||A time-discrete, constrained, Linear Quadratic Gaussian (LQG) production planning problem is formulated to develop a production plan with sub-optimal levels of production and remanufacturing for a single product. With the objective to define a strategy of remanufacturing used product, estimated return rates are used to provide production scenarios based on this plan. Nowadays, specific legislation is applied to many industrial sectors regard to the return of used products. Thus, motivated by environmental factors and a shortage of raw materials, partial or total reuse of return products are a high priority on business's agenda of many companies. This paper uses an approach of literature to solve a production-planning problem of a dynamic system that includes a reverse channel, with a remanufacturing facility. It is assumed that fluctuations of demand for serviceable products are approximated by stationary normal random variables. Thus, the constrained LQG problem here considered is converted to an equivalent but deterministic that can be solved by any quadratic programming method from literature, providing, as a result, sub-optimal inventory and production plans. Managers can use such plans as scenarios to evaluate future opportunities as costsí reduction, for instance. A simple usecase illustrates such ideas.