(12C) Economic Ordering Quantity

[Eddie W. Shore]

Blog Entry: http://edspi31415.blogspot.com/2019/11/h...ntity.html

Introduction

In inventory control, a business may try to determine the optimum level of inventory, which is known as the economic ordering quantity. There are several ways to calculate the economic ordering quantity, each with various approaches of what variables and factors to use. This blog entry will explore two approaches, as described by the HP Step by Step Solutions For Your HP Calculator book for marketing and sales. (see source)

Economic Ordering Quantity Knowing Costs and Sales

A simple approach to determining economic ordering quantity is by use of the following formula:

EOQ = √(2 * CPO * SALES / ( UNIT_COST * HOLD%) )

where:
EOQ = economic ordering quantity
CPO = the cost of place an order
SALES = the company's annual sales
UNIT_COST = cost per unit of inventory
HOLD% = holding cost as a rate of inventory costs

HP 12C Program:

Code:

Step;  Key Code;  Key
01;   2 ;  2
02;  45, 1; RCL 1
03;  20;  *
04;  45, 2;  RCL 2
05;  20;  *
06;  45, 3;  RCL 3
07;  45, 4;  RCL 4
08;  25;  %
09;  34;  x<>y
10;  35;  R↓
11;  10; ÷
12;  43, 21;  √
13;  44, 0;  STO 0
14;  43,33,00;  GTO 00

Instructions:

Store the following values:
R1 = CPO
R2 = SALES
R3 = HOLD%
R4 = UNIT_COST

Press R/S to calculate EOQ, which is stored in R0.

Example:

R1 = CPO = $35.00
R2 = SALES = 10,000 units
R3 = HOLD% = 20% of inventory value
R4 = UNIT_COST = $4.73 cost per inventory unit

Result:
CPO = 860.21

Economic Ordering Quantity Factoring Discounts and Taxes

This next calculation adds discounts rates, units used, and income taxes.

EOQ = √(( 2 * (1 - TAX%) * CPO * UNITS_USED)
/ ( (1 - TAX%) * HOLD% * UNIT_COST + DISCOUNT% * UNIT_COST))

where:
EOQ = economic ordering quantity
TAX% = income tax rate
CPO = the cost of place an order
UNITS_USED = inventory units used in a year
UNIT_COST = cost per unit of inventory
HOLD% = holding cost as a rate of inventory costs
DISCOUNT% = discount rate

HP 12C Program:

Code:

Step;  Key Code;  Key
01;  1 ; 1
02;  45, 1; RCL 1
03;  25 ;  %
04;  30 ;  -
05; 44,1;  STO 1
06;  2  ;  2
07;  20 ;  *
08;  45, 2 ;  RCL 2
09;  20 ;  *
10;  45, 3 ;  RCL 3
11;  20 ;  *
12;  44, 0 ; STO 0
13;  45, 5 ; RCL 5
14;  45, 4 ; RCL 4
15;  25 ;  %
16;  45, 1 ; RCL 1
17;  20 ;  *
18;  45, 5 ; RCL 5
19;  45, 6 ; RCL 6
20;  25 ;  %
21;  34 ;  X<>Y
22;  33;  R↓
23;  40;  +
24; 45, 0 ; RCL 0
25; 34 ;  X<>Y
26;  10 ;  ÷
27;  43, 21 ;  √
28;  44, 0 ; STO 0
29;  43, 33, 00 ;  GTO 00

Instructions:

Store the following values:
R1 = TAX% = income tax*
R2 = CPO
R3 = UNITS_USED
R4 = HOLD%
R5 = UNIT_COST
R6 = DISCOUNT%

R1 gets recalculated as (1 - TAX%)

Press R/S to calculate EOQ, which is stored in R0.

Example:

R1 = TAX% = 22%
R2 = $150.00
R3 = 24,000 units
R4 = 5.1% holding cost
R5 = $8.00 per unit
R6 = 2% discount

Results:
CPO = 3,426.81

Source:
"HP Step By Step Solutions For Your HP Calculator: Marketing and Sales: HP-17B, HP-19B, HP-27S" Hewlett Packard. January 1988. Edition 1