EPQ models with varying setup cost

In this paper, the classical economic production quantity (EPQ) model is generalized by considering a relationship between the setup cost and the production run length. The dependency between the setup cost and run length can be related to process deterioration and learning and forgetting effects. Two models are developed, the first of which is for the case when shortages are not allowed and the other one permits shortages. The cost functions associated with these models are proved to be convex and optimal solutions are determined. Results show that the relationship between setup cost and production run length has a significant impact on the optimal lot size and average total cost in the EPQ model. Numerical examples are presented to demonstrate the utility of the models.