Rudarski radovi br 4 2011 - Institut za rudarstvo i metalurgiju Bor

Rz6+ t9= [ 6 α + 14;25− 5α]<br />
+<br />
[ 2α + 13;17 − 2α] = [ 8 α + 27;42 −7α]<br />
23 + 2 ⋅ 29 + 35<br />
RRz ( 5+ t9)<br />
= = 29,0<br />
4<br />
27 + 2 ⋅ 35 + 42<br />
RRz ( 6+ t9)<br />
= = 34,75<br />
4<br />
RRz ( 6+ t9) f RRz ( 6+ t9)<br />
It follows from the last relation for<br />
early completion for activity no. 9 is the<br />
following fuzzy number:<br />
[ ]<br />
Rz9 = 8 α + 27;42− 7α<br />
The presented procedure is then analogously<br />
applied to all activities taking into<br />
account the structure of the given network<br />
layout. By this way, we come to the last<br />
two activities of the given network layout<br />
which are calculated as follows:<br />
⎡ ⎤<br />
⎢ ⎥<br />
Rz29 = max ⎢Rz27+ t29; Rz28+ t29; Rz26+ t29⎥<br />
⎢ ⎥<br />
⎣ ⎦<br />
27+ 29 = [ 17 + 57;92 − 18 ] +<br />
[ α 2; 4 α] [ 18α 59;96 19α]<br />
Rz t α α<br />
+ + − = + −<br />
28+ 29 = [ 19 + 61;99 − 19 ] +<br />
[ α 2;4 α] [ 20α 63;103 20α]<br />
Rz t α α<br />
+ + − = + −<br />
26+ 29 = [ 18 + 63;98 − 17 ] +<br />
[ α 2;4 α] [ 19α 65;102 18α]<br />
Rz t α α<br />
+ + − = + −<br />
59 + 2 ⋅ 77 + 96<br />
RRz ( 27+ t29)<br />
= = 77,25<br />
4<br />
63 + 2 ⋅ 83 + 103<br />
RRz ( 28+ t29)<br />
= = 83,0<br />
4<br />
65 + 2 ⋅ 84 + 102<br />
RRz ( 26+ t29)<br />
= = 83,75<br />
4<br />
[ ]<br />
Rz29 = 19α + 65;102 − 18α<br />
Rz30 = Rz29+ t30<br />
30 = [ 19 + 65;102 − 18 ] +<br />
[ 2α 8;12 2α] [ 21α 73;114 20α]<br />
Rz α α<br />
+ + − = + −<br />
[ ]<br />
Rz30 = 21α + 73;114 − 20α<br />
The fuzzy number, representing the<br />
last activity of Rz30 project, defines the<br />
project completion possibility function. In<br />
the previous expression, the fuzzy number,<br />
representing the last activity, is defined<br />
by its α intersections.<br />
Analytical shape of the possibility<br />
function is obtained by the following<br />
manner:<br />
−<br />
R z30<br />
= L xR<br />
α<br />
[ α α<br />
x , ] = [ 21α<br />
+ 73,<br />
114 − 20 ]<br />
α<br />
α x − 73<br />
x = 21α<br />
+ 73 → α = L<br />
L<br />
21<br />
α<br />
α 114 − x<br />
x 114 20α<br />
α<br />
D<br />
D = + → =<br />
20<br />
whence we get the analytical expression<br />
for possibility function:<br />
()<br />
[ ] ⎪<br />
⎪ ⎪<br />
⎧ t − 73<br />
⎫<br />
⎪<br />
= 0,<br />
0476t<br />
− 3,<br />
4762,<br />
73 ≤ t ≤ 94<br />
21<br />
⎪<br />
⎪114<br />
− t<br />
⎪<br />
π t = ⎨ = 5,<br />
7 − 0,<br />
05t,<br />
94 ≤ t ≤ 114⎬<br />
⎪ 20<br />
⎪ 0,<br />
t ∉ 73,<br />
114<br />
⎪⎩<br />
⎭<br />
Graphic representation of this expression<br />
is given in Figure 4.<br />
No 4, 2011. 166<br />
MINING ENGINEERING