Inventory Management EOQ & Reorder Point Calculator
Enter annual demand, ordering cost, and holding cost to find the Economic Order Quantity. Visualize the cost tradeoff curve and sawtooth inventory chart. Compute ROP and safety stock instantly.
Parameters
Annual Demand D
Ordering Cost S
Holding Cost H
Unit Price p
Lead Time L
Demand Std. Dev. σ
Service Level
Results: Calculating...
Results
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EOQ [units]
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ROP [units]
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Safety Stock
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Total Annual Cost
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Orders per Year
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Cycle [days]
Inv
Theory & Key Formulas
Economic Order Quantity:
$$EOQ = \sqrt{\frac{2DS}{H}}$$
Total Annual Cost:
$$TC = \frac{D}{Q}S + \frac{Q}{2}H + Dp$$
Reorder Point:
$$ROP = d \cdot L + z \sigma \sqrt{L}$$
What is EOQ & Reorder Point?
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What exactly is EOQ? I see the formula, but what's the big idea behind it?
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Basically, it's about finding the "Goldilocks zone" for ordering inventory. Order too often, and you pay high ordering fees. Order too much at once, and you pay high storage costs. EOQ finds the perfect middle ground. In the simulator, try increasing the "Ordering Cost (S)" slider and watch the EOQ value go up—it tells you to order more each time to spread that higher cost over more units.
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Wait, really? So the "Total Annual Cost" line on the graph is a combination of two costs? What about the unit price?
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Exactly! The graph shows the trade-off. The holding cost line slopes up (more inventory = higher cost), and the ordering cost line slopes down (bigger orders = fewer of them). Their sum has a clear minimum—that's the EOQ. The unit price (p) is just added as a constant, as you pay it for every unit you buy. Change the "Holding Cost (H)" parameter and you'll see the minimum point shift dramatically.
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Okay, I get EOQ. But what's the Reorder Point for? Isn't it just "demand during lead time"?
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Good question! In a perfect world, yes. But demand is often unpredictable. The Reorder Point (ROP) is the inventory level that triggers a new order. It's your "average demand during lead time" PLUS a "safety stock" buffer for surprises. In the simulator, crank up the "Demand Std. Dev. (σ)" or the "Service Level". You'll see the ROP increase because you need more buffer stock to avoid running out.
Physical Model & Key Equations
The core model finds the order quantity (Q) that minimizes the sum of annual ordering and holding costs. The unit cost is constant and added separately.
$$EOQ = \sqrt{\frac{2DS}{H}}$$
D: Annual Demand (units/year). S: Ordering Cost per order ($/order). H: Annual Holding Cost per unit ($/unit/year). This formula is derived by taking the derivative of the total cost function with respect to Q and setting it to zero.
The total annual cost and the reorder point account for both predictable and uncertain demand. Safety stock protects against variability during the lead time.
$$TC = \frac{D}{Q}S + \frac{Q}{2}H + Dp$$
$$ROP = d \times L + (z \times \sigma_d \times \sqrt{L})$$
TC: Total Annual Cost ($). p: Unit Price ($/unit). d: Average Daily Demand (D/365). L: Lead Time (days). z: Z-score (from Service Level). σd: Standard Deviation of Daily Demand. The safety stock term $(z \times \sigma_d \times \sqrt{L})$ is crucial for managing risk.
Frequently Asked Questions
Please check that all input fields (annual demand, ordering cost, holding cost) have been entered correctly with numerical values. If any field is left blank or set to zero, the graph will not be rendered. Also, ensure that JavaScript is enabled in your browser.
EOQ is a theoretical optimal value. For actual ordering, round or round up the calculated value to a whole number. Since the total cost curve on the graph is relatively flat, the cost increase from using a whole number is negligible.
Calculate the standard deviation from historical daily sales data. If data is unavailable, we recommend converting monthly demand fluctuations to a daily basis or assuming an industry average value for simulation purposes.
Yes. The reorder point (ROP) formula includes the term "zσ√L", which accounts for demand variability (σ) and lead time (L) to calculate safety stock. By setting a larger z-value (service level), you can address the risk of sudden surges.
Real-World Applications
Retail & E-commerce: A large online retailer uses EOQ to optimize its purchase of best-selling items, like phone chargers. By balancing warehouse space costs (H) with procurement team costs (S), they determine whether to order 10,000 units monthly or 50,000 units quarterly, directly impacting profitability.
Manufacturing: An automotive plant uses the reorder point model for raw materials like steel coils. With a long, variable lead time (L) from the supplier and unpredictable production schedule changes (high σ), calculating the correct safety stock prevents a $20 million assembly line from shutting down.
Hospital Supply Chains: A hospital manages inventory for critical, high-cost items like surgical stents. They use a high service level (e.g., 99%) in the ROP calculation to minimize the risk of stockouts, as the cost of not having an item available for surgery far exceeds the cost of holding extra inventory.
Restaurant & Food Service: A restaurant chain uses EOQ for non-perishable goods like napkins or canned goods. They adjust the holding cost (H) to account for limited storage space in urban locations, leading to smaller, more frequent orders compared to suburban locations with cheaper storage.
Common Misconceptions and Points to Note
When you start using the EOQ model, there are a few common pitfalls you might encounter. First and foremost, underestimating the parameter H (holding cost). You need to consider not just unit cost × interest rate, but also warehouse rent/utilities, insurance, risk of deterioration/obsolescence, and even the labor costs for inventory management—all bundled together. For example, for a product with a unit price of 1000 yen and an interest rate of 5%, you might think it's 50 yen, but it's not uncommon for the actual calculated cost to be around 150 yen. If this is off by a factor of two, the calculated EOQ changes by a factor of $\sqrt{2}$, or about 1.4 times, so be careful.
Next, forgetting the assumption that demand D is constant. The basic model assumes "flat demand," so applying it directly to seasonal goods or fad items can lead to serious trouble. For instance, if you calculate the EOQ based on the annual demand for electric fans that only sell in summer and place one large order, the inventory will sit idle all winter. In such cases, be mindful of the model's applicability—consider segmenting by demand period and calculating separately.
Finally, remember that EOQ is a "starting point for discussion," not an "absolute value to be strictly followed." Even if the calculated order quantity is 1000 units, if your supplier says they "can only deliver in batches of 500," you'll need to adjust to 1000 or 1500 based on reality. Also, when "quantity discounts" apply for bulk orders that lower the unit price, there can be points where the total cost curve drops significantly. Therefore, you need to compare costs not only around the EOQ but also at order quantities where discounts apply.