Inventory management with hybrid cash-advance payment for time-dependent demand, time-varying holding cost and non-instantaneous deterioration under backordering and non-terminating situations

During the current pandemic period, the number of online transactions to purchase products through a mixed cash and prepayment agreement has increased significantly. Under this agreement, the buyer pays off a predefined percentage of the purchase price in advance, and the rest of the percentage is accomplished through the cash-on-delivery method. Adopting a practical scenario where the buyer has a storeroom with limited capacity, two sustainable inventory procedures for perishable items are developed, viz. (i) the inventory scheme with allowable shortages and fractional backlog, and (ii) the inventory scheme without ending. In both the schemes, not only the demand function but also the decay rate reveal an upward trend against storage time. However, the deterioration commencing moment is not instant but after a specific time interval from the products’ storage moment. The cost of storing items is adopted as a linear function of storing time as the decay rate shows an ascending trend against storing time. A salient criterion is developed to examine when the non-ending situation with salvage values is more economical for the industry manager than the zero ending situation with the regular selling price. Finally, several decision-making findings are presented after completing four numerical examples along with a real-life case study for the validation of the inventory schemes.