Observations on the economic manufacture quantity model with learning and forgetting

The economic order (manufacture) quantity model with learning and forgetting has attracted the attention of researchers since the 1960s. All the models developed have limitations, of which two will be addressed in this article. First, the models found in the literature do not address the problem of when the learning exponent b approaches or exceeds the value 1, where these models are mathematically invalid for the special cases of b=1 and 2, and not investigated for the cases 1<b<2 and b>2. Second, the models found in the literature assume that the holding cost per unit is fixed even though the unit production cost is decreasing because of learning. This limitation would suggest producing in smaller lot-sizes than their optimal values. Mathematical models are developed, and existing learning models are revised to overcome these limitations. Numerical examples are presented with results discussed.