 10 13 50 9 50 60 J 5 G 12 38 40 H 2 8 ( ) B 2 E 8 A 3 C 7 F 6 G 5 D 4 LF LF MIN{ LS} LS LS LF-- t 38 40 E Steve 2 46 0 3 3 13 13 33 33 38 38 48 48 48 113 113 K Jim 113 120 7 120 120 L Jim 120 128 8 128 128 138 A Susan 3 0 3 B Susan 10 3 13 C Susan 20 13 33 D Susan 5 33 38 F Steve 10 38 38 48 50 I Steve 65 48 50 113 55 M Jim 10 128 138 G Andy 12 96 38 108 40 J Andy 5 108 113 H Susan 2 106 108 38 E 2 46 48 38 F 10 0 1 0 A 3 3 3 2 3 3 B 10 13 13 3 13 C 20 13 33 33 4 33 33 38 D 5 38 5 38 50 9 50 60 J 5 108 113 G 12 96 38 40 H 2 106 108 108 38 48 48 7 48 48 113 I 65 113 10 113 113 120 K 7 120 120 11 120 L 8 128 128 12 128 128 138 M 10 138 40 6 13 8 ( ) 3 5 10 18 B 2 E 8 0 3 A 3 3 10 10 16 18 23 C 7 F 6 G 5 3 7 D 4 ( ) LF--EF LS--ES min{ES( )} --EF ( ) ( ) 3 5 10 18 B 8 2 10 E 10 8 18 0 3 A 0 3 3 3 10 10 16 18 23 C 3 7 10 F 12 6 18 G 18 5 23 3 7 D 8 4 12 -- (FTS): : ESj =EFi +FTS EFj =ESj +Dj : LFi =LSj -FTS LSi =LFi - Di : FFi =ESj -FTS -EFi i FTS j ( 1) STS -- (STS): : ESj =ESi +STS LSi =LSj -STS i j : : FFi =ESj -STS -ESi ( 2) -- (FTF): : EFj =EFi +FTF LFi =LFj -FTF i FTF j : : FFi =EFj -FTF -EFi ( 3) STF -- (STF): : EFj =ESi +STF LSi =LFj -STF i j : : FFi =EFj -STF -ESi ( 4) STS : : Max ESj =ESi +STS EFj =ESj +Dj EFj =EFi +FTF ESj =EFj -Dj : Min LSi =LSj -STS LFi =LSi +Di LFi =LFj -FTF LSi =LFi -Di i FTF j Max Min : SS 15 FS 5 1 10 2 30 3 20 SF 15 FF 5 A 1 30 1 B 20 1 C 10 ( ) SS 15 1 10 FS 5 2 40 3 20 ( ) SS 15 0 0 10 15 0 55 30 5 50 1 0 0 FS 5 10 10 2 15 0 40 55 3 35 5 20 55 ( ) SS 15 SF 15 A 1 30 2 B 20 3 C 10 FF 5 ( ) SS 15 SF 15 15 0 35 20 5 30 0 0 30 A 1 0 0 B 30 30 C 20 3 25 5 2 15 0 10 35 35 FF 5 ( ) SS 4 C 7 E 8 A 3 FS 8 B 2 F 6 G 5 FF 3 D 4 ( ) SS 4 3 4 10 7 4 15 C 0 0 3 7 3 0 6 7 14 15 5 E 11 15 8 4 19 0 21 19 15 0 24 A 0 0 3 3 B 9 2 2 11 0 15 F 15 6 0 21 G 5 19 0 24 FS 8 11 FF 3 D 11 4 0 15 IPMP ES NO D LS FF LF TF EF IPMP SS 1 A 2 B 4 C 3 E 1 FF 1 FS 1 D 2 IPMP SS 1 0 0 2 1 0 5 5 0 8 A 2 0 0 2 4 B 4 1 0 5 C 3 5 0 8 8 0 9 E 1 FF 1 FS 1 3 3 5 8 0 9 D 2 6 3 8 PERT . PERT : t to tm tp t 1 optimistic time to 2 most likely time tm 3 pessimistic time tp beta probability distribution te 2 : te = t 0 + 4t m + t p 6 : =( 2 t p - to 6 )2 . 1. 1: 1 5 15 te = 1 + 4 5 + 15 =6 6 2 = ( 15 -1 2 ) = 5.44 6 : 1 t0 5 6 tm te 15 tp 2: 10 15 20 te = 10 + 4 15 + 20 = 15 6 20 -10 2 =( ) = 2.78 6 2 : 10 to 15 te 20 tp te 50 te 50 te -3 -2 -1 68% 95% % % 99% % +1 +2 +3 68 95 99% : -1 a +1 -1 (b) +1 a b a 68% . 