  We analyze the problem of job scheduling with preempting on weighted jobs
that can have either linear or exponential penalties. We review relevant
literature on the problem and create and describe a few online algorithms that
perform competitively with the optimal scheduler. We first describe a na{\"
i}ve algorithm, which yields a high competitive ratio
($\Omega(\frac{M}{s_{\min}})$) with the optimal, then provide an algorithm that
yields a lower competitive ratio ($4\sqrt{\frac{M}{s_{\min}}} +
n\log{\frac{Mn}{s_{\min}}}$). Finally, we make a minor modification to our
algorithm to yield an algorithm that has an even better competitive ratio
($n\log{\frac{Mn}{s_{\min}}}$).
