I have a binary decision variable \(x_{kn}\) and I would like to model a situation like the following: If \(x_{kn}=1\), then
Where, \(p\geqslant2\) is given, \(C_n\) and \(b_k\) are nonnegative integers given as inputs and \(A_n\) is a nonnegative integer decision variable. At least one constraint of the above \(p+1\) constraints has to be true. Can I model this in linear integer programming? I thought of adding binary variables \(y_i\) such that \(x_{kn}=\sum_{i=1}^{p+1}y_{ikn}\) but I cannot continue (if I am even right). asked 10 Jan '18, 11:41 zbir 
I suspect you have some indexing errors in your question. If all \(C_n\) are nonnegative, each constraint implies the next, so the OR operator reduces to the last constraint. answered 10 Jan '18, 12:58 Rob Pratt So you mean I just have to write the constraint like \(A_n+C_{n+1}+\ldots+C_{n+p}\geqslant b_k x_{kn}\) ?
(10 Jan '18, 13:42)
zbir
Yes, if your question is stated correctly.
(10 Jan '18, 14:01)
Rob Pratt
Let me give an example to illustrate my problem. Assume \(p=3\) and \(b_k=3\) and \(C_{n+1}=0\), \(C_{n+2}=0\) and \(C_{n+3}=1\). Also, say, the variable \(A_{n}=2\). Here, \(A_n+C_{n+1}+C_{n+2}+C_{n+3}\geqslant b_k\) but I cannot set \(x_{kn}=1\) because \(A_n+C_{n+1}+C_{n+2}< b_k\).
(10 Jan '18, 14:29)
zbir
I have updated the question.
(10 Jan '18, 14:31)
zbir
