Gurobi Python: Summation Constraint not being satisfied
In my MILP model there are 2 constraints that are related to each other and must be satisfied
knowing that;
o[i,j,k,t] is a binary variable that determine the selected temperature k at time period t when transferring products from plant i to retailer j (i.e when there's and arc between i and j)
x[i,j,q,k,t] is a continuous variable that determine the amount of products to be transferred from i to j with quality q at temperature k at period t
M is a large number
the first constrain is satisfied:
coded as:
for i,j in A:
for t in range(1-w_max, H):
m.addConstr(quicksum(O[i,j,k,t] for k in K ) <=1 , name="Constr 15" )
the solution is:
O(P1,R1,10,-1) 1.000000..................# means that there exist an arc between P1 and R1 at period
-1 and the selected temperature was 10
O(P1,R1,10,0) 1.000000
O(P1,R1,10,1) 1.000000
O(P1,R2,6,-2) 1.000000
O(P1,R2,8,-1) 1.000000
O(P1,R2,8,0) 1.000000
O(P1,R3,2,-2) 1.000000
O(P1,R3,2,0) 1.000000
O(P1,R3,6,-1) 1.000000
O(P1,R4,8,-1) 1.000000
O(P1,R4,8,1) 1.000000
O(P1,R4,10,0) 1.000000
that is fine, the problem occurs as follows;
there is another constraint for x[i,j,q,k,t] that states that there will be transferred products between i and j with different quality levels at a selected temperature k in period t that matches the solution that will be obtained from the previous constraint
coded as:
for i,j in A:
for k in K:
for t in trans_per(i,j) :
m.addConstr(quicksum(x[i,j,q,k,t] for q in Q if q in range ((q_imin[j]+int(DeltaqTR[i,j,k])),151- int(DeltaqTR[i,j,k])+1) ) <= M*O[i,j,k,t] , name="Constr 13" )
the solution obtained;
x(P1,R1,56,10,0) 14.000000
x(P1,R1,56,10,1) 105.000000
x(P1,R1,64,10,-1) 162.000000
x(P1,R1,65,10,0) 200.000000
x(P1,R1,79,10,1) 68.000000
x(P1,R1,83,10,0) 95.000000
x(P1,R1,96,10,0) 57.000000
x(P1,R1,145,10,0) 6.000000
x(P1,R2,64,8,-1) 24.000000
x(P1,R2,83,10,-1) 132.000000
x(P1,R2,91,10,-2) 14.000000 ....#this is an example on one of the conflicts, the solution obtained from the variable O was O(P1,R2,6,-2) 1.000000 that states that the selected temperature form arc P1 to R2 at period -2 will be 6, but as you see the selected temperature from variable x is 10!!!
x(P1,R2,96,10,0) 143.000000
x(P1,R2,145,10,-2) 145.000000
x(P1,R3,145,10,-2) 255.000000
x(P1,R3,145,10,0) 324.000000
x(P1,R3,147,10,-1) 428.000000
x(P1,R4,79,8,1) 54.000000
x(P1,R4,83,8,-1) 54.000000
x(P1,R4,121,10,1) 200.000000
x(P1,R4,145,10,0) 270.000000
x(P1,R4,147,10,-1) 172.000000
I don't know why this conflict happened?
Thanks in advance
Ragia
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Gurobi Staff
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Maybe, this is due to numerical trouble. Can you tell us how large M is?
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M is equal to 1525 (I don't know why exactly the author assumed this value)
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Can you post an .lp or .mps file of your model?
One thing seems strange: In your first constraint, you interate t over range(1-w_max, H) and in the second constraint, you iterate t over trans_per(i,j). Is this the same?
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Hi Thomas,
trans_per(i,j) is a subset of (1-w_max, H)
trans_per(i,j) is a list that contains the periods where transshipment will occur between i and j,
while (1-w_max, H) is a list that contains the whole planning horizonI've tried your suggestion to unify them but nothing had changed.
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