In this paper, a two echelon supply chain with one manufacturer and one retailer is developed for multi products. The retailer faced with the uncertain demand for all products which follows a normal distribution. The production process is assumed to be imperfect, and the defectiveness is assumed to follow a beta distribution. The manufacturer produces and delivers the products in a number of equal-sized batches to the manufacturer's warehouse, and thereby it is delivers in a number of equal batches to the retailer's warehouse. Shortages are allowed to occur, at the retailer side, and it is backordered partially. The retailer offers a price discount for backordered items to his customers. Both the lead time crashing cost and the partial backorder ratio are considered as the inverse function of lead time. Under these assumptions, there are three inventory models proposed in this paper, one with non-integrated approach, the other with an integrated approach without trade credit and finally an integrated approach with trade credit. A new iterative algorithmic procedure has been developed to minimise the total cost. Finally, numerical examples are given to illustrate the models and the sensitivity analysis is conducted over various model parameters.

This paper studies five different stock control policies in the supply chain management. The lead time can be shortened by extra investment between two entities. The vendor produces a single product and delivers the order quantity in a number of unequal shipments to the buyer. The unit holding cost is divided into financial and storage components. The vendor takes care of financial component until the products are sold to the end customers to encourage them to buy more products. In order to reduce emissions from production and to protect the environment, some legislative actions have been taken such as implementing taxes and penalties. The cost function also includes these taxes and penalties. The optimal solutions of this constrained mixed integer non-linear programming problem are obtained by using the Genetic Algorithm (GA). Numerical examples are employed and comparison works are carried out with other existing literatures. Results show that the performance of the system is better when it is operated under unequal shipment policies and vendor-managed inventory (VMI) agreement.