What is economic order quantity?

The economic order quantity, or EOQ, is the order size that gives the lowest total of ordering costs and holding costs. Ordering often means many small orders and high ordering costs, while ordering rarely means large batches that cost a lot to store. EOQ finds the balance point between the two.

How it works

The formula is EOQ = the square root of (2 x D x S / H), where D is yearly demand, S is the cost of placing one order and H is the cost of holding one unit for a year. As the order size grows, ordering costs per year fall because there are fewer orders, while holding costs rise because average stock is half the order size. The total cost is lowest where the two lines cross.

The model assumes steady demand, a fixed ordering cost and no discounts for large orders. Real cases often break these assumptions, so EOQ works best as a starting point. The total cost curve is also flat near the minimum, which means an order size a little off the optimum costs little extra.

Example

Say a cafe uses 1,200 kg of coffee beans a year, each order costs $50 to place, and holding a kilogram for a year costs $3. EOQ = the square root of (2 x 1,200 x 50 / 3) = the square root of 40,000 = 200 kg. That means 1,200 / 200 = 6 orders a year, costing 6 x $50 = $300, and average stock of 100 kg costing 100 x $3 = $300. The two costs are equal at the optimum. The numbers are an illustration.

How to model it in Machinations

Model the stock as a Pool, filled by a Source in batches through a Delay and drained steadily by a Drain for usage. Put the order size in a Register or make it a Lever, and add Registers for ordering cost and holding cost that sum into a total cost. Play with different order sizes and chart the total cost to find the lowest point.