An EPQ Model with Imperfect Production Process without Derivatives

A different approach to obtain the Economic Order Quantity (EOQ) and Economic Production Quantity (EPQ) models with partial backordering and several extensions without taking derivatives is presented.  We use limiting values on a finite planning horizon without reference to the use of derivatives, neither for necessary conditions nor for second order sufficient conditions. Furthermore, the algebraic derivation immediately provided the value of the average cost function in optimum.   An efficient and easy procedure is developed to find the optimal production run length, order quantity, optimal process quality and the optimal fill rate.  Numerical examples are provided to show the solution procedure.