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Pert & Cpm Ασκήσεις & Πράξεις 14-9-2012
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/ PERT & CPM & . 2012 2013
. , . , , - 1 24
( E N T E R P R I S E M A N A G E M E N T )
:
(Introduction to Enterprise Management: A concise approach)
- (Review of Project Management Concepts - Methodology)
PERT/CPM (Analysis of PERT/CPM Algorithm)
(Typical Contents of Project Proposal)
1st Draft
, 2012
.
.
/ PERT & CPM & . 2012 2013
. , . , , - 2 24
1. ,
. :
( , , ); , , Cost f P T S P performance T time S scope= = = = cost , performance , time scope .
2. Gantt charts, PERT CPM (Critical Path Method). 3. PERT (Program Evaluation Review Technique )
. PERT .
4. PERT (precedence) . (arcs) . (nodes) . . (dummy) .
5. PERT , (slack time) . ( ).
6. (critical path) .
7. , - (three-time estimate approach), Beta distribution.
Beta distribution ( 4 ) / 6t a m b= + + ( )( )22 / 6b a = . a () , b () m .
8. , three-time estimate approach, . .
9. CPM (Critical Path Method - ), , jt , jc , (crashed) jt , jc .
10. CPM, (time reduction), jM , j , : j j jM t t= . j , jK ,
: ( ) /j j j jK c c M = . 11. (Linear programming) CPM
. ( ).
12. PERT/COST . (Work packages). .
13. (cost status report) . . . .
/ PERT & CPM & . 2012 2013
. , . , , - 3 24
PERT/CPM
PERT . . 1. PERT : 1
2 3, . i , i . ( , )i j , i :
i. () i . ( 1 0).
ii. (EXO) : ( ) + ( () ( , )i j ). , EXO = + ij.
iii. .
2. PERT : N , 1N , 2N , . j , j . ( , )i j :
i. () j . ( N , ). , XO = min ().
ii. () : ( ) ( ( , )i j ). , X = - ij.
3. () : ( ) ( ) / ( ) ( ). , X = , / X = .
4. , 1 N , 0 .
(Linear programming)
: : ; ij i , j )
=
ix = i
ijy = ij
ijM = ij
ijK = ij
ij = ij
:
ij ij
min
: y M
ij iji j
N
i j ij ij
K y
subject to x T where N is the completion nodefor each activity ij
x x y for each activity ij
+ +
, 0i ijx y
&
: A. :
a. ( ) PERT/CPM .
b. i i , .
B. / :
/ PERT & CPM & . 2012 2013
. , . , , - 4 24
= ( ) ( ) = ( ) ( )
, ! ( ) .
C. , : a. ( )
. b. .
(s) .
?
- s.
?
1.
?
.
.
(s) .
?
- s.
?
1.
?
.
.
1: Krafts Custom Cars . , Kraft . Kraft . . . , C . D . . E . . , . .
3 3 C 2 D 3 E 7 F 3 G 6 H 2
/ PERT & CPM & . 2012 2013
. , . , , - 5 24
: A. PERT . B. .
? ? C.
? D. (D) 4 .
? : PERT .
----- 3 3 C 2 D 3 E C 7 F , C 3 G D, 6 H C 2
PERT . ( ). . :
1 2 5
4
3 6
7A3
B3
2
3
3
6
2
70
0C
O1
O2
D
E
F
H
G
1 2 5
4
3 6
7A3
B3
2
3
3
6
2
70
0C
O1
O2
D
E
F
H
G
(: 5 B C .
3 B 4 C . , O1 O2, 3 5 4 5, , 5. (0) ).
: () 1 (0). () : = + ( , XO). = max ( ). [, ]. :
( = Max in)
( = + XO)
1 0 0 + 3 = 3 2
C 3 3
3 + 3 = 6 3 + 2 = 5
3 D 1
6 6
6 + 3 = 9 6 + 0 = 6
4 2
5 5 5
5 + 0 = 5 5 + 7 = 12 5 + 2 = 7
5 F max (5, 6) = 6 6 + 3 = 9 6 G max (9, 12) = 12 12 + 6 = 18
/ PERT & CPM & . 2012 2013
. , . , , - 6 24
(max ) 7 18. , 18. () . () -1 : = - ( , XO). = min ( ). [, ]. :
( = Min out)
( = - )
7 G F
18 18 18
18 - 2 = 16 18 6 = 12 18 3 = 15
6 D
12 12
12 - 7 = 5 12 3 = 9
5 1 2
15 15
15 - 0 = 15 15 - 0 = 15
4 C min (15, 5, 16) = 5 5 - 2 = 3 3 min (9, 15) = 9 9 - 3 = 6 2 min (6, 3) = 3 3 - 3 = 0
PERT :
1 2 5
4
3 6
7A3
B3
2
3
3
6
2
70
0
C
O1
O2
D
E
F
H
G
[, ][E, O]
[6, 9][9, 12]
[0, 3][0, 3]
[3, 6][6, 9]
[3, 5][3, 5]
[5, 7][16, 18]
[5, 12][5, 12]
[6, 9][15, 18]
[12, 18][12, 18][6, 6]
[15, 15]
[5, 5][15, 15]
( = X = ) :
-
()
()
()
()
()
0 3 0 3 0 3 6 6 9 3 C 3 5 3 5 0 D 6 9 9 12 3 E 5 12 5 12 0 F 6 9 15 18 9 G 12 18 12 18 0 H 5 7 16 18 11
C: A, C, E, G 0 . . D: D 3. 4 D 4 3 = 1 .
