upper bound for variable 1 = value of variable 2

hello everyone,

i have a question about my aimms project:

i have two variables: x(t,k) and y(t,k)

now i want to determine, that

if x(t,k) < y(t,k) then y(t,k) = x(t,k)

i already know that this is not possible with an if-statement.

has anybody an idea?

Thanks in advance.

Seb

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What type of variables are x and y? Binary, integer, or continuous?

both are integer variables.

But kan x also be greater than y? That is not completely clear to me from what you write.

yes, that’s right. x can also be greater than y.

so in short i compare two variables and want both to adopt the lower value.

One way to approach this is to introduce an auxillary variable z(t,k) and solve for following

Max z(t,k)

s.t

z(t,k) <= x(t,k)

z(t,k) <= y(t,k)

Other way, you can try out is:

Write following constraints (introduce dummy binary variable delta(t,k) and build following relations)

x(t,k) <= y(t,k) + (big-M)*delta(t,k)

x(t,k) >= y(t,k) -(big-M) *(1-delta(t,k))

Write Indicator constraints in AIMMS as

if delta(t,k)=0 then z(t,k) = x(t,k)

if delta(t,k)=1 then z(t,k) = y(t,k)

Best Wishes,
Kumar.

Hi @Sebastian Schäfer

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