Abstract: Inventory management is one subject based on Operations Research, and has been one of the most popular topics in the area of Operations Research and Management Science in the last few decades. Ordering cost is one class of essential costs in inventory systems, and it includes product cost, shipping cost, loading/unloading cost, etc. The ordering cost is often a nonlinear function of order quantity. This paper will introduce several well-known nonlinear ordering cost functions, such as quantitydependent fixed/setup cost, incremental quantity discount, all-unit quantity discount, truckload discount, convex ordering cost, etc. We review the literature of inventory models with nonlinear ordering cost based on periodic-review and continuous-review models, respectively. Although the inventory models with nonlinear ordering cost functions have been studied in recent decades, the optimal policies of many models haven't been fully characterized due to their complexity. This paper tries to discuss the challenges and chances in this topic, by reviewing related works.

Key words: inventory management, ordering cost, quantity discount, incremental quantity discount, all-unit quantity discount, setup cost, truckload discount, convex ordering cost