OPTIMAL POLICIES FOR AGGREGATE PRODUCTION AND CAPACITY PLANNING UNDERRAPIDLY CHANGING DEMAND CONDITIONS

This paper presents an optimal control approach to continuous-time agg regate production planning problems. The proposed approach describes t he production and capacity expansion processes in the form of differen tial equations with regular production, overtime and capacity expansio n rates controllable on one hierarchical level. In this way, the tradi tional disadvantages of the two-level problem consideration (one level for strategic capacity planning and the other for production smoothin g) are avoided and optimal control policies can be obtained. This appr oach is of special importance when taking into account highly changing demand profiles and nonlinear cost functions. Study of the maximum pr inciple results in analytical properties for the optimal production an d capacity expansion policies and conditions for their changeover. Bas ed on these results, insight into the optimal behaviour of the product ion system is gained and a fast numeral method is developed to identif y and sequence the optimal policies for arbitrary demand profiles. A c omputational example illustrates the effectiveness of the approach.