Simultaneous Nonlinear Learning Curve Estimation

Over the years, it has been demonstrated repeatedly [Gulledge and Womer (1986)] that the learning curve is not appropriate for modeling variable cost in made-to-order production programs unless production rate is constant. The effects of production rate changes are not considered in models which employ only learning curve techniques, even though the theoretical foundations for investigating production rate impacts on costs have been considered by economists for many years. These learning curve models consider cumulative output to be the most important cost determinant. After Alchian (1959) implicitly combined a learning curve hypothesis with economic theory in a study related to military airframes, research has appeared that integrates the approaches [Rosen (1972), Washburn (1972), Womer (1979), Womer and Gulledge (1983), Gulledge and Womer (1986)]. Most of these studies are based on production models that are continuous in both time and output rate. The model presented in this paper considers the number of units being produced as a discrete variable within a multistage optimization problem framework.