\begin{align}\label{eq_opt}
    \max_{z_{ip}}\sum_{i=1}^{I}\sum_{p\in\mathcal{P}}z_{ip}\tau_{i}^{p} \text{ s.t. }\sum_{i=1}^{I}z_{ip} \leq Q^{p} \thickspace \forall p \text{ \& }\sum_{p\in\mathcal{P}}z_{ip} = 1\thickspace\forall i,
\end{align}
