  We consider a singular control problem where the reward function depends on
the state of the process. The main objective of this paper is to establish
sufficient conditions for determining the optimality of the one-barrier and
$(2n+1)$-barrier strategies in two distinct scenarios. Firstly, when the
uncontrolled process $X$ follows a spectrally negative L\'evy process with a
L\'evy measure defined by a completely monotone density. Secondly, when $X$ is
a Brownian motion with a drift. Additionally, we provide an algorithm to
compute the barrier values in the latter case.

Optimization and Control