Abstract
Price rebate is only permitted when purchases made by the customer exceed a predefined limit and they later buy other items from the purchaser. There are various forms of rebate used by production companies. This study provides a deteriorating inventory model of four-level production rates and derives the rebate-value-based demand with the product selling price under shortages. This model gives preference to optimal replenishment time, ordering quantity, rebate value, and selling price while maximizing total profit. This model first explores and discusses the demand function, which discretely hinges on the selling price of rebate value, followed by discussions on demand based on the selling price. This study proposes a solution through unique propositions and the construction of two algorithms that are suitable for four-level production; this has not yet been explored in-depth in the literature. Illustrative examples and a sensitivity analysis demonstrate the applicability of the proposed algorithms; the customer decides to buy a product that is larger than the minimum suitable for a price rebate and the buyer can then deal with a higher price rebate. The benefit of rebate marketing helps production companies increases conversion rates and encourages customers to purchase goods. This model demonstrates that proposing rebates can consume substantial pricing and inventory inferences and can result in a substantial increase in profit.