Economic Order Quantity
Chapter Thirteen
Syllabus topic 3, "Compute Economic Order Quantity and determination of various stock levels"
Pages 33 to 36 of 82
In one line
The economic order quantity is the order size at which ordering cost and carrying cost are equal, and therefore the size at which their total is least.
Why there is a best size at all
Two costs pull in opposite directions.
Ordering cost is incurred each time an order is placed - the buyer's time, the paperwork, inspection, follow-up. Order more often and this rises.
Carrying cost is incurred on stock held - interest on the money locked up, storage, insurance, obsolescence, deterioration. Order larger quantities and average stock rises, so this rises.
Ordering in tiny quantities makes ordering cost enormous; ordering a year's supply at once makes carrying cost enormous. Somewhere between, their total is least, and that quantity is the EOQ.
The formula
EOQ = the square root of (2 multiplied by A multiplied by O, divided by C) where A = annual consumption in units O = ordering cost per order C = carrying cost per unit per year
C is the term that goes wrong. It must be per unit per year. Where the question gives carrying cost as a percentage of the unit price - say 20 per cent of Rs 25 - then C is Rs 5, and the percentage must be applied before the formula.
The assumptions, and why they are worth stating
The formula holds only if:
- consumption is steady and known;
- the ordering cost per order is constant, whatever the size;
- the carrying cost per unit is constant;
- the price per unit is constant, whatever the quantity; and
- material is available whenever ordered.
Assumption 4 is the one a discount breaks, and that is the second worked example.
Worked example 1: the basic computation
A factory consumes 10,000 units of a material a year. Each order costs Rs 250 to place. Carrying cost is Rs 5 per unit per year. Compute the economic order quantity, the number of orders, and the total of ordering and carrying cost at that quantity.
| Working note | Computation | Value |
|---|---|---|
| WN 1. Annual consumption, A | as given | 10,000 |
| WN 2. Ordering cost per order, O | as given | 250 |
| WN 3. Carrying cost per unit per year, C | as given | 5 |
| WN 4. Two A O divided by C | 2 times 10,000 times 250, divided by 5 | 10,00,000 |
The economic order quantity is the square root of 10,00,000, which is 1,000 units.
| Particulars | Amount, Rs |
|---|---|
| Ordering cost: 10 orders of 1,000 units at Rs 250 | 2,500 |
| Carrying cost: average stock of 500 units at Rs 5 | 2,500 |
| Total, being the cost of ordering and carrying | 5,000 |
Average stock is half the order quantity. Stock runs from 1,000 down to nil and back, so on average 500 units are held.
The rest of this chapter
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The rest of this subject
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