Equation Left Alignment and centered numbering

Question

I have the following equation and ended up feeling defeated after trying several environments to make it the way I want. To have the Bigg[ and \Bigg], I changed my preferred \begin{equation}\begin{split}...\end{split}\end{equation} to the align environment. This made one thing better and everything else horrible. I need to have the equation numbers in the center and left aligned equations for all lines (indeed, I could use \qquad to shift the lines coming after the first to make it look better). And, yes, I use a two column IEEEtrans document.

\begin{align}
      \min \sum_{v\in \mathcal{V}} C^{AV}y_v + \sum_{\substack{a\in \mathcal{A},\\v\in \mathcal{V}}}
      \Bigg[ C^{FUEL}T_{o_a d_a}x_{av}
      \notag\\
      + \left(C^{FUEL}+C^{ZOV}\right)u_{av}
      \notag\\
      +C^{TAXI}\left(1-x_{av}\right)
      \notag\\
      +C^{PARK}_{d_a}\left(q_{av}-g_{av}\right)h_{av}\notag\\
      +C^{PARK}_0\left(q_{av}-g_{av}\right)\left(1-h_{av}\right)\Bigg]
      \notag\\
      +\sum_{a\in \mathcal{A}}\left(C^{EARLY}e_a +C^{LATE}l_a\right).
\end{align}

Based on the accepted answer, I made some modifications and could achieve what I wanted to have. For future reference, here is the code:

\begin{equation}\label[eq]{obj_fn}
\begin{alignedat}{2}
      \min\phantom{ + } & \sum_{v\in \mathcal{V}} C^\textrm{AV}y_v + \smash[b]{\sum_{\substack{a\in \mathcal{A},\\v\in \mathcal{V}}}}
     \Bigl[C^\textrm{FUEL}T_{o_a d_a}x_{av}\\[2ex]
     +~ &\left(C^\textrm{FUEL}+C^\textrm{ZOV}\right)u_{av}\\[1ex]
    +~ & C^\textrm{TAXI}\left(1-x_{av}\right)\\[1ex]
    +~ & C^\textrm{PARK}_{d_a}\left(q_{av}-g_{av}\right)h_{av} \\[1ex]
     +~ & C^\textrm{PARK}_0\left(q_{av}-g_{av}\right)\left(1-h_{av}\right)\Bigr] \\[1ex]
      +~ & \sum_{a\in \mathcal{A}}\mathrlap{\left(C^\textrm{EARLY}e_a +C^\textrm{LATE}l_a\right).}
\end{alignedat}
\end{equation}

Answer 1

A proposition with alignedat. I used only \Big brackets, which I think are large enough. Inside these brackets, I grouped some lines. Last, words used as indices of exponents should be treated as roman text, to have the proper spacing between the letters in the words (a word is not a product of variables)

\documentclass{article}

\usepackage{mathtools}

\begin{document}

\begin{equation}
\begin{alignedat}{2}
      \min\phantom{ + } & \sum_{v\in \mathcal{V}} C^\textrm{AV}y_v & + \smash[b]{\sum_{\substack{a\in \mathcal{A},\\v\in \mathcal{V}}}}
     \Bigl[ &C^\textrm{FUEL}T_{o_a d_a}x_{av} + \left(C^\textrm{FUEL}+C^\textrm{ZOV}\right)u_{av}\\[-1ex]
        & & &{} +C^\textrm{TAXI}\left(1-x_{av}\right) +C^\textrm{PARK}_{d_a}\left(q_{av}-g_{av}\right)h_{av} \\
       & & &{} +C^\textrm{PARK}_0\left(q_{av}-g_{av}\right)\left(1-h_{av}\right)\Bigr] \\
      + & \sum_{a\in \mathcal{A}}\mathrlap{\left(C^\textrm{EARLY}e_a +C^\textrm{LATE}l_a\right).}
\end{alignedat}
\end{equation}

\end{document} 

Answer 2

I'd preserve the inner structure, with one part per summation (the second one split across lines)

\documentclass{IEEEtran}
\usepackage{amsmath}
\usepackage{lipsum} % for mock text

\begin{document}

\lipsum[1][1-3]
\begin{equation}
\begin{aligned}
\min
 & \sum_{v\in \mathcal{V}} C^{AV}y_v \\
 & +\sum_{\substack{a\in \mathcal{A},\\v\in \mathcal{V}}}
   \Bigl[\begin{aligned}[t]
     &   C^{\mathrm{FUEL}}T_{o_a d_a}x_{av} \\
     & + (C^{\mathrm{FUEL}}+C^{\mathrm{ZOV}})u_{av} \\
     & + C^{\mathrm{TAXI}}(1-x_{av}) \\
     & + C^{\mathrm{PARK}}_{d_a}(q_{av}-g_{av})h_{av} \\
     & + C^{\mathrm{PARK}}_0(q_{av}-g_{av})(1-h_{av})\Bigr]
   \end{aligned} \\
 & +\sum_{a\in \mathcal{A}}(C^{\mathrm{EARLY}}e_a +C^{\mathrm{LATE}}l_a).
\end{aligned}
\end{equation}
\lipsum

\end{document}

If you adopt Times also for the math material, you're possibly able to squeeze more material in a line:

\documentclass{IEEEtran}
\usepackage{amsmath}
\usepackage{newtxtext,newtxmath}
\usepackage{lipsum} % for mock text

\begin{document}

\lipsum[1][1-3]
\begin{equation}
\begin{aligned}
\min
 & \sum_{v\in \mathcal{V}} C^{AV}y_v \\
 & +\sum_{\substack{a\in \mathcal{A},\\v\in \mathcal{V}}}
   \Bigl[\begin{aligned}[t]
     &   C^{\mathrm{FUEL}}T_{o_a d_a}x_{av} + (C^{\mathrm{FUEL}}+C^{\mathrm{ZOV}})u_{av} \\
     & + C^{\mathrm{TAXI}}(1-x_{av}) + C^{\mathrm{PARK}}_{d_a}(q_{av}-g_{av})h_{av} \\
     & + C^{\mathrm{PARK}}_0(q_{av}-g_{av})(1-h_{av})\Bigr]
   \end{aligned} \\
 & +\sum_{a\in \mathcal{A}}(C^{\mathrm{EARLY}}e_a +C^{\mathrm{LATE}}l_a).
\end{aligned}
\end{equation}
\lipsum

\end{document}

In any case, the textual superscript should be in upright type, like C^{\mathrm{FUEL}}.