The economic production lot size model extended to include more than one production rate

We study an extension of the economic production lot size model, where more than one production rate can be used during a cycle. Moreover, the production rates, as well as their corresponding runtimes are decision variables. We decompose the problem into two subproblems. First, we show that all production rates should be chosen in the interval between the demand rate and the production rate which minimizes unit production costs, and should be used in an increasing order. Then, given the production rates, we derive closed-form expressions for all optimal runtimes as well as the minimum average cost. This analysis reveals that it is the size of the setup cost that determines the need for being able to use several production rates. We also show how to derive a near-optimal solution of the general problem.