Third International Conference on Production Research – Americas’ Region 2006 (ICPR-AM06) IFPR – ABEPRO - PUCPR - PPGEPS A Constrained Sequential Stochastic Production Planning Problem A Constrained Sequential Stochastic Production Planning Problem A Constrained Sequential Stochastic Production Planning Problem A Constrained Sequential Stochastic Production Planning Problem Under Imperfect Information of Inventory Under Imperfect Information of Inventory Under Imperfect Information of Inventory Under Imperfect Information of Inventory Oscar S. Silva Filho Affiliation – oscar.salviano@cenpra.gov.br Wagner Cezarino Affiliation – wagner.cezarino@cenpra.gov.br Renato Archer Research Center - CenPRA/MCT Rod. D. Pedro I, (SP 65) Km. 143,6 13089-500 - Campinas – São Paulo - Brazil Email: oscar.salviano@cenpra.gov.br Abstract Abstract Abstract Abstract: In this paper, a constrained stochastic optimal control problem is formulated to represent a multi-period production planning problem with constraints on decision variables. It is assumed that inventory levels are not known exactly; then, a device, known as Kalman Filter, is used to estimate the inventory levels over the periods. Moreover, the complexity of this stochastic problem makes very difficult to provide a global optimal solution. In order to overcome such a difficulty, the stochastic problem is converted into a deterministic equivalent problem, which preserves the two first statistic moments related to inventory balance system. In sequence, a suboptimal heuristic named Open-Loop Feedback Controller (OLFC) is applied to this deterministic problem; and a quasi-optimal solution is then provided. The OLFC heuristic is easier to implement computationally than many other suboptimal heuristics; and it also allows revising the quasi-optimal solution periodically. At last, an illustrative example is introduced. The objective is to develop a production plan for a family of products from a stochastic production planning problem. The suboptimal plans provided by the application of the OLFC heuristic to the equivalent problem under perfect and imperfect