Quantity discount decisions considering multiple suppliers with capacity and quality restrictions

This article considers a supply chain inventory problem for a particular type of raw material with multiple suppliers, where each supplier offers all-unit quantity discounts as a motivation mechanism to increase the placed order quantities, and hence reduce the average the replenishment cost. In addition, multiple orders to the selected suppliers with different frequencies are allowed during a repeating order cycle. In this research, we propose a mixed integer nonlinear programming (MINLP) model to find the optimal number of orders and corresponding order quantities for the selected suppliers that minimise the total replenishment and inventory cost per time unit under suppliers' capacity and quality constraints. A numerical example is provided to illustrate the proposed MINLP model. We also compare the results of our model with those from other researchers, where at most one order can be allocated to each supplier per repeating order cycle.