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A general model of rotational grazing is constructed where in each of P consecutive time periods a mob of animals grazes one of m paddocks. The optimal grazing sequence is that which maximises their total herbage intake and satisfies the physical constraints of the grazing system. The total herbage intake is compared for four grazing strategies: continuous grazing, strict cyclic rotation, greedy rotation and optimal rotation. A branch-and-bound algorithm is used to find the global optimum strategy. A 100 ha system is simulated carrying 300-400 dairy cows for 60 days in late winter and early spring with a range of subdivisions and grazing durations to ascertain the effectiveness of the different strategies in maximising intake. It is shown that (1) continuous grazing maximises intake when pasture growth is in surplus to animal requirements, (2) that animals' herbage intake under rotational grazing is likely to be poor unless the rate of rotation is carefully synchronised to the pasture growth rate, (3) that grazing management makes little difference to productivity in comparison to stocking rate and average initial pasture, (4) that there is no reason to expect subdivision of land to increase productivity unless reasons such as pasture trampling on wet soil mitigate against long grazing durations. Greedy rotational grazing is found to increase herbage intake on multipaddock systems with an initially inhomogeneous distribution of pasture.