center part of equation

Question

I have an equation, as shown in the following picture:

I want to center the second part of the objective function ( + \alpha \sum_{j} \left(Qp_j + Qn_j\right) ) between the two red lines. How can I achieve that. The following is my MWE:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
The objective is to minimize the total operational cost:
\begin{equation}
\begin{gathered}
\min z = \mathrm{fa} \left(N_{\mathrm{h}} \mathrm{CFW} \sum_{j} Fw_j + 
             \mathrm{CHU} \sum_{k} Q_k^{\mathrm{HU}} + \mathrm{CCU} \sum_{k} Q_k^{\mathrm{CU}}\right) \\ 
           + \alpha \sum_{j} \left(Qp_j + Qn_j\right) 
\end{gathered}
\end{equation}
\end{document}

Answer 1

Unless the material on the second row falls in the scope of "fa" (which, judging by the screenshot you've posted, isn't the case), I would not center the material on the second row with respect to the parentheses on the first row. Instead, I would use a split environment, as is shown in the screenshot below. Why not center the material on row 2? Because doing so risks "losing it" in the clutter, visually/typographically speaking.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
    \begin{equation}\begin{split}
    \min z &= \mathrm{fa} \biggl(N_{\mathrm{h}} \mathrm{CFW} \sum_{j} Fw_j 
             + \mathrm{CHU} \sum_{k} Q_k^{\mathrm{HU}} 
             + \mathrm{CCU} \sum_{k} Q_k^{\mathrm{CU}}\biggr) \\ 
    &\quad+ \alpha \sum_{j} \bigl(Qp_j + Qn_j\bigr) 
    \end{split}\end{equation}
\end{document}

---

If you must center the second row relative to the RHS of the first row, you could so via an array environment embedded in the equation environment.

\documentclass{article}
\usepackage{amsmath,array}
\begin{document}
The objective is to minimize the total operational cost:
\begin{equation}
\min z = 
\begin{array}[t]{@{}>{\displaystyle}c@{}}
\mathrm{fa} \biggl(N_{\mathrm{h}} \mathrm{CFW} \sum_{j} Fw_j 
             + \mathrm{CHU} \sum_{k} Q_k^{\mathrm{HU}} 
             + \mathrm{CCU} \sum_{k} Q_k^{\mathrm{CU}}\biggr) \\ 
{}+ \alpha \sum_{j} \bigl(Qp_j + Qn_j\bigr) \\
\end{array}
\end{equation}
\end{document}

Answer 2

Mico's answer is great. I just wanted to point out that if you want the centering, an easier (but perhaps more hacky) way to do it is to simply push the second line to the right:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
The objective is to minimize the total operational cost:
\begin{equation}
\begin{gathered}
\min z = \mathrm{fa} \left(N_{\mathrm{h}} \mathrm{CFW} \sum_{j} Fw_j + 
             \mathrm{CHU} \sum_{k} Q_k^{\mathrm{HU}} + \mathrm{CCU} \sum_{k} Q_k^{\mathrm{CU}}\right) \\ 
             \hphantom{\min z = {}} % Pushes content to the right by the right amount
           + \alpha \sum_{j} \left(Qp_j + Qn_j\right) 
\end{gathered}
\end{equation}
\end{document}