Economic production quantity for a manufacturing system with a controllable production rate

Jamal and Sarker developed a model for determining the economic production quantity for fixed-interval demands. Some researchers have suggested that controlling production rate might be a solution to some quality and inventory problems. In this paper, we extend Jamal and Sarker's model by considering the production rate to be controllable. We develop mathematical models for this problem to minimize the total cost for two cases: (i) shortages are not allowed; (ii) shortages are allowed. These models find optimal production quantity and optimal production rate for both cases. The Hooke and Jeeves search algorithm is used to optimize the models, and numerical examples are provided. Sensitivity analyses of the given models are presented.