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How EOQ, EPR, Re-Order Point, Safety Stock Determined and Computed?



How are Economic Order Quantity (EOQ), Economic Production Run (EPR), Re-order Point, and Safety Stock determined and computed? Read this post for the answers. Typically it is a technical topic. And as usually, for such technical topic we use determinations, formulas, and calculations (computation) example for easier understanding.



Economic Order Quantity (EOQ)

Companies making purchasing (rather than production) decisions often compute the economic order quantity (EOQ), which represents the least costly number of units to order. The EOQ indicates the optimal balance between ordering and carrying costs by mathematically equating total ordering costs to total carrying costs. The EOQ is a tool that is used in conjunction with traditional “push production and inventory management systems“. Because EOQ implies acquiring and holding inventory before it is needed, it is incompatible with “pull systems such as JIT“.

Purchasing managers should first determine which supplier could offer the appropriate quality of goods at the best price in the most reliable manner. After the supplier is selected, the most economical inventory quantity to order—at a single time—is determined. The EOQ formula is:

Economical Order Quantity (EOQ) Formula 


EOQ = economic order quantity in units
Q = estimated annual quantity used in units (can be found in the annual purchases budget)
O = estimated cost of placing one order
C = estimated cost to carry one unit in stock for one year

Note that unit purchase cost is not included in the EOQ formula. Purchase cost relates to the question of from whom to buy, which is considered separately from the question of how many to buy at a single time. Inventory unit purchase cost does not affect the other EOQ formula costs; except to the extent that opportunity cost is calculated on the basis of investment.

All inventory-related costs must be evaluated when purchasing or production decisions are made. The costs of ordering and carrying inventory offset each other when estimating the economic order quantity.

Case & Calculation Example:

Lie Dharma Company uses 80,000 pounds of a particular plastic in producing the Lie Dharma’s dolls. The cost associated with placing each order is $12.25. The carrying cost of 1 pound of the plastic is $1.00 per period. Therefore, Lie Dharma’s EOQ for this plastic is calculated as follows:

EOQ Calculation Example 



Economic Production Run (EPR)

In a manufacturing company, managers are concerned with how many units to produce in a batch in addition to how many units (of raw material) to buy. The EOQ formula can be modified to calculate the appropriate number of units to manufacture in an economic production run (EPR). This estimate reflects the production quantity that minimizes the total costs of setting up a production run and carrying a unit in stock for one year.

The only change in the EOQ formula is that the terms of the equation are redefined as manufacturing, rather than purchasing, costs. The formula is:

Economical Production Running (EPR) Formula 


EPR = economic production run quantity
Q = estimated annual quantity to be produced in units (can be found in annual production budget)
S = estimated cost of setting up a production run
C = estimated cost to carry one unit in stock for one year


Case & Calculation Example:

Another product manufactured by Lie Dharma Company is a doll crib. A total of 162,000 units of this product are made each year. The setup cost for a doll crib production run is $40 and the annual carrying cost for each doll crib is $4. The economic production run quantity of 1,800 doll cribs is determined as:

EPR Calculation Example


The cost differences among various run sizes around the EPR may not be significant. If such costs were insignificant, management would have a range of acceptable, economical production run quantities.


The critical element in using either an EOQ or EPR model is to properly identify costs. Identifying all the relevant inventory costs (especially carrying costs) is very difficult, and some costs (such as those for facilities, operations, administration, and accounting) traditionally viewed as irrelevant fixed costs may, in actuality, be long-term relevant variable costs. The EOQ model also does not provide any direction for managers attempting to control all of the separate costs that collectively comprise purchasing and carrying costs. By only considering the trade-off between ordering and carrying costs, the EOQ model does not lead managers to consider inventory management alternatives that may simultaneously reduce both categories of costs.

Additionally, as companies significantly reduce the necessary setup time (and thus cost) for operations and move toward a stockless inventory policy, a more comprehensive cost perspective will indicate a substantially smaller cost per setup and a substantially larger annual carrying cost. If the setup and carrying cost information given for Molly Memories were reversed, the EPR would be only 180 units. Using either a new perspective of variable cost or minimizing setup cost will provide much lower economic order or production run quantities than indicated in the past.


Re-Order Point and Safety Stock

The economic order quantity or production run model indicates how many units to order or produce. But managers are also concerned with the order point. Quantity of Re-order Point and Safety Stock reflects the level of inventory that triggers the placement of an order for additional units.

Determination of the order point is based on three factors:

  1. Usage – Usage refers to the quantity of inventory used or sold each day
  2. Lead Time – The lead time for an order is the time in days it takes from the placement of an order to when the goods arrive or are produced. Many times companies can project a constant, average figure for both usage and lead time
  3. Safety Stock – The quantity of inventory kept on hand by a company in the event of fluctuating usage or unusual delays in lead time is called safety stock.


If usage is entirely constant and lead time is known with certainty, the order point is equal to daily usage multiplied by lead time:

Order point = Daily usage x Lead time

Case & Calculation Example:

Assume that Lie Dharma Company produces rhinestone tiaras for sale to chain department stores. Lie Dharma Company uses 400 rhinestones per day, and the supplier can have the stones to Lie Dharma Company in four days. When the stock of rhinestones reaches 1,600 units, Lie Dharma Company should reorder.

The order point formula minimizes the dollars a company has invested in its inventory. Orders would arrive at precisely the time the inventory reached zero.

Note: This formula, however, does not take into consideration unusual events such as variations in production schedules, defective products being provided by suppliers, erratic shipping schedules of the supplier, or late arrival of units shipped. To provide for these kinds of events, managers carry a “buffer” safety stock of inventory to protect the company from stock-outs.

When a safety stock is maintained, the order point formula becomes:

Order point = (Daily usage x Lead time) + Safety stock


Safety stock size should be determined based on how crucial the item is to production or to the retail business, the item’s purchase cost, and the amount of uncertainty related to both usage and lead time.

One way to estimate the quantity of safety stock is to allow one factor to vary from the norm. For example: either excess usage during normal lead time or normal usage during an excess lead time can be considered in the safety stock calculation.


Case & Calculation Example:
Assume that Lie Dharma Company never uses more than 500 rhinestones in one day. One estimate of the necessary safety stock is 400 stones, computed as follows:

Maximum daily usage = 500 stones
Normal daily usage = (400) stones
——————————————————- [+]
Excess usage = 100 stones
Lead time x 4 days
—————————————————- [x]
Safety stock = 400 stones

Using this estimate of safety stock, Lie Dharma Company would re-order rhinestones when 2,000 stones = (1,600 original order point + 400 safety stock) were on hand.

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