CAT / FIA FMA Syllabus C. Cost Accounting Techniques - Optimal reorder quantities - Notes ^{5 / 23}

This is the quantity of inventory which is to be ordered when inventory reaches the reorder level.

If the re-order quantity is set so as to minimise the total costs associated with holding and ordering inventory, then it is known as the economic order quantity.

Economic order quantity (EOQ)

When determining how much to order at a time, an organisation will recognise that:

• as order quantity rises, average stock rises and the total annual cost of holding stock rises

• as order quantity rises, the number of orders decreases and the total annual re-order costs decrease.

• The economic order quantity (EOQ) is the order quantity which minimises the total costs associated with holding and ordering stock.

  At this quantity, holding costs are equal to ordering costs.

The formula for the EOQ will be provided in your examination.

Where:

Ch = cost of holding one unit of inventory for one time period
C0 = cost of ordering a consignment from a supplier
D = demand during the time period
Q = the reorder quantity (EOQ)

Total Annual Costs (TAC) = purchasing costs + holding costs + ordering costs

Where:
D= demand during the time period
P = purchase price per unit
Ch = cost of holding one unit of inventory for one time period
C0 = cost of ordering a consignment from a supplier
Q = the reorder quantity (EOQ)

This formula is not given in the exam

Illustration

Greg has demand for 40,000 chairs per annum. 

The purchase price of each chair is $25.

The cost to place one order is $20.

Inventory holding costs for 1 unit for 1 year amount to 10% of the Purchase price.

a) What is the EOQ?

b) What is the total annual cost if the organisation uses the EOQ?

Solution

a) Ch = $25 x 10% = $2.5
EOQ = Sq Root ((2 x 20 x 40,000) / 2.5)
EOQ = 800 units

b) Total purchase cost 40,000 x $25 = $1,000,000
Total order cost 40,000 / 800 x $20 = $1,000
Total holding cost 800 / 2 x $2.5 = $1,000
Total annual cost is $1,002,000

What happens if Co or Ch change?

• If Co (cost to place one order) falls, then we can place more orders for the same total annual order cost.

  Therefore, if we are placing more orders, we will order a smaller quantity at a time and the EOQ will fall. 

  If the EOQ falls, we will be holding less inventory at a time, and therefore our annual holding cost will also fall.

• If Ch (cost to hold 1 unit for 1 year) falls, then we can hold more units for the same annual total holding cost. 

  Therefore, if we are holding more units for the same cost, then we will order more units at a time, so EOQ will rise. 

  If the EOQ rises, we are ordering more units at one time, therefore we will place fewer orders and our annual order cost will fall.