Resize an eqnarray environment

with use of mathtools and nccmath you can slightly reduce size of equation (without changing font size):

\documentclass[hyperref={pdfpagelabels=false}]{beamer} \usepackage{mathtools, % instead amsmath, provide `\mathclap` nccmath, % for smaller `sum` symbol amssymb} \begin{document} \begin{frame}{test} \begin{align} & \textbf{TP} ~~\max \medop\sum_{\mathclap{i \in N\setminus\{4\}}} J_{i} z_{i} \label{S1}\\ & \text{st } \medop\sum_{j \in N} xv_{ij} = z_{i},\ \forall i \in N \label{S2} \end{align} \end{frame} \end{document} 

note: eqnarray is long time deprecated and replaced with math environment from amsmath.

for comparison result with your mwe:

Don't use \resizebox or scalebox unless you're fine with making your document look like an attempt at a ransom note.

To conserve some (vertical) space, don't place the "such that" statement on a separate line, and do place the limits of summation to the right of the summation symbols rather than below and above them; do this by writing \sum\nolimits. And, do use LaTeX "operators" such as \max for some standard math notation.

Since there seems to be no reason to perform vertical alignment, just use a gather environment. A final comment: The eqnarray environment is badly deprecated and should be avoided. If you must perform alignment across equations, use the align environment (provided by the amsmath package).

The following screenshot provides a before-and-after comparison; the first two equations generate your code, and the next two show a space savings of more than a third -- all without having to resort to \resizebox-based tricks.

\documentclass{beamer} \begin{document} \begin{frame}{test} \hrule \begin{eqnarray} && \textbf{TP} ~~\text{Max} \sum_{i \in N\setminus\{4\}} J_{i} z_{i} \label{S3}\\ && \text{st} \nonumber\\ && \sum_{j \in N} xv_{ij} = z_{i}, ~~\forall i \in N \label{S4} \end{eqnarray} \hrule \begin{gather} \mathbf{TP}\quad \max \sum\nolimits_{i\in \mathbb{N}\setminus\{4\}} J_{i} z_{i} \label{S1}\\ \text{s.t. } \sum\nolimits_{j \in N} xv_{ij} = z_{i}\quad \forall i\in \mathbb{N} \label{S2} \end{gather} \hrule \end{frame} \end{document}