FIND MINIMUM TIME OF COMPLETING THE PROJECT BY PERT

Compute following:

• Mean
• Variance
• Latest Completion Time
• Early Start Time
• Critical Path with Critical Activites

Source Code:

start=input("Press any key to start PERT simulation.")
n=10
O=[5 1 1 1 1 1 2 4 2 2]
M=[6 3 4 2 2 5 2 4 5 2]
P=[7 5 7 3 9 9 8 10 8 8]
Activity = ['ABCDEFGHIJ']//use part(Activity,[i])to retrieve
Predecessor = ["","","","A","B","C","C","EF","D","HG"]//part(Predecessor(10),1)
Mean=[]
Variance=[]
for i=1:n
    Mean(i)=(O(i)+4*M(i)+P(i))/6
    Variance(i)=((P(i)-O(i))/6)**2
end
disp("Mean time of all activities is :- ")
disp(Mean)
disp("Variance of all activities is :-")
disp(Variance)
LCT=[0 0 0 0 0 0 0 0 0 0]
EST=[9999 9999 9999 9999 9999 9999 9999 9999 9999 9999]
funcprot(0)

for i=1:n
    //finding EST using forward pass
    //if null
    if Predecessor(i) == ''
        LCT(i) = Mean(i)
    else if length(Predecessor(i)) == 1
            LCT(i) = Mean(i)+ LCT(strindex(Activity,Predecessor(i)))
         else
             //finding for more than one predecessor
             len=1
             maximum=0
             while len <= length(Predecessor(i))
                 if LCT(strindex(Activity,part(Predecessor(i),len))) >maximum
                     maximum = LCT(strindex(Activity,part(Predecessor(i),len)))  
                 end
                 len=len+1             
             end
             //found the maximum LCT of predecessor
             LCT(i)=Mean(i)+maximum
             //also changing LCT of predecessor
             len=1
             while len <= length(Predecessor(i))
                LCT(strindex(Activity,part(Predecessor(i),len)))= maximum
                len=len+1
             end
         end
    end
    
end

//one last thing to check the ending nodes
end_nodes=Activity
for i=1:length(strcat(Predecessor))
   end_nodes=strsubst(end_nodes,part(strcat(Predecessor),i),"")
end

//now finding latest completion time
completion_time=0
for i=1:length(end_nodes)
    if LCT(strindex(Activity,part(end_nodes(1),i))) > completion_time
        completion_time= LCT(strindex(Activity,part(end_nodes(1),i)))
    end
end
//set LCT for end nodes as same
//also EST of all activities is easy to find now
for i=1:length(end_nodes)
    LCT(strindex(Activity,part(end_nodes(1),i))) = completion_time
    EST(strindex(Activity,part(end_nodes(1),i))) = completion_time - Mean(strindex(Activity,part(end_nodes(1),i)))
end

disp("Latest Completion Time of all activities are : - ")
disp(LCT)

//now backward pass for remaining nodes
//finding nodes where backward pass needs to be find
i=length(Activity)
while i>=1
    len=1
    while len <= length(Predecessor(i))
        if EST(i)-Mean(strindex(Activity,part(Predecessor(i),len))) < EST(strindex(Activity,part(Predecessor(i),len))) 
            //check for start activity
            if Predecessor(strindex(Activity,part(Predecessor(i),len))) == ""
                EST(strindex(Activity,part(Predecessor(i),len)))=0
            else
                EST(strindex(Activity,part(Predecessor(i),len))) = EST(i)-Mean(strindex(Activity,part(Predecessor(i),len)))
            end
        end
        len=len+1
    end
    i=i-1
end

//now finding common predecessor...they should have common minimum start time
//function to find character count
function [k]=char_count(A, c)
    k = 0
    for p=1:length(A)
        if part(A,p) == c then
            k=k+1
        end
    end
endfunction

for i=1:length(Activity)
    if char_count(strcat(Predecessor),part(Activity(1),i)) > 1
        //found part(Activity(1),i) is common predecessor       minimum=999999999
        //now finding minimum of that common activity 
        for j=1:n
            len=1
            while len <= length(Predecessor(j))
                if part(Predecessor(j),len) == part(Activity(1),i)
                    if EST(j) < minimum
                        minimum = EST(j)
                    end
                end    
                len=len+1
            end
        end
        //now replacing that minimum throughout the EST of that Activity
        for j=1:n
            len=1
            while len <= length(Predecessor(j))
                if part(Predecessor(j),len) == part(Activity(1),i)
                    EST(j)=minimum 
                end    
                len=len+1
            end
        end
    end
end
//completed backward pass
disp("Early Start Time of all activities are : - ")
disp(EST)

//now the critical path
disp("Critical path of the network is ")
function [k]=EST_successor(c)
    k=0
    for j=1:n
        len=1
            while len <= length(Predecessor(j))
                if part(Predecessor(j),len) == c
                    k = EST(j) 
                end    
                len=len+1
            end
    end
    //check if the node is ending node
    for j=1:length(end_nodes)
        if part(end_nodes(1),j) == c then
            k=LCT(strindex(Activity,c))
        end
    end
endfunction
    
tot=0//to store the path weight
for i=1:length(Activity) 
    if tot+Mean(i) == EST_successor(part(Activity(1),i))
        tot=LCT(i)
        disp(" "+part(Activity(1),i)+"-> ")
    end
end

disp("Expected project completion time is " + string(completion_time)+" weeks")