Economic Order Quantity (Wilson EOQ)

Order in big lots and you tie up cash in stock nobody is using. Order in small ones and you pay the ordering cost over and over. Ford Whitman Harris worked out the balance in 1913, R. H. Wilson popularised it, and the answer is $Q = \sqrt{2DS/H}$. Ten thousand units a year, $50 to raise a purchase order, $4 a year to hold one unit: $\sqrt{2 \ imes 10000 \ imes 50 / 4} = \sqrt{250000} = 500$ units an order.

The check worth knowing is that at the true EOQ the two costs are equal, and you can verify any answer without the square root at all. At 500 units you place twenty orders a year at $50, which is $1,000, and you hold 250 on average at $4, which is also $1,000. If those two numbers do not match, the lot size is not the optimum.

What surprises people is how flat the cost curve is near the bottom. Order 20% away from EOQ in either direction and the total cost rises by about 2%. That insensitivity is a gift: it means you can round the answer to a pallet quantity, a case pack or a truckload without meaningfully hurting anything. The classic mistake is the opposite belief, treating the EOQ output as a precise instruction and ordering 500 units when the supplier's carton holds 480. Take the 480.