Inventory EOQ (Economic Order Quantity) Calculator

What is Economic Order Quantity (EOQ)?

Economic Order Quantity (EOQ) is a classic inventory management model that determines the optimal order quantity to minimize total inventory costs. It balances two competing costs: the cost of ordering (which decreases with larger, less frequent orders) and the cost of holding inventory (which increases with larger orders).

The EOQ model was developed by Ford W. Harris in 1913 and remains one of the most widely taught concepts in operations management and supply chain courses. While simplified, it provides valuable intuition about inventory trade-offs.

The EOQ Formula and Its Components

• D (Annual Demand): The total number of units needed per year. If you have monthly or weekly demand, multiply appropriately.
• S (Ordering Cost): The fixed cost to place one order, regardless of order size. Includes setup costs, shipping fees, administrative processing, and receiving costs.
• H (Holding Cost): The cost to hold one unit in inventory for one year. Includes storage costs, insurance, capital tied up (opportunity cost), and obsolescence or spoilage risk.

The formula shows that EOQ increases with higher demand (D) or ordering cost (S), and decreases with higher holding cost (H). This makes intuitive sense: if ordering is expensive, order more each time; if holding is expensive, order less but more frequently.

Interpreting EOQ, Number of Orders, and Total Cost

Once you calculate EOQ, several related metrics follow:

• Number of Orders per Year: D / EOQ. If EOQ is 500 and annual demand is 12,000, you order 24 times per year.
• Cycle Time: Working days per year divided by number of orders. This tells you how many days between orders.
• Annual Ordering Cost: (D / EOQ) × S. With EOQ, this equals the annual holding cost.
• Annual Holding Cost: (EOQ / 2) × H. Average inventory is half the order quantity (assumes inventory depletes linearly).
• Total Annual Inventory Cost: Sum of ordering and holding costs. At EOQ, this is minimized.

A key insight from EOQ is that at the optimal point, annual ordering cost equals annual holding cost. This is visible on the cost curve chart where the two cost lines intersect at the EOQ.

Reorder Point, Lead Time, and Safety Stock

The Reorder Point (ROP) tells you when to place a new order so inventory arrives before you run out:

• Daily Demand: Annual demand divided by working days per year.
• Lead Time: Days between placing an order and receiving it.
• Safety Stock: Extra inventory to buffer against uncertainty in demand or lead time.

For example, if daily demand is 48 units, lead time is 5 days, and safety stock is 100 units, then ROP = (48 × 5) + 100 = 340 units. When inventory drops to 340 units, place a new order.

Limitations of the Basic EOQ Model

The classic EOQ model makes several simplifying assumptions that may not hold in real-world scenarios:

• Constant demand: Real demand often varies seasonally, weekly, or randomly.
• Constant lead time: Suppliers may have variable delivery times.
• Instantaneous replenishment: Orders arrive all at once, not in batches over time.
• No quantity discounts: Real suppliers often offer price breaks for larger orders.
• Single item: EOQ doesn't account for multi-item coordination or shared shipments.
• No stockouts: The model doesn't penalize running out of inventory.

Despite these limitations, EOQ provides a useful starting point and helps build intuition about inventory trade-offs. For critical decisions, consider more sophisticated models that account for variability, service levels, and constraints.