Determining the “Best” Quantity of a Product to Buy
By Jon and Matt Schreibfeder
Over the past several months we have been reviewing the basics of setting replenishment parameters to ensure that you achieve the goal of effective inventory management: meeting or exceeding your customers’ expectations of product availability while maximizing your net profits. Last month we finished up our discussion of when you should issue a replenishment order. This month we will explore how much of a product you should actually order.
When placing a replenishment order, how do your buyers decide how much of each item to order? Often reorder quantities are based on “habit” (i.e., “this is the way we’ve always done it”) rather than logic. Or, you may order “up to” a subjectively set number of months’ supply of a product (we’ll discuss “up to” replenishment next month).
There is a better way. The economic order quantity (EOQ), derived by a formula available in most software packages, calculates a “best buy” quantity of each item. This is the quantity that will minimize your total cost of each piece of each product that you buy. The EOQ balances four factors:
- The current forecast demand for the product
- The cost of carrying inventory (also known as the “K” cost)
- The cost of issuing a replenishment order (also known as the “R” cost)
- The replacement or landed cost per piece of the item
It is important that these four factors of the EOQ are accurate. In previous newsletters, we’ve discussed forecast accuracy. You can also find articles on the subject on our web site, www.EffectiveInventory.com. We also provide free help in calculating your “K” and “R” costs in the Resources section of our web site. By utilizing an accurate EOQ you will ensure that you are buying the quantity that will maximize your corporate profitability.
The EOQ is calculated with the formula:
The square root of:
(24 * R Cost * Forecast Demand) ÷ (K Cost * Cost per Piece)
Don’t be intimidated by this formula (the idea of a “square root” is kind of scary). Just be able to interpret the results. Let’s look at a couple of examples:
Forecast = 25 pcs per month
K Cost = 21% per year
R Cost = $5 per line item
Cost per Piece = $10
The EOQ = Square Root of: (24*$5*25) ÷ (.21 * $10) = 37.7 ≈ 38 pieces
38 pieces represents about a 46-day supply of the product [38 ÷ (25pc. ÷ 30 Days) ≈ 46]. If the cost per piece is raised to $50, we get a different result:
Forecast = 25 pcs per month
K Cost = 21% per year
R Cost = $5 per line item
Cost per Piece = $50
The EOQ = Square Root of: (24*$5*25) ÷ (.21 * $50) = 16.9 ≈ 17 pieces
17 pieces represents about a 20-day supply [17 ÷ (25pc. ÷ 30 Days) ≈ 20]. Why the difference? The dollars moving through inventory (i.e., the Forecast * Cost per Piece). The EOQ will suggest that if you have a lot of money moving through inventory, you buy smaller quantities, more often. Fewer dollars moving through inventory? The EOQ will encourage you to buy larger quantities, less often. Remember that the EOQ will guide you to buy quantities that will maximize your net profitability.
But sometimes the result is not a practical stocking quantity. For this reason, many distributors apply the following limits to the results of the EOQ formula:
- REDUCE THE EOQ QUANTITY, IF NECESSARY, TO EQUAL A MAXIMUM OF “X” TIMES THE DEMAND FORCAST. If you have an inexpensive item that is consistently sold, but in small quantities, the EOQ will suggest you buy a large number of months’ supply of the product. For example:
Forecast = 5 pcs per month
K Cost = 21% per year
R Cost = $5 per line item
Cost per Piece = $0.10
The EOQ = Square Root of: (24*$5*5) ÷ (.21 * $0.10) = 169 pieces
An EOQ of 169 pieces would equal a 33.8 month supply (169 ÷ 5 pc./month = 33.8)! The EOQ formula assumes that demand, unit cost, the reordering cost, and carrying cost will remain constant for nearly three years! While the reordering cost and carrying cost change infrequently, the forecast and the unit cost of many items will fluctuate on a regular basis. And it is an unfortunate fact that inventory shrinkage (loss, theft, breakage, etc.) and obsolescence increase dramatically when inventory remains in a warehouse for an extended period of time. For this reason, best practice is to put an upper limit on the replenishment quantity. Most companies will limit the economic order quantity to equal a three to six-month supply of a product.
- LIMIT THE EOQ TO THE SHELF LIFE OF THE ITEM. If a product has a shelf life of three months, you never want to order a six-month supply, regardless of the results of the EOQ formula. Most companies specify a shelf life in their computer equal to half the
actual shelf life of the product. After all, very few people want to buy a product the day before its expiration date. - LIMIT THE EOQ TO AVAILABLE STORAGE SPACE. This is particularly true for large, bulky items or material that needs to be stored in a special environment. You don’t want to order a two-month supply of an item if you only have available space for a one-month supply.
- ROUND THE EOQ TO THE NEAREST PACKAGE QUANTITY. If a product comes in a vendor package of 144 pieces, you probably cannot order an economic order quantity of 131 pieces or 165 pieces. The EOQ should be rounded to the nearest multiple of the vendor’s standard package quantity. But, when a product needs to be replenished, at least one vendor package must be ordered, regardless of the EOQ quantity.
The EOQ modified by these limits is commonly referred to as the standard order quantity or SOQ. Have your buyers evaluate calculated economic order quantities. You will probably find that it provides you with an automated method of determining your “best buy” purchase amounts of each stocked product.
Next month, we will discuss the “Up To” method of ordering and finish our discussion of best practice replenishment. In the meantime, please let us know if you have any questions.
Matt Schreibfeder (matts@EffectiveInventory.com)
Jon Schreibfeder (jons@EffectiveInventory.com)