Inventory management

Introduction: In this section we study a model in which a company wants to determine an order quantity such that the total inventory costs are minimized.

Model: The inventory costs in an Economic Order Quantity (EOQ) model are given by

$$TC(q)=\dfrac{cd}{q}+pd+\dfrac{hq}{2},$$
with parameters

• $d$ the fixed annual demand for a product
• $c$ the fixed costs per order
• $p$ the price per unit
• $h$ the annual holding costs per unit

and variable $q$, which denotes the order quantity.

Theorem: The optimal order quantity is $q=\sqrt{\dfrac{2cd}{h}}$.