/ PERT & CPM & . 2012 2013
. , . , , - 7 24
2: :
()
()
()
---- 4 6 8 ---- 1 4.5 5 C 3 3 3 D 4 5 6 E 0.5 1 1.5 F , C 3 4 5 G , C 1 1.5 5 H E, F 5 6 7 I E, F 2 5 8 J D, H 2.5 2.75 4.5 K G, I 3 5 7
A. PERT .
B. .
C. .
D. (24 )? A: , A, B, C, E F, D H G I:
1 4
3
2
A
B K
G
I
J
C
D
E
F
H
7
6
5
1 4
3
2
A
B K
G
I
J
C
D
E
F
H
7
6
5
B: , t , , 2 ,
( 4 ) / 6t a m b= + + ( )( )22 / 6b a = :
, ()
a
, ()
m
, ()
b
, ()
t
, 2
4 6 8 6 4/9 1 4.5 5 4 4/9 C 3 3 3 3 0 D 4 5 6 5 1/9 E 0.5 1 1.5 1 1/36 F 3 4 5 4 1/9 G 1 1.5 5 2 4/9 H 5 6 7 6 1/9 I 2 5 8 5 1 J 2.5 2.75 4.5 3 1/9 K 3 5 7 5 4/9
/ PERT & CPM & . 2012 2013
. , . , , - 8 24
1 :
-
()
()
()
()
() 0 6 0 6 0 0 4 5 9 5 C 6 9 6 9 0 D 6 11 15 20 9 E 6 7 12 13 6 F 9 13 9 13 0 G 9 11 16 18 7 H 13 19 14 20 1 I 13 18 13 18 0 J 19 22 20 23 1 K 18 23 18 23 0
C: (0) : C F I K. max 7 = 23. D: :
2 2 2 2 2 2 4 / 9 0 1/ 9 1 4 / 9 2 1.414A C F I K = + + + + = + + + + = = . : (24 23) / 1/1.414 0.71z = = = . ( ) ( 0.71) 0.5 0.2612 0.7612P z < = + = . 3: National Business Machines (NBM) . PERT 1000 .
1
4
3
2
A
B
K
G
I
J
C
D
E
F
H
9
7
5
6
8
L
M
ij ( i j)
() ()
12 (A) 2 2.000 1,5 3.000 13 (B) 4 3.000 3 3.500 14 (C) 1 1.500 1 1.500 25 (D) 4 5.300 2,5 8.000 35 (E) 6 5.400 5 7.000 58 (F) 10 6.000 8 9.000 36 (G) 8 4.800 5 9.900 37 (H) 2 2.800 1 2.900 48 (I) 5 4.500 4 5.000 47 (J) 12 6.000 6 9.600 89 (K) 7 7.000 4 9.700 69 (L) 11 8.800 9 9.200 79 (M) 4 1.000 1 7.000
/ PERT & CPM & . 2012 2013
. , . , , - 9 24
: M, M = [( ) ( )], , K, K = ([ ] [ ] / M).
ij ( i j) M K ()
12 (A) 0,5 2.000 13 (B) 1 500 14 (C) 0 0 25 (D) 1,5 1.800 35 (E) 1 1.600 58 (F) 2 1.500 36 (G) 3 1.700 37 (H) 1 100 48 (I) 1 500 47 (J) 6 600 89 (K) 3 900 69 (L) 2 200 79 (M) 3 1.000
:
xi = i
ijy = ij J () :
{}
min 2000 500 0 1800 1600 1500 170012 13 14 25 35 58 36
100 500 600 900 200 200037 48 47 89 69 79
J y y y y y y y
y y y y y y
= + + + + + +
+ + + + + +
(subject to):
1. 24 , 249x . 2. :
0,512y 113y 014y 1,525y 135y
336y 137y 647y 148y 258y
269y 379y
389y
3. , :
( ) ( ) + [( ) ( )].
