An economic production quantity model with flexibility and reliability considerations

The classical economic production quantity (EPQ) model assumes that items are produced by a perfectly reliable production process with a fixed set-up cost. While the reliability of the production process cannot be perfect without a price, its set-up cost can be reduced with investment in flexibility improvement. An EPQ model with a flexible and imperfect production process is proposed in this paper. This inventory optimization problem is then formulated as a geometric program (GP) and solved to obtain closed-form optimal solutions. After the theoretical treatment, a numerical example is provided to illustrate how the GP theories are applied to solve a given problem. Finally some aspects of post-optimality sensitivity analysis based on the GP approach are discussed.