An economic order quantity model with partial backordering and a special sale price

A constant unit purchase cost is one of the main assumptions in the classic economic order quantity model. In practice, suppliers sometimes offer special sale prices to stimulate sales or decrease inventories of certain items. In this paper we develop an EOQ model with a special sale price and partial backordering. We prove the convexity of the cost-reduction function if a special order is placed at the special sale price. A solution method is proposed and numerical examples are presented.

► We combine two of the extensions of the basic EOQ found in the literature.
► Partial backordering of demand during a stockout period and responding to a short-term one-time opportunity for a discount.
► We develop and prove optimality of the solution.