A single product, multi-period, aggregate production planning problem is formulated as a Linear-Quadratic Gaussian (LQG) optimal control problem with probabilistic constraints on state and control variables. This stochastic problem is based on a classical model developed by Holt, Modigliani, Muth and Simon, and known in the literature as HMMS model. The central idea is to extend the original HMMS model in order to take into account both chance-constraints on the decision variables and an ARMA forecasting model to represent the fluctuation of demand. Essentially, the paper discusses the main features that allow transforming the problem into a chance constrained LQG pattern. In addition, two sub-optimal techniques for solving this kind of problem are briefly described. At last, an illustrative example of how to provide aggregate production plans from the proposed problem is presented.
production planning; decision-making hierarchy; stochastic control; sub-optimal control; forecasting
