For the same model, when the range of parameters is larger, the minimum value of the target is also larger
Awaiting user inputF=set(range(1, 2))
for r in R:
for f in F:
for (i,j) in L :
m.addConstr(CC>=f*I[r, (i,j), f], name='c39')
# m.addConstr(CC>=f*X[r, (i,j), f]+f*Y[r, (i,j),f], name='c39')
m.setObjective(CC, GRB.MINIMIZE)
Only in this equation the variable is multiplied by f
When F=set(range(1, 2)), the result CC is 1, but when F=set(range(1, 3)), the result CC is 2. If the range of F is further expanded, the CC remains unchanged. for 2 I[r, (i, j), f] is a binary variable, and CC is the maximum value of f in the binary variable I[r, (i, j), f]. F is a set, and f is a number in this set. f represents resources, where the larger the range of F, the more resources are available. r is a request and (i, j) is a partition. CC represents the maximum resource consumption among all partitions.
The goal is to minimize the variable CC. When F is set to range(1, 3) or expanded further compared to F=set(range(1, 2)), the CC value increases. I did not modify the model or other input parameters, just changed the range of the resource F. I Don't understand why under the same conditions, when the resource scope increases, the CC increases. Generally, other things being equal, an increase in resources should cause the resource consumption that needs to be minimized to remain the same or decrease

Hi,
When F=set(range(1, 2), the result CC is 1, but when F=set(range(1, 3), the result CC is 2, if the range of F is further expanded, then CC does not change, and it is still 2
I am not sure I understand your question. What do you expect to see as a value for the variable \(\texttt{CC}\) as the range of \(\texttt{F}\) increases? I am not sure why there should be a correlation between the range of \(F\) and the optimal value of variable \(\texttt{CC}\). What does \(\texttt{I[r, (i,j), f]}\) represent in your code snippet? Is it a variable or an input data? What values can it take?
 If \(\texttt{I[r, (i,j), f]}\) is a nonnegative decision variable, the optimal solution might be the one where these variables are assigned to 0 and then increasing the range of \(\texttt{F}\) would not have an impact on the value of \(\texttt{CC}\).
Best regards,
Maliheh
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