A Constrained Stochastic Production Planning Problem with Imperfect Information of Inventory
Abstract
In this paper, an aggregate production planning problem is formulated as a chance-constrained stochastic control problem under imperfect information of states (i.e., the inventory levels). Using the Kalman filter device, the mean and covariance of state variables are estimated. Then the certainty equivalence principle is applied, resulting in a deterministic problem that is equivalent to the original formulation. In order to provide a sequential optimal solution to the equivalent problem, the Naive Feedback Controller (NFC) approach is used. It provides a revised sub-optimal production policy to the stochastic problem. An example illustrates the applicability of this approach
