maximization argument in a minimisation objective Value

Question

Hi All,I would like to write the following equation in my objective variable in AIMMS. I cannot manage to insert a correct notation for the max argument that works. I want to pick the v with the highest value for Zkpv, and minimize this value. My current objective (without the max argument) variable looks like this at the moment.Could somebody please help me? Kind Regards

mohansx · Accepted Answer

@samlobo , this is a minimax objective which has been discussed in section 6.2 of the AIMMS modelling guide. Based on my understanding of your question,

Declare a variable as

max_OrderInTry(k, p)

with a constraint, forall (k, p, v)

max_OrderInTray(k, p) >= OrderInTray(k, p, v)

Now your objective function can be:

Min summ(k,p), MultiPlicity(k) * max_OrderInTray(k, p)]

max_OrderInTray(k, p) will be greater than OrderInTray(k, p, v) across all v and because you are including this term in the minimization objective, it will be equal to the maximum value in OrderInTray(k, p, v).

samlobo · Answer

@mohansxThank you very much for your time and effortto explain it so clearly to me.I just implemented your suggested changes, and it works like charm.

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