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( 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) . . . .

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. , . , , - 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. / :

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. , . , , - 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

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: 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

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. , . , , - 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 .

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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

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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

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: 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 .

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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 [, ] .

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. , . , , - 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

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. , . , , - 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 + = .

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. , . , , - 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 , .

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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. : ,

, , . : , , . ; , , . . , , .

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. , . , , - 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

() () ()

.