Quantity discounts decisions considering multiple suppliers, with capacity and quality restrictions

This article considers a supply chain inventory problem with a buyer and multiple suppliers, where each supplier is offering all-unit quantity discounts as a motivation mechanism to increase the buyer's order quantity, and hence reduce the average replenishment cost. The buyer is allowed to submit multiple orders to the selected suppliers during a repeating order cycle. In this research, we propose a mixed integer nonlinear programming (MINLP) model to find the buyer's optimal number of orders and the corresponding order quantities in order to take advantage of the quantity discounts while minimizing the total replenishment 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.