Abstract
Abstract The necessary and sufficient conditions are derived for determining the optimal number of replenishment cycles and their start times in a deterministic continuous-time finite replenishment inventory model with a finite planning horizon. The differences between this model and its instantaneous replenishment counterpart are pointed out. It is shown that an optimal solution can always be found when the number of replenishment cycles is preset, the demand function is increasing and the replenishment rate is sufficiently large. It is also shown that when the number of replenishment cycles is unspecified, the problem can be solved by first determining the optimal cycle start limes for a given number of cycles m and then optimizing over m.
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