In this paper, we address the problem of dynamically scheduling jobs with abandonments. Processing times and release dates are arbitrarily distributed while patience times are exponentially distributed. The objective is to minimize holding costs and abandonment costs, either in the class of static list scheduling policies or in the class of dynamic policies with preemption. We first show an equivalence between holding costs and abandonment costs. When processing times are exponentially distributed and all jobs are available at time 0, we provide conditions under which a strict priority rule is optimal in the class of static list scheduling policies. Then we extend this result to the class of dynamic scheduling policy with preemption and arbitrary stochastic release dates.