Question

A unit of inventory costs a company $40. Annual carrying costs are 1% for interest charges, 1% for insurance, 2% allowance for obsolescence, $2 per unit for building overheads, $1.50 per unit for damage and loss, and $4 per unit for miscellaneous costs. Annual demand for the item is constant at 1000 units and each order costs $100 to place.

1. Calculate the economic order quantity and the total costs associated with stocking the item
2. If the supplier of the item will only deliver batches of 250 units, how are the inventory carrying costs affected?
3. If the supplier relaxes his order size requirement, but the company has limited warehouse space and can stock a maximum of 100 units at any time, what would be the optimal ordering policy and associated costs?

Use the $40 price to convert dollar cost to percentages. Remember to think carefully about which costs should and should not be included in the calculation of inventory carrying cost percentage. You have to do this calculation before you can calculate EOQ. The rule is only include those costs which vary directly with inventory levels.

Use Excel to show all the answer.

Answer 1

The formula that we use for economic order quantity is

Q = sqrt(2DS/H)

Now, once we have that, we can calculate the cost of operation

TC = DS/Q + HQ/2 + PD

The cost associated with inventory only is

C = DS/Q + HQ/2

Here

D = 1000

S = 100

H = Insurance does not depend on the amount of inventory level. Hence the holding cost is (0.01 + 0.02)*40 + 2 + 1.5 + 4 = 8.7 per unit

P = 40

Now, we can use them on excel. The formulas are shown below

a.

The EOQ is 152.

Total cost is 1319.09

b.

If the quantity has to be in multiples of 250, then the nearest value to EOQ is 250 units. We will order 250 units and the associated cost is 1487.5

c.

We see that the EOQ amount has an average inventory of 76. This is well within the stock limit of the average inventory. However, if we order 152 units and they arrive, we will not be able to store all of them. This means we can at most order 100 units.

This means the total cost will be 1435.

The excel solution is shown below