  This paper presents a general class of dynamic stochastic optimization
problems we refer to as Stochastic Depletion Problems. A number of challenging
dynamic optimization problems of practical interest are stochastic depletion
problems. Optimal solutions for such problems are difficult to obtain, both
from a pragmatic computational perspective as also from a theoretical
perspective. As such, simple heuristics are highly desirable. We isolate two
simple properties that, if satisfied by a problem within this class, guarantee
that a myopic policy incurs a performance loss of at most 50 % relative to the
optimal adaptive control policy for that problem. We are able to verify that
these two properties are satisfied for several interesting families of
stochastic depletion problems and as a consequence identify efficient
near-optimal control policies for a number of interesting dynamic stochastic
optimization problems.
