  Many drugs used therapeutically or recreationally induce tolerance: the
effect of the substance decreases with repeated use. This phenomenon may reduce
the efficacy of the substance unless dosage is increased beyond what is healthy
for the individual. Restoring the effect of the substance can often be obtained
by taking a break from consumption. We propose designing dosing schedules that
maximize the desired effect of the substance with a given total consumption,
while factoring in the effect of tolerance. We provide a simple mathematical
model of response to consumption and tolerance that can be fit from data on
substance administration and response. Using this model with given parameters,
we determine optimal consumption schedules to maximize a given objective. We
illustrate with the example of caffeine, where we provide a schedule of
consumption for a user who values the effects of caffeine on all days but needs
extra alertness on some days of the week.
