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Stochasticscheduling problems are difficult stochastic control problemswith combinatorial decision spaces. In this paper we focus ona class of stochastic scheduling problems, the quiz problem andits variations. We discuss the use of heuristics for their solution,and we propose rollout algorithms based on these heuristics whichapproximate the stochastic dynamic programming algorithm. Weshow how the rollout algorithms can be implemented efficiently,with considerable savings in computation over optimal algorithms.We delineate circumstances under which the rollout algorithmsare guaranteed to perform better than the heuristics on whichthey are based. We also show computational results which suggestthat the performance of the rollout policies is near-optimal,and is substantially better than the performance of their underlyingheuristics.