Abstract
The paper presents an economic production quantity model in which a fraction β(t) (backorder ratio) of the demand is backordered and the remaining fraction 1-β(t) is lost during the stockout period. Under the assumptions of deterministic demand rate and deterministic production rate, an objective function representing the annual cost of a production system by defining a time-weighted backorder cost and a lost sales penalty cost per unit lost is developed. This paper suggests a numerical iteration method for the solution of economic production quantity and stockout quantity per period by definingβ(t) function representing the backorder ratio when backorder time is t. In case β(t)=1,the presented model reduces to the Fabrycky's model with complete backorders.
