Price discounts for increased profitability under partial backordering

If some, but not all, customers are willing to wait for an out-of-stock product to become available, sellers may be able to increase their profits by offering a price discount to increase the number of backordered demands rather than losing those sales. We modify an existing model for the deterministic economic order quantity with partial backordering by making the backordering percentage a function of the size of the discount. We combine results about the optimal solution for a partial backordering model with a fixed backorder percentage and a search procedure to determine whether offering a discount is optimal and, if so, how large the discount should be to maximize profit.