Trade credit mainly signifies increase in order quantity when retailer offers a trade credit to the customer. From the customer’s view, granting trade credit not only increases sales and revenue but also increases opportunity cost. So, the choice to offer trade credit is an important managerial consideration. Moreover another significant decision on purchasing is to include (or not to include) cash discount benefits and the motivations behind it. Therefore, the major objective of this article is to derive the inventory models for deteriorating items by maximizing the total profit of the retailer. The models includes the cash discount for the retailer depending on ordering quantity and also cash discount for the customer depending on the time. The customer’s demand is expressed as a function of time and price, which is appropriate for the products for which demand increases initially and after sometime it starts to decrease. Lastly, numerical examples along with sensitivity analysis are done, which extracts some fruitful managerial insights.

In this paper, the problem of lot sizing for the case of a single item is considered along with supplier selection in a two-stage supply chain. The suppliers are able to offer quantity discounts, which can be either all-unit or incremental discount policies. A mathematical modeling formulation for the proposed problem is presented and a dynamic programming methodology is provided to solve it. Computational experiments are performed in order to examine the accuracy and the performance of the proposed method in terms of running time. The preliminary results indicate that the proposed algorithm is capable of providing optimal solutions within low computational times, high accuracy solutions.