Optimal hierarchical stochastic production planning and control

The paper explores the problem of optimal hierarchical stochastic production planning and control in agile manufacturing workshops (AMW). A stochastic nonlinear programming model of production with delay interaction (which is a static optimization model to solve the dynamic optimization problem) is built up and transformed into a deterministic nonlinear programming model and further into a linear programming model by adding constraints. Then, Karmarkar's algorithm and an interaction/prediction algorithm are used to solve the model, and the corresponding programs have been written. Through hierarchial stochastic production planning examples, Karmarkar's algorithm, interaction/prediction algorithm and linear programming method in Matlab are compared, thus showing that the proposed approaches are very suitable for optimally decomposing AMW's random product demand plans into short-term stochastic plans to be executed by flexible manufacturing system (FMS) in AMW, especially for the case where work pieces are transferred between FMS through a shop storage with a delay of a production period.