Installment for advance payment and pricing decisions for an inventory system under power demand pattern and all-units discount

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Advance payment method has emerged as an effective mechanism to control not only any company's cash flow but also order cancellations. To encourage customers to use the prepayment mechanism, companies offer a reduction opportunity on the products per unit purchase cost based on the purchased quantity. This work analyzes a retailer's joint installment for advance payment, pricing, and inventory policies to maximize profit under a combined order-sensitive advance payment and all-units discount system. To make the model more representative, the demand is incorporated as a multiplicative form of the effects of selling price as logit and time as power patterns, and shortages are also taken into account during the model's formulation. Theoretical expressions are derived to identify whether the inventory process is unprofitable under a joint link-to-order advance payment and all-units discount arrangement. Utilizing all the derived analytical expressions, an efficacious algorithm is built to attain the optimal installment frequency for prepayment, selling price, order quantity, and shortage amount for the inventory manager. To further study the effects of a combined link-to-order prepayment and all-units discount scheme, the outcomes of several numerical examples are documented. Finally, an exploration is carried out by varying the values of all demand parameters and inventory cost parameters under or in the absence of the combined link-to-order prepayment and all-units discount scheme to provide useful guidelines for the industry manager. A noteworthy and advantageous finding for the inventory management practitioner is that by adopting a linked-to-order prepayment and discount system, certain inventory strategies previously considered unprofitable in the absence of quantity-based advance payment and discount programs have the potential to become profitable. To minimize the cost related to prepayment amounts, the inventory manager should increase the optimal installment number when the installment cost is low but decrease it when the installment cost is high. Moreover, to mitigate the impact of high price sensitivity on demand, the practitioner ought to reduce the optimal selling price and decrease the order quantity per cycle, thereby maintaining customer demand.