On a finite production model with random defective rate and shortages allowed and backordered

Chiu and Chiu studied the problem of random defective rate on the Economic Production Quantity model with backorder permitted. They considered a random defective rate and all defective items assumed not repaired. In this note, we will offer a simple algebraic approach to replace their differential calculus skill to find the optimal production lot size and optimal maximal backorder level allowed under the expected annual cost minimized.