# A unified presentation of inventory models under quantity discounts, trade credits and cash discounts in the supply chain management

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## Abstract

As is well known, trade credit represents one of the most flexible sources of short-term financing available to firms, principally because it arises spontaneously with the firm’s purchases. The decision to offer trade credit and the determination of the firm’s terms of sale are important managerial considerations. In addition, the purchasing firm’s decision to take (or not to take) advantage of a cash discount and the motivations behind such a decision are also important. Our literature review reveals the fact that the research about the inventory model under the conditions of cash discount and trade credit is still a popular topic in the area of operations and inventory management. The main object of this paper is, therefore, to present a combination of all such important factors as (for example) quantity discounts, trade credits and cash discounts in order to establish and investigate a new inventory model when the cash discount for the retailer depends on the ordering quantity and the cash discount for the customer depends on the time when the customer buys an item. We first develop the annual total relevant cost. Then, by using the mathematical analytic tools and techniques dealing with the functional behaviors (such as continuity, discontinuity, increasing, decreasing, convexity, and so on) of the annual total relevant cost, we prove four theorems to determine the optimal replenishment cycle time. Finally, the sensitivity analysis is executed to study the variation of different parameters on the optimal policy. By including citations of a number of closely-related recent works, we also propose to try to incorporate the concepts of quantity discounts into the inventory model considered thus far in order to develop a newer unified inventory model. It is sincerely believed that this proposal should be a rather interesting research topic for future investigations.

## Keywords

Inventory control and integrated model Quantity discounts Trade credits Cash discounts Ordering quantity Inventory models and optimization Pricing and finance Supply chain management Optimal replenishment cycle time Mathematical solution procedures## Mathematics Subject Classification

Primary 91B24 93C15 Secondary 90B30## References

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