How much to order at a time? Order in tiny batches and you pay the fixed cost of ordering over and over; order huge and you pay to store the pile. Balance the two and there’s a single cheapest quantity — the EOQ — and at that exact point your ordering cost equals your holding cost. Slide the order size and find the bottom of the cost valley.
The Economic Order Quantity balances two opposing costs over a year: ordering cost D/Q·K (annual demand D, fixed cost K per order — falls as you order bigger, less often) and holding cost Q/2·h (average inventory Q/2 times holding cost h — rises with batch size). Their sum is U-shaped and minimised at Q* = √(2DK/h), where — elegantly — the ordering cost exactly EQUALS the holding cost. It underlies inventory policy everywhere from warehouses to (in spirit) how often to batch any fixed-cost task. A fail-loud self-check throws unless total cost is minimised at Q* and there the two costs are equal. ◆ real operations research, node-verified.
The classic constant-demand EOQ (the exact √(2DK/h) and equal-costs-at-optimum result); real inventory adds variable demand, quantity discounts and lead-time safety stock — the balance-two-costs sweet spot is exact.