Aggregate production planning by stochastic control

Three stochastic control methods (Certainty Equivalence, Passive Learning and Active Learning) are applied to Holt, Modigliani, Muth and Simon’s classical aggregate production planning problem. The average results of the time paths of the optimal state and control variables are presented along with those of the total costs of the objective functinal. A statistical analysis is then conducted to study the variability of the sampling distribution of these Monte Carlo runs. When cost is used as a criterion for comparison, the Passive Learning method seems to yield the least cost among the three stochastic methods, and to have added little additional cost when compared to a deterministic model. This is encouraging because under uncertainty little additional cost would be incurred if decision-makers were advised to the appropriate stochastic method.