Formulate a constraint considering T as a set rather than a parameter
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Hello!
I am formulating a mathematical model and I encountered a problem, I am trying to simplify it through the following example:
First of all, I assumed T as a parameter (positive number).
Y_t is a binary parameter, where t in 1..T.
y_t is a binary variable, where t in 1..T.
Mathematically, I have formulated the following constraint:
(Y_t) + (y_t) + (Y_t+1) + (y_t+1) <= 1 for t in 1..T-1 if T > 1
For many reasons (too long to talk about and hard to explain), I need to consider T as a set instead of considering it as a parameter. In this case, how can the previous constraint be formulated mathematically?
Thank you in advance!
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Hi,
I don't know whether it makes sense for your application, but you could define everything over each element of \(T\).
\[\begin{align*}
Y_{i,t} &\in \{0,1\} &&\quad \forall i \in \{1,\dots,t\},\, t \in T\\
y_{i,t} &\in \{0,1\} &&\quad \forall i \in \{1,\dots,t\},\, t \in T\\
Y_{i,t} &+ y_{i,t} + (Y_{i,t}+1) + (y_{i,t}+1) \leq 1 &&\quad \forall i \in \{1,\dots,t-1\},\, t \in T \text{ if } t > 1
\end{align*}\]Best regards,
Jaromił1
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