Following the method described in Formula label outside of formula
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\noindent text
\begin{flalign}
\text{(P)}&&\min_{x_{ij},\delta_i} \sum_{i=1}^m (P_i^{svr} + P_i^{cool})&&\phantom{\text{(P)}}
\end{flalign}
text
\end{document}

As daleif points out in the comments, the textual superscripts like "svr" and "cool" should be in upright, not italic, text. I left them italic, mimicking the OP's original effort, since they had nothing to do with placing the label on the left. More properly, one should use \mathrm{} or one of the several other ways to force those superscripts upright.
And here is another way to achieve the leftward label, using my stackengine package instead of amsmath (the only quirk is the \rule that I added because the vertical space above the equation was otherwise too short).
\documentclass{article}
\usepackage{stackengine}
\begin{document}
\noindent text
\begin{equation}
\renewcommand\useanchorwidth{T}
\renewcommand\stacktype{L}
\stackon[0pt]{$\displaystyle\min_{x_{ij},\delta_i} \sum_{i=1}^m (P_i^{svr} + P_i^{cool})
$}{\makebox[\textwidth][l]{(P)}\rule{0ex}{5.5ex}}
\end{equation}
text
\end{document}

One flexibility of this approach is that you could make the \makebox of width, for example, [.9\textwidth] which would provide for a constant indent of the label with respect to the left margin.
Finally, If one didn't need the label left-aligned, but merely offset to the left (let's say a fixed amount), a third approach could use \llap{(P)\hspace{1in}} at the beginning of the equation in the equation environment.
(6), you could use the command\tag{(P)}together with\labelfor your equation. It will change the(6)by(P), and each time you call the equation it compiler put a(P). Note: the packageamsmathneeds to be loaded. – Dox Feb 11 '14 at 11:30(P)and(6)schizophreny, but do as you wish :) – yo' Feb 11 '14 at 12:09