The digital computer algorithm produced by the methods of dynamic programming, generates optimal reactor-shutdown programs that (i) minimize the post-shutdown xenon concentration maximum, or that (ii) minimize the xenon concentration itself at a given post-shutdown time. Such shutdown programs are found to consist of pulsing the reactor at specified intervals. The number and duration of the pulses depend on the parameters involved, especially the magnitude of the flux constraints, and the constraints on the xenon override reactivity available in a given fuel loading.