  We study a risk-aware robot planning problem where a dispatcher must
construct a package delivery plan that maximizes the expected reward for a
robot delivering packages across multiple epochs. Each package has an
associated reward for delivery and a risk of failure. If the robot fails while
delivering a package, no future packages can be delivered and the cost of
replacing the robot is incurred. The package delivery plan takes place over the
course of either a finite or an infinite number of epochs, denoted as the
finite horizon problem and infinite horizon problem, respectively. The
dispatcher has to weigh the risk and reward of delivering packages during any
given epoch against the potential loss of any future epoch's reward. By using
the ratio between a package's reward and its risk of failure, we prove an
optimal, greedy solution to both the infinite and finite horizon problems. The
finite horizon problem can be solved optimally in $O(K n\log n)$ time where $K$
is the number of epochs and $n$ is the number of packages. We show an
isomorphism between the infinite horizon problem and Markov Decision Processes
to prove an optimal $O(n)$ time algorithm for the infinite horizon problem.