:
49 7 79119 6 6979 8 89
x x y
x x y
x x y
+
+
+
58 4 48108 5 58
x x y
x x y
+
+
127 4 4727 3 37
x x y
x x y
+
+ 86 3 36x x y +
65 3 3545 2 25
x x y
x x y
+
+ 14 1 14x x y + 43 1 13x x y + 22 1 12x x y +
4. . , 0; x for all ii 0; , y for all i jij .
/ PERT & CPM & . 2012 2013
. , . , , - 10 24
1: :
() ---- 7 ---- 10 C 4 D 30 E 7 F , C 12 G , C 15 H E, F 11 I E, F 25 J E, F 6 K D, H 21 L G, J 25
A. PERT .
B. E G ?
C. A, G I ?
D. G L ?
E. G 7 L 4 ? .
A: PERT . PERT :
1
3
2
A
B L
G
K
C
D
F
7
6
5
7
10
4
30
12
15
21
4
E7 H
I
11
25J 256
[, ][E, O]
[0, 7][0, 7]
[7, 37][7, 37]
[7, 14][19, 26]
[11, 23][14, 26]
[11, 26][18, 33]
[7, 11][10, 14]
[0, 10][4, 14]
[23, 34][26, 37]
[23, 48][33, 58]
[23, 29][27, 33] [29, 54]
[33, 58]
[37, 58][37, 58]
7, =+, max . ( [, ]). 58 . . PERT [, ] .
/ PERT & CPM & . 2012 2013
. , . , , - 11 24
-
()
()
()
()
() 0 7 0 7 0 0 10 4 14 4 C 7 11 10 14 3 D 7 37 7 37 0 E 7 14 19 26 12 F 11 23 14 26 3 G 11 26 18 33 7 H 23 34 26 37 3 I 23 48 33 58 10 J 23 29 27 33 4 K 37 58 37 58 0 L 29 54 33 58 4
D K. B: E G , . . C: A, G I , G I . . D: G 7 L 4 . G 7 L 4 . E: G 7 L 4 4 PERT [, ] . 2: PERT , :
1 4
3
2A
B
C
D
E
:
t A 6 2 B 3 1 C 6 1 D 15 2 E 12 2
/ PERT & CPM & . 2012 2013
. , . , , - 12 24
100.000 26 . E , . , , E, E 8 ( 2), 15.000 , . , , ? : 1, E :
()
()
()
()
A 0 6 0 6 B 0 3 9 12 C 6 12 6 12 D 6 21 9 21 E 12 24 12 24
A C E 24. : 2 2 2 2 2 2 22 1 2 9EA C = + + = + + = . 3 = . 26 , :
(26 24) / 2 / 3 0.67z = = = . ( ) 26 ( 0.67)P z < . (0 0.67) 0.2486P z< < = . 26 0.5 0.2486 0.7486+ = . , E : 0.7486 100.000 0.2514 0 74.860 + = . , E :
()
()
()
()
A 0 6 0 6 B 0 3 10 13 C 6 12 7 13 D 6 21 6 21 E 12 20 13 21
A D 21. : 2 2 2 2 22 2 8DA = + = + = . 2.828 = . 26 , ,
(26 21) / 5 / 2.828 1.77z = = = . ( ) 26 ( 1.77)P z < . (0 1.77) 0.4616P z< < = . 26 0.5 0.4616 0.9616+ = . , E : 0.9616 100.000 0.0384 0 96.160 + = .
/ PERT & CPM & . 2012 2013
. , . , , - 13 24
/
/
1 PERT
.
2 PERT .
3 PERT .
4 PERT - .
5 PERT F G . , .
6 .
7 PERT F G . , .
8 .
9 PERT F . .
10 PERT .
11 CPM (Critical Path Method), () .
12 . 13 CPM (Critical Path Method),
B 10.000.00 15.000.00, 13.000.00 B, 6,8 .
14 G 80% 50.000.00. 45.000.00 . .
15 . 3: P3. P3 12 P1 8 P2 7 . P1 P2 9 . P1 P2 6 . P1 P2 P3, P2 10 . : () PERT P3. () P3 ? () P3 () ?
() P2 2 , P3? () P1 9 , P3?
/ PERT & CPM & . 2012 2013
. , . , , - 14 24
: PERT P3 , , :
----- 6 ----- 9 C P1 , 8 D P2 , 7 E P2 D 10 F P1 P2 C, E 12
PERT . ( ). . .
1
2
3
A6
B9
C8 F1265
4
D7E10
[0, 6][3, 9]
[9, 17][18, 26]
[9, 16][9, 16]
[0, 9][0, 9]
[16, 26][16, 26]
[26, 38][26, 38]
max inEXE EXO=EXO EXE XO= +
min outBXO BXE=BXE BXO XO=
AX BXE EXE BXO EXO
max inEXE EXO=EXO EXE XO= +
min outBXO BXE=BXE BXO XO=
AX BXE EXE BXO EXO
[ ][ ]
,
,
EXE EXO
BXE BXO
d0
[9, 9][9, 9]
d0=dummy
38 . A=3 C=9 . B-D-E-F. (2) P2 ( D) (2) P3. P1 ( C) (9) , ( ), P3 .
