## Appendix B - EOQ, Order Point, and Safety Stock Calculations

### Overview

A primary objective of inventory management is to minimize the total relevant costs of the inventory. This is done primarily by gathering information to assist in making two central decisions: How much should be bought (or manufactured) at a time? When should we buy (or manufacture)?

The Economic Order Quantity (EOQ), Order Point (also referred to as reorder point) and Safety Stock calculations are used in the process of managing inventory levels to minimize costs and protect against stock-outs. Each inventory item has its own EOQ and order point which may be either manually entered or automatically calculated by the Inventory EOQ, Order Point, Safety Stock Report. The formulas for calculating these figures are explained in this section, and the model for these formulas has been taken from the reference shown at the end of this section. Any alterations to these formulas may be made through program modifications to the EOQ, Order Point, Safety Stock Report.

### Economic Order Quantity (EOQ)

The EOQ for an item represents the optimum for either a normal purchase order (when buying) or a shop order for a production run (when manufacturing). This quantity, which is expressed in the standard unit of measure for an item, will result in the minimum total annual costs of the item in question. The factors that enter into the EOQ calculation are annual quantity used in units (A), cost per purchase order (P) (called set-up costs), and annual cost of carrying one unit in stock for one year (S) (called carrying costs). Using this information, we may compute EOQ as:

EOQ = Square root of (2 times A times P divided by S)

Where: A=Estimated Annual Usage, P=Set-up Cost, S=Carrying Cost

Set-up and carrying costs are defined in the Inventory Factor option of the Parameter Maintenance task, and apply to every inventory item. The usage amounts are specific to each item and are found in the Status Inquiry option of the Inventory Item Maintenance task.

### Reorder Point

The question of when to order requires that we know the lead time, which is the time interval between placing an order and receiving delivery; know the EOQ; and be certain of demand during lead time. The reorder point for an item is commonly computed as safety stock plus the average usage during the lead time.

To approximate these figures, the following information from the Inventory system is used.

A = Current Usage for an item times ABC factor (refer to the following for a description of the ABC Factor)

B = (Sum of Prior Usage) divided by Number of Periods times (1 - ABC factor)

Note: The definition of prior usage is the number of GL period of history (up to 13) or the number of periods that exist at the time if actual history is less than that.

Weighted Monthly Usage (WMU) = A plus B

This provides an approximation of monthly usage for each item by applying an ABC factor.

Lead time, which is carried in the Inventory masterfile in days, is converted to months by dividing by the average number of days per month.

Lead times in months = Lead Time in days divided by 30.55 days per month

Therefore:

-and-

Reorder Point = Safety Stock plus WMU During Lead Time

### The ABC Factor, as used in Reorder Point Calculation

The following variables are used in this explanation. Note that the ABC factor discussed in this section is not the same as the ABC percentages used in the ABC Analysis Report.

 Variable Description Current Current use this period, from the warehouse usage file. Day The day of the month. On 2/21/94, Day equals 21. ECU Extrapolated Current Use; ECU equals Current times 30.55 divided by Day (Current use is multiplied by 30.55 -- the average number of days per month -- and divided by X2 -- the day of the month -- to adjust for the remaining days in the month.) Factor(X) ABC Factor where ‘X’ indicates an item. WMU Weighted Monthly Usage; WMU equals (Current times Factor(x) times .01) plus (Sum of Prior Usage divided by Number of Periods) times (1-Factor (x) times .01)

Note: The definition of prior usage is the number of GL period of history (up to 13) or the number of periods that exist at the time if actual history is less than that.

This is actually an average of the extrapolated current usage and the average of the prior usage. The ABC factor is used to “weigh” the current month versus the prior average. A higher factor (0 to 100 is possible) more heavily weighs the current month (extrapolated), while a lower factor more heavily weighs the average from the prior usage. A factor of zero considers only the prior average, and a factor of 100 considers only the current usage.

### Description

LTM

• expressed in months.

• equals days in month divided by 30.55

• entered in days, so divide the entered lead time by 30.55 to calculate lead time in months

Safe

Safety Stock

• equals WMU times Lead times 0.5
• is calculated as half the Weighted Monthly Usage during lead time in months

OP

Calculated reOrder Point; OP equals Lead times WMU plus Safe Reorder point is calculated as average monthly usage times the lead time in months, plus the safety stock allocated to the  item.

### Sample

Given the following data and assuming 3 months prior usage:

 Current = Current usage = 100 Day = Current date, 2-21-12 = 21 Lead = Lead time in days = 14 Factor(X) = ABC factor = 30 Prior1 = Prior period 1 = 75 Prior2 = Prior period 2 = 60 Prior3 = Prior period 3 = 40

Calculate the following data:

 ECU 100 times 30.55 divided by 21 = 145.476 WMU 145.476 times 30 times .01 plus (75 plus 60 plus 40) divided by 3 times (1 minus 30 times .01) 145.476 times .30 plus 175 divided by 3 times (.70) 43.643 plus 40.833 equals 84.476 LTM 14 divided by 30.55 equals .458 Safe 84.476 times 0.458 times 0.5 equals 19.345 OP .458 times 84.476 plus 19.345 equals 58.035

Using the same given data and a 90% factor, calculate the following:

 WMU 145.476 times 90 times .01 plus (75 plus 60 plus 40) divided by 3 times (1 minus 90 times .01) 145.476 times .90 plus 175 divided by 3 times (.10) 130.928 plus 5.833 equals 136.761 Lead 14 divided by 30.55 equals .458 Safe 136.761 times 0.458 times 0.5 equals 31.319 OP .458 times 136.761 plus 31.319 equals 93.319

### Safety Stock

Safety stock represents a hedge against uncertainty. Replenishment uncertainty can be the result of unusual usage during the replenishment cycle or uncertain delivery schedules. Safety stock helps to prevent stockouts should any of these unexpected conditions occur. There are many formulas for calculating the right amount of safety stock. The simplest is to base safety stock on 50% usage during lead time. This is an easy formula to calculate and represents a median calculation of other more advanced formulas.

To calculate safety stock the following information is used:

A equals Current Usage for an item times ABC weight factor times .01

B equals (Sum of Prior Usage divided by Number of Periods) times (1 - ABC factor times .01)

Weighted Monthly Usage (WMU) equals A plus B

Lead times in months equals Lead Time in days divided by 30.55 days per month

Safety Stock equals WMU during lead time times .5

References:

• Cost Accounting, A Managerial Emphasis (Fourth Edition, 1977), Charles T. Horngren, Ph.D., C.P.A., Prentiss-Hall, Inc., Englewood Cliffs, N.J. 07632

• Distribution Survival in the 21st Century, Gordon Graham, Inventory Management Press, Copyright 1992

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