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.
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.