Linearizing constraint ( multiplication of binary variables)

Question

I am trying to think of contraint(s) that can linearize constraint below.

$\sum_{T} \sum_{TR} Z_{(T,D)}* Y_{(TR,T)} \leq CAP_{(D)} \forall D$

Both Z nad Y are Binary Variables and CAP is capacity parameter.

I tried to apply big M but without luck.

Answer 1

Although the usual linearization of a product of two binary variables requires three inequalities, you can get by with only one here. You can enforce $(Z \land Y) \implies X$ via linear constraint $Z + Y - 1 \le X$.