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from __future__ import print_function

n = 20

N = range(n)



from random import Random



rand = Random()



D = [rand.randint(1,10) for i in N] # processing time

R = [rand.randint(1,10) for i in N] # revenue

tt = sum(D); tt -= tt//5

L = [rand.randint(1,tt) for i in N] # arrival time

U = [L[i]+D[i]+rand.randint(10,30) for i in N] # duedate



#overlapping jobs

M = [(i,j) for i in N for j in N 

   if i<j and L[i]<U[j] and L[j]<U[i]] 



#i must preceed j and they could bump into each other

P = [(i,j) for i in N for j in N if i!=j

   and L[i]<U[j] and L[j]<U[i]

   #lastest start < earliest finish

   and U[i]-D[i]<L[j]+D[j]]





from pymprog import *



begin("job-scheduling")

x = var('x', N ) #start time

#MD[i,j] = (D[i]+D[j])/2.0

#T[i] = x[i] + D[i]

#y[i,j]<= |T[i]-x[j]-MD[i,j]|

#y[i,j] < MD[i,j] <==> overlap betw jobs i,j

y = var('y', M) 

#w[i,j]: the 'OR' for |T[i]-x[j]-MD[i,j]|

w = var('w', M, bool)

# z[i,j] >= MD[i,j] - y[i,j]

z = var('z', M )

#u[i] = 1 iff job i is scheduled.

u = var('u', N, bool)



maximize(sum(R[i]*u[i] for i in N), 'revenue')



sum(z[i,j] for i,j in M) == 0 #single

#w[i,j]=0  ==> 

#x[j] + D[j]/2 >= x[i]+D[i]/2 + y[i,j]

#That is: i preceed j when w[i,j]=0.

for i,j in M:

   ((D[i]+D[j])/2.0 - (x[i]+D[i]- x[j]) + 

        (U[i]-L[j]) * w[i,j] >= y[i,j])



   ((x[i]+D[i]- x[j]) - (D[i]+D[j])/2.0 +

        (U[j]-L[i])*(1-w[i,j]) >= y[i,j])



   ((D[i]+D[j])/2.0 - y[i,j] <= z[i,j] + 

       (2-u[i]-u[j])*(D[i]+D[j])/2.0)



   if (i,j) in P or (j,i) in P:

       w[i,j] == (0 if (i,j) in P else 1)



#set bounds on x

for i in N:

   L[i] <= x[i] <= U[i] - D[i] 





solver(int, 

    #this branching option often helps 

    br_tech=glpk.GLP_BR_PCH, 

)

solve()



print("status:", status())

print("revenue:", vobj(), 'max:', sum(R))

print("schedule:")

for i in N:

   start = x[i].primal

   used = u[i].primal

   print("job %i:"%i, start, start+D[i],

          "Accept" if used else "Reject",

          R[i]/float(D[i]))