Autonomous and induced learning: an optimal control approach

The paper considers a production and process improvement problem of a firm in which the total manufacturing costs of a specific product depend on the output rate as well as the effects of autonomous and induced learning. Autonomous learning typically results from the repetition of a particular task, whereas induced learning is a result of explicit investments in production process improvements. The cumulative effects of the learning processes are represented by two stocks of knowledge. The stock of autonomous knowledge is built up at a rate corresponding to current output. Induced knowledge is built up by process improvement investments. Both stocks are subject to decay, due to obsolescence or forgetting knowledge. For short and long-term planning situations, we study the optimal evolution over time of the output rate, the process improvement expenditure rate and the two stocks of knowledge.