7.2.2 The economic order quantity (EOQ)
We can use decision models to help manage inventory. The economic order quantity model (EOQ) is concerned with answering the question, 'how much inventory should be ordered'? It seeks to identify the size of the order that will minimise the total of ordering costs (that decrease with the size of orders) plus holding costs (that increase as a greater quantity of inventory is held).
As the textbook shows, the economic order quantity is calculated by using the equation:
EOQ = 2DC
H
Where:
D = the annual demand for the item of inventory
C = the cost of placing an order
H = the cost of holding one unit of inventory for one year
The limiting assumptions for the basic EOQ model are that:
- The demand for an item can be predicted accurately and is constant over time. This means that sales are distributed evenly (and don't fluctuate) over the relevant time period
- Inventory is received immediately . This means that the quantity ordered is received as one batch at one point in time and without delay.
- Relevant costs are the variable costs of ordering (ordering costs) and of holding inventory (holding costs). The EOQ model is essentially a trade-off between the relationship of total ordering costs and total holding costs as they change with changes in order quantities
- The lead-time between placing and receiving an order is known with certainty. This means orders can be placed at the 'right' time to avoid any possible shortages and 'stock-out' conditions
Quantity discounts are not possible
Inventory levels over time (implied by the basic assumptions). The following reading shows how inventory levels will vary over time under the basic assumptions of the EOQ model.
Reading 3
Meredith, GG. 1994. Extract from topic 11 'Management of capital'. In Accounting and Financial Management for Business Decisions . McGraw-Hill Book Company of Australia Pty Ltd, Roseville . Pages 382-384.
Graphical representation of EOQ: The next reading extends the calculation of EOQ to a graphical analysis.
Text reading
Atrill, Mclaney, Harvey & Jenner, pages 411-415
See figures 12.2, 12.3 and 12.4. Note the MRP and JIT systems
Note, in figure 12.4 that total relevant costs fall at first because the total ordering costs fall more than total holding costs increase.
However, total costs don't continue to fall as reductions in total ordering costs become smaller because the order size increases. The total holding cost increases will more than offset any savings in total ordering costs and the total cost curve changes direction and starts to rise. The optimum order quantity is, therefore, the point when total costs are at a minimum.
Also note that the total holding cost and total ordering cost curves intersect at the EOQ level. That is to say, at the EOQ level, the total holding costs and the total ordering costs are equal.
For example
A company is trying to determine an appropriate inventory policy and has gathered the following information about one of the products it sells.
Actual demand = 3 600 units per year
Ordering cost = $15 per order
Holding cost = $1.20 per order
The current policy is to order in lots of 400 units
Use the EOQ model to evaluate the current policy and suggest any improvements.
Answer
Economic order quantity
EOQ = 2 x D x C = 2 x 3600 x 15 = 90 000 = 300 units per order
H 1.20
Total relevant cost of EOQ (Q = 300 units)
TRC EOQ = H x EOQ = 1.2 x 300 = $360
Total relevant costs at present order quantity (Q = 400 units)
TRC = (D/Q)C + (Q/2)H = (3600/400)15 + (400/2)1.20 = $375
Thus if the order quantity is reduced to 300 units per order, the total relevant costs of the inventory policy will be reduced from $375 to $360 per order
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