TeX forces the scriptstyle when typesetting denominators in display math.
This way the min
operator loses the limits, which are typeset in a nolimit
way.
I suggest to typeset \limits
as suggestd by PeterGrill:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
s_j=\frac{e_j}{\min\limits_{1 \leq k \leq m-1} \big\{ t_{jk} + t_{j(k+1)} \big\}}
\end{equation*}
\end{document}
Producing:

As correctly remarked by @Thurston, you can also achieve a similar using the \displaystyle
cmmand, which yields the same result here, but it's not recommended since it changes all of the group style. Anyway here it is:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
s_j=\frac{e_j}{\displaystyle\min_{1 \leq k \leq m-1} \big\{ t_{jk} + t_{j(k+1)} \big\}}
\end{equation*}
\end{document}
Outputting:

\limits_
after the\min
. For future reference, while code snippets are useful in explanations, it is always best to compose a fully compilable MWE that illustrates the problem including the\documentclass
and the appropriate packages so that those trying to help don't have to recreate it.