An optimal control method for aggregate production planning in large-scale manufacturing systems with capacity expansion and deterioration

An optimal control approach to continuous-time aggregate production planning problems is presented. The proposed approach describes the production and capacity evolution (expansion, sell and deterioration) processes in the form of differential equations with regular production, subcontracting and capacity change rates controllable on one hierarchical level. In this way, the traditional disadvantages of the two-level problem consideration (one level for strategic capacity planning and the other for production smoothing) are avoided. Analytical properties for optimal production and capacity control regimes and conditions for their changeover are derived by the maximum principle. Based on these results, an insight into the optimal behaviour of the production system is gained and a fast numerical method is developed to identify and sequence the optimal regimes for arbitrary demand profiles. A computational example illustrates the effectiveness of the approach.