Critical path: (0,1)(1,3)(3,5)(5,7)(7,8)(8,9)(9,10)(10,13)(13,14) – O1, A, C, D, G, I, J, K, M

Answer

We introduce a fictitious work to properly display the data: Y (12;13), X (10;11), O1(0;1), O2(0;2).

We have duration and crash duration, so we should have expected time

t_expected (i,j)=(3 t_min(i,j)+2 t_max(i,j))/5

Dispersion index is used to characterize the degree of dispersion of possible values around the expected level:

S²(i,j)=0,04(t_max(i,j)-t_min(i,j))²

t_expected (0,1)=(3*0+2*0)/5=0

t_expected(0,2)=(3*0+2*0)/5=0

t_expected(1,3)=(3*2+2*2)/5=2.8

t_expected(2,4)=(3*3+2*3)/5=4.2

t_expected(3,5)=(3*3+2*3)/5=4.2

t_expected(4,6)=(3*5+2*5)/5=6.6

t_expected(5,7)=(3*2+2*2)/5=3.2

t_expected(7,8)=(3*2+2*2)/5=2.8

t_expected(8,9)=(3*2+2*2)/5=2.8

t_expected(5,9)=(3*3+2*3)/5=4.2

t_expected(9,10)=(3*2+2*2)/5=3.2

t_expected(6,11)=(3*3+2*3)/5=3.8

t_expected(10,11)=(3*0+2*0)/5=0

t_expected(11,12)=(3*3+2*3)/5=4.2

t_expected(12,13)=(3*0+2*0)/5=0

t_expected(10,13)=(3*3+2*3)/5=4.6

t_expected(13,14)=(3*1+2*1)/5=1.8

S²(0,1)=0.04(0-0)²=0

S²(0,2)=0.04(0-0)²=0

S²(1,3)=0.04(4-2)²=0.16

S²(2,4)=0.04(6-3)²=0.36

S²(3,5)=0.04(6-3)²=0.36

S²(4,6)=0.04(9-5)²=0.64

S²(5,7)=0.04(5-2)²=0.36

S²(7,8)=0.04(4-2)²=0.16

S²(8,9)=0.04(4-2)²=0.16

S²(5,9)=0.04(6-3)²=0.36

S²(9,10)=0.04(5-2)²=0.36

S²(6,11)=0.04(5-3)²=0.16

S²(10,11)=0.04(0-0)²=0

S²(11,12)=0.04(6-3)²=0.36

S²(12,13)=0.04(0-0)²=0

S²(10,13)=0.04(7-3)²=0.64

S²(13,14)=0.04(3-1)²=0.16

	Activity (i,j)	tmin(i,j)	tmax(i,j)	m(i,j)	t expected (i,j)	S^2(i,j)
0^1	0,1
0^2	0,2
A	1,3				2.8	0.16
B	2,4				4.2	0.36
C	3,5				4.2	0.36
F	4,6				6.6	0.64
D	5,7				3.2	0.36
G	7,8				2.8	0.16
I	8,9				2.8	0.16
E	5,9				4.2	0.36
J	9,10				3.2	0.36
H	6,11				3.8	0.16
X	10,11
L	11,12				4.2	0.36
Y	12,13
K	10,13				4.6	0.64
M	13,14				1.8	0.16

event i	The early period of accomplishment events	t^e(i)
	Later date achievements events	t^l(i)
	Reserve time for an event	R(i)
Activity/work (i, j)	duration of work	t(i,j)
	Early start of work	te^н(i,j) t^es(i,j)
	Early finish of work	t^po(i,j)
	Late start of work	t^пн(i,j)
	Late finish of work	t^по(i,j)
	Full-time working allowance	R^п(i,j)
the path L	duration of path	t(L)
	The duration of the critical path	tcr
	Reserve time path	R(L)

t^e(i) = max(t(L_ni)) t^e(j) = max[t^e(i) + t(i,j)]

t^l(i) = t_cr - max(t(L_ci)) t^l(i) = min[t(j) - t(i,j)]

R(i) = t^l(i) - t^e(i)

Critical events reserves do not have time, as any delay in the accomplishment of events, which lies on the critical path, cause the same delay in the accomplishment of the final event.

i=0 te(0)=0.

i=1: t^e(1) = te(0) + t(0,1) = 0 + 0 = 0.

i=2: te(2) = te(0) + t(0,2) = 0 + 0 = 0.

i=3: t^e(3) = t^e(1) + t(1,3) = 0 + 2.8 = 2.8.

i=4: t^e(4) = t^e(2) + t(2,4) = 0 + 4.2 = 4.2.

i=5: t^e(5) = t^e(3) + t(3,5) = 2.8 + 4.2 = 7.

i=6: t^e(6) = t^e(4) + t(4,6) = 4.2 + 6.6 = 10.8.

i=7: t^e(7) = t^e(5) + t(5,7) = 7 + 3.2 = 10.2.

i=8: t^e(8) = t^e(7) + t(7,8) = 10.2 + 2.8 = 13.

i=9: max(te(5) + t(5,9); te(8) + t(8,9)) = max(7 + 4.2;13 + 2.8) = 15.8.

i=10: t^e(10) = t^e(9) + t(9,10) = 15.8 + 3.2 = 19.

i=11: max(t^e(6) + t(6,11); t^e(10) + t(10,11)) = max(10.8 + 3.8;19 + 0) = 19.

i=12: t^e(12) = t^e(11) + t(11,12) = 19 + 4.2 = 23.2.

i=13: max(t^e(10) + t(10,13); t^e(12) + t(12,13)) = max(19 + 4.6;23.2 + 0) = 23.6.

i=14: t^e(14) = t^e(13) + t(13,14) = 23.6 + 1.8 = 25.4.

The length of the critical path is the early date of the final accomplishment of events 14: t_kp=tp(14)=25.4

Table 1 - The calculation of provisions events

number of events	Terms accomplishments events: early t^e(i)	Terms accomplishments events: late t^l(i)	R(i)
		4.8	4.8
	2.8	2.8
	4.2		4.8
	10.8	15.6	4.8
	10.2	10.2
	15.8	15.8
		19.4	0.4
	23.2	23.6	0.4
	23.6	23.6
	25.4	25.4

Table 2 - Analysis of the network model with respect to time

Work (i,j)	Number of previous work	duration tij	ES early period: the start tij^e.s^.	EF Early period: the end tij^e.e^.	LS Later periods: the start tij^l.s^.	LF Later date: end tij^l.e^.	Reserves of time: full time reserve Rij^f
(0,1)
(0,2)					4.8	4.8	4.8
(1,3)		2.8		2.8		2.8
(2,4)		4.2		4.2	4.8		4.8
(3,5)		4.2	2.8		2.8
(4,6)		6.6	4.2	10.8		15.6	4.8
(5,7)		3.2		10.2		10.2
(5,9)		4.2		11.2	11.6	15.8	4.6
(6,11)		3.8	10.8	14.6	15.6	19.4	4.8
(7,8)		2.8	10.2		10.2
(8,9)		2.8		15.8		15.8
(9,10)		3.2	15.8		15.8
(10,11)					19.4	19.4	0.4
(10,13)		4.6		23.6		23.6
(11,12)		4.2		23.2	19.4	23.6	0.4
(12,13)			23.2	23.2	23.6	23.6	0.4
(13,14)		1.8	23.6	25.4	23.6	25.4

critical path: (0,1)(1,3)(3,5)(5,7)(7,8)(8,9)(9,10)(10,13)(13,14) – O1, A, C, D, G, I, J, K, M

Дата добавления: 2015-07-18