Nowadays, the reverse logistics of products has become an indispensable mechanism to preserve the equilibrium of industrial market. Besides, it can reduce the environment impact related to raw material extraction, and, additionally, it can increase productivity and profitability of a company. This article is concerned with this issue, because it models the production planning problem as a closed-loop system in which returned products are recovered. In this problem, demand for new products and return of used-products are random variables with known probability distributions. Since physical constraints on inventory and production variables are considered, chance-constraints are explicitly introduced into the problem's formulation. A sub-optimal approach is considered, since arriving to an optimal global solution would be either unfeasible or unpractical due to complexities such as randomness and dimensionality. A Linear-Quadratic-Gaussian (LQG) problem with chance-constraints is provided as an example of sub-optimal production planning policy for a closed-loop system. Thus, it is possible to show the applicability of this strategy in creating production scenarios that help managers to make decisions about the use of company's resources.
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