Business studies
Economic order quantity with the Wilson formula
Enter the annual demand, the cost of each order and the cost of holding stock: get the order size that minimises costs, how often to order and when to reorder.
How much to order: the economic order quantity
Ordering small quantities often costs in orders: paperwork, delivery, inspection. Ordering large quantities rarely costs in storage: space, tied-up capital, insurance, spoilage. The economic order quantity is the size that minimises the sum of the two, and at the optimum the two costs are exactly equal.
The Wilson formula gives it in one line: Q = √(2 × demand × order cost ÷ holding cost per unit). With 12,000 units a year, 50 per order and 3 per unit to hold (20% of a 15 unit cost), the order size is about 632 units, placed about 19 times a year.
The reorder point says when to order: the usage during the lead time plus the safety stock. With 250 working days, usage is 48 units a day; with a 5-day lead time and 100 units of safety stock, reorder when stock falls to 340 units.
Common mistakes
- Using a holding cost per order instead of per unit per year: the formula needs consistent annual quantities.
- Leaving the cost of capital out of the holding cost: stock sitting in a warehouse is money not earning.
- Applying the formula when demand is very irregular: the model assumes steady usage.
Frequently asked questions
Why are the two costs equal at the optimum?
Ordering cost falls as the order size grows, holding cost rises linearly. Their sum is lowest exactly where they meet: a property of this shape of function.
What if my cost estimates are a little off?
Little changes: the total cost curve is flat near the minimum. Ordering 20% more or less than the optimum raises total cost by only about 2%.
What if the supplier offers quantity discounts?
The basic formula ignores them. Work out the total cost, purchase price included, for the Wilson quantity and for each discount threshold, and take the lowest.
How this calculation works
Economic order quantity Q* = √(2 × D × S ÷ H), with D annual demand, S the cost of one order, H the cost of holding one unit for a year (or unit cost × rate). Orders per year = D ÷ Q*; cycle length = working days ÷ orders. Ordering cost = D ÷ Q × S; holding cost = Q ÷ 2 × H. Reorder point = D ÷ working days × lead time + safety stock.
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