  In this paper, we consider an infinite horizon, continuous-review, stochastic
inventory system in which cumulative customers' demand is price-dependent and
is modeled as a Brownian motion. Excess demand is backlogged. The revenue is
earned by selling products and the costs are incurred by holding/shortage and
ordering, the latter consists of a fixed cost and a proportional cost. Our
objective is to simultaneously determine a pricing strategy and an inventory
control strategy to maximize the expected long-run average profit.
Specifically, the pricing strategy provides the price $p_t$ for any time
$t\geq0$ and the inventory control strategy characterizes when and how much we
need to order. We show that an $(s^*,S^*,p^*)$ policy is optimal and obtain the
equations of optimal policy parameters, where $p^*=\{p_t^*:t\geq 0\}$.
Furthermore, we find that at each time $t$, the optimal price $p_t^*$ depends
on the current inventory level $z$, and it is increasing in $[s^*,z^*]$ and is
decreasing in $[z^*,\infty)$, where $z^*$ is a negative level.
