Multi-item inventory model with variable backorder and price discount under trade credit policy in stochastic demand

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.