3: 0, 40 : 1 A 2--4--6 B 2 5--13--15 3 C 13--18--35 4 (1) : , 2 + 4 4 + 6 A te = =4 6 B C te = te = 5 + 4 13 + 15 = 12 6 13 + 4 18 + 35 = 20 6 te te = 4+12+20=36 : , A B C te = to 2 5 13 20 tm tp 4 6 13 15 18 35 35 56 20 + 4 35 + 56 = 36 6 36 0.5 36 0.5 (2) A : B : C: 2 =( 6-2 2 ) = 0.444 6 15 - 5 2 ) = 2.778 6 35 - 13 2 ) = 13.444 6 2 =( 2 =( : = 0.444+2.778+13.444 = 16.666 = 2 = 16.666 = 4.08 2. 1 2 3 23.76 31.92 27.84 36 1 2 3 40.08 48.24 44.16 31.92 40.08 68% 27.84 44.10 95 23.76 48.24 99% 23.76 48.24 99% 0.99 27.84 44.16 95 0.95 27.84 36 47.5% 0.475 36 44.16 47.5 0.475 31.92 40.08 68% 0.68 31.92 36 34 0.34 36 40.08 34 0.34 1 2 3 23.76 31.92 27.84 36 1 2 3 40.08 48.24 44.16 1 2 3 23.76 31.92 27.84 36 1 2 3 40.08 48.24 44.16 27.84 31.92 13.5 0.135 47.5%-34% = 13.5% 40.08 44.16 13.5% 0.135 47.5%-34% = 13.5% 23.76 0.5 0.005 50%-49.5% = 0.5% 48.24 0.5 0.005 50%-49.5% = 0.5% . Z= LF - EF t LF---- EF---- t ---- : A 1 2--4--6 2 5--13--15 B 3 C 13--18--35 4 te = 36 = 2 = 16.666 = 4.08 EF=36 LF=42 Z= LF - EF 42 - 36 6 = = = 1.47 t 4.08 4.08 =0.42922 36 42 42 36 36 42 0.50000+0.42922 0.92922 42 0.92922 92.922 (2) -- . 1 normal time crash time normal cost crash cost 2 3 4 5 - - B N=9 80000 C=6 110000 : A N=7 50000 C=5 62000 C N=10 40000 C=9 45000 D N=8 30000 C=6 42000 N= C= A N=7 50000 C=5 62000 B N=9 80000 C=6 110000 C N=10 40000 C=9 45000 D N=8 30000 C=6 42000 A C B : D : :16; :130000 :18; :70000 D C : : 18 : 200000 A N=7 50000 C=5 62000 B N=9 80000 C=6 110000 C N=10 40000 C=9 45000 D N=8 30000 C=6 42000 A C : : 15 B : D : C :11; :172000 :15; :87000 D : 259000 -- A N=7 50000 C=5 62000 B N=9 80000 C=6 110000 C N=10 40000 C=9 45000 D N=8 30000 C=6 42000 : A 6000 C 5000 B 10000 D 6000 C D 18 17 C D C 5000 A N=7 50000 C=5 62000 D 6000 B N=9 80000 C=6 110000 C N=10 40000 C=9 45000 D N=8 30000 C=6 42000 9/45000 : : 17 : 205000 C D 17 16 A--B 16 C--D 17 C--D C 5000 A N=7 50000 C=5 62000 D 6000 B N=9 80000 C=6 110000 C =9 45000 C=9 45000 D N=8 30000 C=6 42000 7/36000 : : 16 : 211000 C D A B C D C ---- 9 D . 1 16 15 16 15 1 A N=7 50000 C=5 62000 B N=9 80000 C=6 110000 6/56000 C =9 45000 C=9 45000 D =7 36000 C=6 42000 6/42000 A C : : 15 : 223000 B D A 6000 A D 6000 C D A B D B 10000 15 14 1 A =6 56000 C=5 62000 B N=9 80000 C=6 110000 C =9 45000 C=9 45000 D =6 42000 C=6 42000 C D A--B -- 18 17 16 15 C--D C--D C--D C--D A--B 200000 200000+5000 = 205000 205000+6000 = 211000 211000+6000 = 223000 l 5000 2 l1000 3 23000 : , : : ( ) ( ) ( ) ( ) , , , . A B C D F I K L M 38 40 E Steve 2 46 0 3 3 13 13 33 33 38 38 48 48 48 113 113 K Jim 113 120 7 120 120 L Jim 120 128 8 128 128 138 A Susan 3 0 3 B Susan 10 3 13 C Susan 20 13 33 D Susan 5 33 38 F Steve 10 38 38 48 50 I Steve 65 48 50 113 55 M Jim 10 128 138 G Andy 12 96 38 108 40 J Andy 5 108 113 H Susan 2 106 108 I 5 A B C D G J K LM 38 40 E Steve 2 48 0 3 3 13 13 33 33 38 38 50 48 48 I Steve 50 50 53 5 55 55 55 K Jim 55 62 7 62 62 L Jim 62 70 8 70 70 80 A Susan 3 0 3 B Susan 10 3 13 C Susan 20 13 33 D Susan 5 33 38 F Steve 10 40 38 50 50 M Jim 10 70 80 G Andy 12 38 38 50 40 J Andy 5 50 55 H Susan 2 48 50 I . E 2 8 6 8 . 38 46 E Steve 8 40 0 3 3 13 13 33 33 38 38 48 48 48 113 113 K Jim 113 120 7 120 120 L Jim 120 128 8 128 128 138 A Susan 3 0 3 B Susan 10 3 13 C Susan 20 13 33 D Susan 5 33 38 F Steve 10 38 38 48 50 I Steve 65 48 50 113 55 M Jim 10 128 138 G Andy 12 96 38 108 40 J Andy 5 108 113 H Susan 2 106 108 II E 2 12 10 8 A B CDEIKLM 38 50 E Steve 12 38 0 3 3 13 13 33 33 38 38 50 48 50 115 115 K Jim 115 122 7 122 122 L Jim 122 130 8 130 130 140 A Susan 3 0 3 B Susan 10 3 13 C Susan 20 13 33 D Susan 5 33 38 F Steve 10 40 38 50 50 I Steve 65 50 50 115 55 M Jim 10 130 140 G Andy 12 98 38 110 40 J Andy 5 110 115 H Susan 2 108 110 3. (1) ---- ---- ---- ---- ---- ---- 2 1 : () -- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 20 20 80 140 40 200 200 355 180 60 40 20 100 100 80 60 0 2001 7 2 2001 7 2 2001 7 30 2001 8 27 2001 9 24 2001 9 24 2001 7 2 2002 4 8 2002 4 8 2002 6 3 2003 8 18 2003 11 10 2004 1 5 2004 2 2 2004 2 2 2004 6 21 2004 10 11 2004 12 31 2001 7 2 2001 7 27 2001 8 24 2001 12 14 2002 4 5 2001 11 16 2002 4 5 2003 1 10 2003 8 15 2003 2 7 2003 11 7 2004 1 2 2004 1 30 2004 6 18 2004 6 18 2004 10 8 2004 12 31 2004 12 31 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% ---- (2) ---- : 4. "" 4. ( ) (1)---- (2)---- ---- ---- (1) ---- WBS (2) ---- (2) 1 ---- (2) ---- 2 i. ii. i. ii. iii. iv. v. i. ii. iii. iv. v. : , i. ii. iii. ---- (IBM) / (IBM) : : : 1 10% 2 10% 3 10% 4 5 6 7 8 : : : : : : : : : : : : : 5.3 : SS 1 A 2 B 4 C 3 E 1 FF 1 FS 1 D 2 5. 4 95% , ? ? 12 95% 32 5.5 138 , 130 . t ( ) 6, ? 5.6 17 24 90% 1--2 1--3 1--4 2--6 3--6 3--7 3--5 4--5 5--7 6--7 5 10 2 1 4 4 2 0 2 1 11 10 5 7 4 7 2 6 8 4 11 10 8 13 10 10 2 6 14 7 18 10000 22 5000 ...
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