Abstract
This paper presents two economic order quantity models in which a fraction β(t) 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 lead time, an objective function representing the annual cost of an inventory system by defining an ordering cost, an inventory holding cost, a time-weighted backorder cost and a lost sales penalty cost is developed. Model A suggests an annual inventory cost function defined by introducing the function of backorder ratio that is linearly decreasing in proportion to the length of backorder period. In model B, the annual inventory cost function is defined with the assumption that backorder ratio, β(t), follows the negative exponential function. Both proposed models provide numerical iteration methods to obtain the economic order quantity, respectively. In case β(t)=1,the presented both models reduce to the backorder model, respectively.
