Economic Order Quantity, or EOQ, is a model used to choose the order size that minimizes inventory costs. It matters because ordering too little causes frequent purchasing and possible stockouts, while ordering too much ties up money and warehouse space. In logistics and warehouse systems, EOQ helps managers balance delivery schedules, storage limits, and customer demand.
The model turns a practical warehouse decision into a clear cost optimization problem.
EOQ compares two main costs that move in opposite directions: ordering cost and holding cost. Larger orders reduce the number of orders per year, but they increase the average inventory stored on shelves. Smaller orders reduce storage needs, but they increase purchasing, shipping, and receiving activity.
The optimal order quantity occurs where the total annual inventory cost is lowest, often where annual ordering cost equals annual holding cost.
Understanding Logistics & Warehouse Systems: Economic Order Quantity
The EOQ model depends on a picture of inventory that falls steadily as items are used, then jumps upward when a delivery arrives. This creates a sawtooth pattern on an inventory graph. The usual average stock is half of the order amount because stock moves from a full delivery down to zero.
That idea only works well when demand is fairly steady and each delivery arrives as expected. It assumes the supplier can provide the full order at one time, shortages are not planned, and the price per unit does not change with order size. Real warehouses rarely match every assumption, so EOQ is best treated as a useful starting point rather than a perfect answer.
Order cost means more than the transport charge on a delivery. It can include staff time to prepare a purchase order, approve it, book a delivery slot, inspect goods, enter records, and put stock away. Holding cost is broader than shelf space.
Money tied up in stock cannot be used for wages, equipment, or other purchases. Holding cost can include insurance, security, spoilage, damage, shrinkage, and the risk that products become outdated. Many businesses estimate it as a percentage of the item value per year.
A poor estimate of either cost gives a poor EOQ result. Students should notice that the purchase price of an item is usually left out when every unit has the same price, since that cost stays the same regardless of order size.
The order quantity answers how much to buy, but the reorder point answers when to place the order. These are separate decisions. A warehouse may order 500 units each time, yet need to send the order before the shelves are low.
If average sales are 20 units per day and delivery takes five days, the basic trigger is 100 units remaining. The stock used during those five days is called lead time demand. In practice, managers often add safety stock above this level.
Safety stock protects against late deliveries or unexpectedly high demand. It raises holding cost, but it can prevent lost sales, production stoppages, and disappointed customers.
EOQ needs regular review because its inputs change. Seasonal demand makes a single annual average misleading. A retailer may need more stock before a holiday period, even if the calculated EOQ is smaller.
Quantity discounts can make a larger order worthwhile because the lower purchase price may outweigh extra storage cost. Limited warehouse capacity, refrigerated storage, expiry dates, supplier minimum orders, and full truckload deliveries can all limit the result. Some factories make items gradually instead of receiving one complete shipment, so their inventory pattern differs from the basic model.
Good inventory work combines the calculation with actual data on demand, lead times, supplier reliability, and available space. The most important learning step is keeping time units consistent, such as using annual demand with annual holding cost and matching daily demand with lead time measured in days.
Key Facts
- EOQ formula: Q* = sqrt(2DS / H), where D is annual demand, S is order cost per order, and H is holding cost per unit per year.
- Annual ordering cost = (D / Q)S.
- Annual holding cost = (Q / 2)H, assuming inventory is used steadily between orders.
- Total relevant cost = (D / Q)S + (Q / 2)H.
- At the EOQ, annual ordering cost = annual holding cost.
- Reorder point formula: ROP = dL, where d is average demand per time period and L is lead time in the same time units.
Vocabulary
- Economic Order Quantity
- The order size that minimizes the combined annual ordering and holding costs for inventory.
- Ordering Cost
- The cost of placing and receiving one order, including purchasing paperwork, shipping setup, and receiving labor.
- Holding Cost
- The cost of keeping one unit in inventory for a year, including storage, insurance, damage, and capital tied up.
- Lead Time
- The time between placing an order and receiving the goods into usable inventory.
- Reorder Point
- The inventory level at which a new order should be placed to avoid running out before delivery arrives.
Common Mistakes to Avoid
- Using monthly demand with annual holding cost is wrong because the EOQ formula requires consistent time units. Convert demand, holding cost, and lead time to matching units before calculating.
- Including the purchase price in the basic EOQ cost curve is wrong when the unit price is constant. Basic EOQ minimizes ordering and holding costs, not the total cost of buying the goods.
- Assuming EOQ is the same as the reorder point is wrong because they answer different questions. EOQ tells how much to order, while the reorder point tells when to order.
- Ignoring demand uncertainty is risky because the basic EOQ model assumes steady, known demand. Real warehouses may need safety stock when demand or lead time varies.
Practice Questions
- 1 A warehouse has annual demand D = 12,000 units, ordering cost S = 3 per unit per year. Calculate the EOQ.
- 2 A product has annual demand of 8,000 units and an EOQ of 400 units. If each order costs 2 per unit per year, calculate the annual ordering cost, annual holding cost, and total relevant cost.
- 3 A warehouse manager wants to place very large orders to get fewer deliveries, but shelf space is limited and some products become obsolete quickly. Explain how the EOQ cost tradeoff helps evaluate this decision.