Learning curves and production functions: An integration

This paper explores a class of dynamic cost models that are designed for made-to-order production and are particularly applicable to the airframe industry. In these models we use optimal control theory to describe the time paths of resource use and production rate. The analytic solution for the most general specification of the model is unknown, however the imposition of a restriction on the relation between production rate and experience rate leads to a straightforward solution. The model implies that there exists an optimal trade-off between learning and production rate during the life of a program and that production rate should be changing throughout the life of the program in order to minimize cost. The model is compared with the learning curve, and the applicability of the model is explored by performing various parametric sensitivity analyses. The model's behavior is consistent with the dynamics of actual made-to-order production programs.