Economic Order Quantity (EOQ)

The classic EOQ model assumes: (1) demand is constant, known, and continuous throughout the year; (2) lead time is known and constant; (3) each order arrives in one instantaneous batch; (4) no quantity discounts — unit cost is constant regardless of order size; (5) holding and ordering costs are constant; (6) no stockouts are permitted. These assumptions simplify the real world considerably. The model is most applicable to stable, commodity-type products with predictable demand. For products with lumpy, seasonal, or highly variable demand, more sophisticated methods (simulation, dynamic programming) may be needed.

Ordering costs are all costs associated with placing and receiving a single purchase order, regardless of order size. Typical components include: purchasing department labor time to create and approve the PO, electronic transmission costs, supplier setup charges (in manufacturing: machine changeover time and materials), inbound freight and handling for the minimum shipment, receiving and inspection labor, and quality testing costs. Ordering costs can range from as low as $5–$10 for fully automated EDI orders to hundreds or thousands of dollars for complex custom procurement. Accurately estimating ordering cost is critical because errors here have significant impact on EOQ.

The holding cost rate (expressed as a percentage of unit value per year) typically includes: cost of capital (6–12%, reflecting the interest rate on the money tied up in inventory or the company's WACC), storage space (2–5% of value, including rent, utilities, and racking), insurance (0.5–1%), obsolescence and spoilage risk (1–5%, depending on product type), deterioration and damage (0.5–2%), and inventory management overhead (0.5–1%). Total holding cost rates typically range from 15% to 35% of inventory value per year. For perishable or rapidly obsolescing products, rates can be 40% or higher.

The reorder point (ROP) is the inventory level at which a new order should be triggered so that replenishment arrives before stockout. ROP = (Average daily demand × Replenishment lead time in days) + Safety stock. EOQ determines how much to order; ROP determines when to order. Together they form a complete inventory policy: order EOQ units whenever inventory falls to ROP. Safety stock protects against demand or lead time variability and is typically calculated as a multiple of the standard deviation of demand during lead time, based on the desired service level (e.g., 95% in-stock probability).

Yes. The manufacturing equivalent is the Economic Production Quantity (EPQ), also called the production run quantity. EPQ = EOQ × √(D / (D − P)) where P is the daily production rate. The EPQ is always larger than EOQ because production replenishes inventory gradually (unlike an instantaneous purchase delivery), so the average inventory during a production run is lower than it would be for an equivalent purchase order. EPQ minimizes the total of setup costs (equivalent to ordering costs) and holding costs for a production environment. It is widely used in production scheduling for batch manufacturing.

Since EOQ = √(2DS/H), doubling H reduces EOQ by a factor of √2 ≈ 1.414 — so EOQ decreases by about 29%. Higher holding costs make large inventory less economical, so the optimal strategy shifts to ordering smaller quantities more frequently. Conversely, doubling ordering cost S increases EOQ by the same factor — more expensive orders encourage fewer, larger orders. This square root relationship means EOQ is relatively insensitive to moderate errors in cost estimation: a 100% error in H or S produces only a 41% error in EOQ, and a much smaller percentage error in total cost.

Total cost at EOQ = √(2DSH). At EOQ, ordering cost equals holding cost (each = TC/2). The total cost curve has a flat bottom near the EOQ — total cost is relatively insensitive to moderate deviations. For example, ordering 20% more or less than EOQ only increases total cost by about 2%. This 'robust' property is practically important: it means you don't need perfect precision in your estimates. However, for very high-value inventory, even small percentage errors in total cost represent significant dollar amounts, so precision matters more in high-stakes situations.