K. Kogan et E. Khmelnitsky, AN OPTIMAL-CONTROL METHOD FOR AGGREGATE PRODUCTION PLANNING IN LARGE-SCALE MANUFACTURING SYSTEMS WITH CAPACITY EXPANSION AND DETERIORATION, Computers & industrial engineering, 28(4), 1995, pp. 851-859
An optimal control approach to continuous-time aggregate production pl
anning problems is presented. The proposed approach describes the prod
uction and capacity evolution (expansion, sell and deterioration) proc
esses in the form of differential equations with regular production, s
ubcontracting and capacity change rates controllable on one hierarchic
al level. In this way, the traditional disadvantages of the two-level
problem consideration (one level for strategic capacity planning and t
he 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 syst
em is gained and a fast numerical method is developed to identify and
sequence the optimal regimes for arbitrary demand profiles. A computat
ional example illustrates the effectiveness of the approach.