In this article, we propose a new continuous-time stochastic inventory model with deterioration and stock-dependent demand items. We then formulate the problem of finding the optimal impulse control schedule that minimizes the total expected return over an infinite horizon, as a quasivariational inequality (QVI) problem. The QVI is shown to lead to an (s, S) policy, where s and S are determined uniquely as a solution of some algebraic equations.