/ 1 , , ( , , , ). 2 & (, , ,
PERT/CPM, & , , , , , , (resources), /, , (), , .).
3 Gantt chart, , , . 4 ( , ,
, , , , , .).
/ PERT & CPM & . 2012 2013
. , . , , - 15 24
, . , , . : 1.
. 2.
, . . :
.
. .
. .
3. .
, .
4.
. :
5. .
. 6.
. .
7. , , .
------- (Time Management) , , , ,, , , . :
. (planning) . ' ' . . .. ' . 1.
1.1 .
1.2 , .
/ PERT & CPM & . 2012 2013
. , . , , - 16 24
1.3 .
2.
2.1 2.2 2.3 2.4
3. ' . :
3.1 . 3.2 . 3.3 . 3.4 .
. 3.5 . 3.6 ,
.
4. 4.1 . 4.2 .
.
4.3 , .
4.4 . .
4.5 .
4.6 .
. , , ' . : ' . , : 1. : , ,
. .
2. : ( . , , ,
, .), .
. , . .
/ PERT & CPM & . 2012 2013
. , . , , - 17 24
IKA
-
/ . , . , . , . 10 : ( , Business Development Director. City Unity College) 1. :
. , , . ; , , . , .
2. : , managers,
. , , , , . , , . ; : manager. . ; .
3. : ,
, , . : , , . ; , , . . , , .
/ PERT & CPM & . 2012 2013
. , . , , - 18 24
4. SUPERMAN: ; , , , , ( ), , . . ; , , , standards . , standards .
5. (JOB DESCRIPTION): 10
. job description , , , . , .
6. : ,
, , . , , , .
7. :
, , . , , , .
8. : , ,
, .
9. :
. , . 10. MANAGERS KEY EMPLOYEES:
manager , , job description .
: , (Stogdill, 1950; Koontz and ODonnell, 1982). , , (Bass,1990). , () (, 2005). Bennis (1990) . , , . :
/ PERT & CPM & . 2012 2013
. , . , , - 19 24
1:
1. . 2. . 3. . 4. , , ,
, . 5. . 6. ,
. 7. - . 8.
. 9. . 10. ,
, (status quo).
11. , , .
12. . 13.
.
14. . 15. . 16. ,
. 17. . 18. .
1. 2. . 3. . 4. , , , . 5. , , ,
. 6. -
. 7. , . 8. , , . 9. . 10. , ,
, . 11.
.
12. . 13. ,
, . 14.
, . 15. .
. . 16. ,
, , . 17. . 18. .
. , . . . , :
1. . 2.
. 3. ,
. 4. . 5. . 6. . 7. . 8.
/, . / /, . , , . , , , .
/ PERT & CPM & . 2012 2013
. , . , , - 20 24
: 1. / :
. . , , . . , . , . , ( & ) . (sender) , , . (receiver), , . :
. . , .
. . ,
. . ,
. . , .
, , . . , , , . , . .
2. (projects performance reporting), ( ) : (Performance Reporting) , . . : (performance review meetings), / . (variance analysis), ( , , , , ). (Earned Value Analysis-EVA), () ( ).
/ PERT & CPM & . 2012 2013
. , . , , - 21 24
(Financial and Output Performance Indicators), . (Progress Reports) (Project Status Reports), . (Progress Report) ( ) ( ), . , , . , . , , . (Project Status Report) ( ), , , . , / , , . , , . :
. .
. , :
, , .
. : Gantt, , , , . . , . , . , ( ). , (Status Meeting),
/ PERT & CPM & . 2012 2013
. , . , , - 22 24
( / ). . , , , , . , , ( ), , .
(Project Budget) , . . ( ) :
(, , & ) & (, , , , , , .) (, , .) / (
.) , ( /
, , .) , ( , , ,
) , ( ,
) (contingencies) (
. , ).
, , . (overheads) (.. , , , , , ). , , . , . , . ( : ) / , . , , . , . , , . , ( ). . , . .
/ PERT & CPM & . 2012 2013
. , . , , - 23 24
. . :
( - ) .
1. .
1.1 : . :
() , .. , , , . () , .. , , .
1.2 : . . . 1.3 : . .
2.
2.1 . 2.2 . 2.3 2.4 2.5 2.6 2.7
3
3.1 . : () :
() :
() : ( , .. ) ( , ... )
() : .
3.2 . :
() () ()
/ PERT & CPM & . 2012 2013
. , . , , - 24 24
() () ()
.