Inventory Optimization (EOQ)

Business Calculus · Axiom Academy

REAL WORLD Inventory Optimization The Economic Order Quantity (EOQ) model Every business that keeps inventory faces a fundamental trade-off: how much to order at a time? Find the Economic Order Quantity (EOQ) - the order size that minimizes total inventory costs. Let Q = order quantity (what we're optimizing) Total Inventory Cost = Ordering Cost + Holding Cost D = annual demand, S = cost per order H = holding cost per unit per year Finding the Optimal Order Quantity Take the derivative with respect to Q and set it to zero: The Economic Order Quantity (EOQ) Formula TC''(Q) = Q^3 > 0 for all positive Q The second derivative is always positive, confirming this is a minimum. Real-World Example: Electronics Retailer A retailer sells 10,000 smartphones per year. Each order costs 200 to process, and it costs 50 per phone per year to store inventory (warehouse space, insurance, opportunity cost of capital). At EOQ, the ordering cost equals the holding cost: This is another way to derive the EOQ formula! Round to practical sizes: Order 300 instead of 283 if supplier requires round lots Safety stock: Real systems add buffer inventory for demand uncertainty Quantity discounts: May override EOQ if bulk discounts are significant Storage constraints: Warehouse capacity may limit order size

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