Optimal policies for aggregate production and capacity planning under rapidly changing demand conditions

This paper presents an optimal control approach to continuous-time aggregate production planning problems. The proposed approach describes the production and capacity expansion processes in the form of differential equations with regular production, overtime and capacity expansion 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 and optimal control policies can be obtained. This approach is of special importance when taking into account highly changing demand profiles and nonlinear cost functions. Study of the maximum principle results in analytical properties for the optimal production and capacity expansion policies and conditions for their changeover. Based on these results, insight into the optimal behaviour of the production system is gained and a fast numeral method is developed to identify and sequence the optimal policies for arbitrary demand profiles. A computational example illustrates the effectiveness of the approach.