I have a constrained Optimization problem:
Decision variables:
Xih = Amount of item i in item group h . Xih is a real number.
Aih = Cost of item i in item group h
Cihj = property j of item i (in each unit) in item group h.
Bj = Minimum total property j.
Dj = Maximum total property j.
mih = Minimum of Xih
Mih = Maximum of Xih
Problem Formulation:
Min/Max z1= ∑h ∑i Aih Xih
s.t.
Bj ≤ ∑h∑i Cihj * Xih ≤Dj
where j is number of properties of items
mih ≤ Xih ≤ Mih
So, how do formulate this problem if I need only N elements from a group
something like
OR(X1h , X2h , X3h) == 1
OR(X1h , X2h , X3h) == 2 etc.
means can I constraint number of items in each group.
If I understood your problem, you should introduce new (binary) variables Y_ih which are 1 if X_ih > 0 and 0 otherwise. Then you can add two constraints:
1) X_ih
Dear Daveen
I think that your problem is solvable, but I need more information, and I agree with Davide that probably you would need binary variables because you are working with exclusive restrictions
What is a 'property' Bj and Dj?
Perhaps one way to solve it is to give each criterion 2 values, a maximum, and a minimum, and let the software work with those, and determine perhaps an intermediate value.
It would be a great help if you can put an example
Looks like a MILP problem (MILP = Mixed Integer Linear Programming). Check www.gams.com for modeling and suitable solvers.
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