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How to declare variable depends on other variable as a constraint in AMPL?

How to declare variable depends on other variable as a constraint in AMPL?

I'm trying to solve the minimize the difference between "maximum number of variable - minimum number of variable"

So, my objective equation is minimize max{t in 0..T}production[t] + min{t in 0..T}production[t]; (t is index and T is time periods parameter and production is decision variable.)

However, it is not linear algebra. Thus, I'm trying to declare 'max{t in 0..T} production[t]' as a variable 'y'. So, I would like to write 'var y >= all production'. But it's not working.

Solution

  • The constraint

    s.t. max_production{t in 0..T}: y >= production[t];

    will ensure that y is greater or equal than production[t] for all t in 0..T. If you minimize y then it will be exactly max{t in 0..T} production[t].