Capacity Expansion and Reliability Evaluation on the Networks Flows with Continuous Stochastic Functional Capacity

Pseudocode 1

Start

Read the nominal capacities,  s, and subset of the transmission factors,   s, of the original network, .

Calculate functional capacity,   s, of each arc.

Find the maximum flow, MAX.

While  MAX <   Do

 Define the residual graph and (cost) as follow

and

and let a label for each arc which show the cost of arc expansion as following:

For  each   Do

if   and   then

set and

else

if   and

if     then

   set and

    else if     then

   set and

    else if     then

   set and

end if

end if

end if

 Find the shortest path in (cost) regarding value

if   (sum of the costs on the shortest path < +∞)

  replace the new capacity in as follow:

if   and then

set and

else  if   and or and then

set and

end if

end if

end For

Calculate functional capacity using new capacity

Find maximum flow, MAX.

end while

end.