A lot-sizing model with backordering under hybrid linked-to-order multiple advance payments and delayed payment

•A hybrid linked-to-order multiple advance payments and delayed payment is developed.•Backordering shortage is permitted.•Incorporating this payment scheme can efficiently stimulate sales due to applying delayed payment.•Provides the benefits of advance payment such as controlling the risk of cash flow.•The optimal and closed form solutions using proofing several theorems are obtained.

An economic order quantity model with backordering is investigated under a hybrid payment scheme. The payment scheme, which is also linked to order quantity, involves multiple advance payments as well as delayed payment. Incorporating this payment scheme can efficiently stimulate sales due to applying delayed payment; besides it provides the benefits of advance payment such as controlling the risk of cash flow. The developed model seeks to optimize the order and shortage quantities. Theoretical results are developed to determine the conditions of existence and uniqueness of the optimal solutions. Numerical examples illustrate the proposed model and solution method.