Multi-Item Probabilistic Inventory Models Considering Discount, Expiration, Warehouse Capacity, and Capital Constraints

In general, companies have inventory stored in warehouses to be used or sold in the future. To optimize inventory, companies require a model to determine the appropriate order quantity and optimal reorder timing to minimize total inventory costs. To stay within the set capacity, several factors need to be considered in inventory management, such as a product's shelf life, warehouse capacity, and capital. On the other hand, suppliers may offer discounts, and companies tend to take advantage of them. However, they must consider the warehouse capacity and capital availability. This paper constructs two probabilistic multi-item inventory models, considering discounts, expiration, warehouse capacity, and capital constraint. The first model considers all-unit discounts, while the second deals with incremental discounts. We consider three items to be managed and examine three replenishment policies, namely individual order, joint order, and a combined policy of individual and joint order, to minimize the total inventory cost. Sensitivity analysis is performed on the joint order policy to determine the influence of parameter values' changes on the reorder time and total inventory cost.