Question

Central University has a demand level of 80 units per day, for a particular toner cartridge in the student computer labs each year. The cost of each unit is 10.95. The purchasing director of the university estimates the ordering cost at $45 and thinks that the university can hold this type of inventory at an annual storage cost of 22%. Operating days are 250. The lead time is for orders to arrive is four days. a. To minimize the total annual cost of purchasing and carrying how many toner cartridges should be ordered? b. What are the numbers of orders that need to be placed? c. What is the total cost of managing the inventory? $ d. What are the number of days in between orders? e. What is the re-order point? f. What is the total cost, including the cost of the cartridges? $

Answer 1

a. 864 units

b. 23.14 orders

c. $2,081

d. 10.8 days

e. 320

f. $221,081

Step-by-step explanation:

a. The computation of the economic order quantity is shown below:

=
`\sqrt{\frac{2* \text{Annual demand}* \text{Ordering cost}}{\text{Carrying cost}}}`

where,

Annual demand = 80 units per day × 250 days = $40,000

And, the carrying cost = $10.95 × 22% = $2.409

The other items values would remain the same

Now put these values to the above formula

So, the value would be equal to

=
`\sqrt{\frac{2* \text{20,000}* \text{\$45}}{\text{\$2.409}}}`

= 864 units

b. The number of orders would be equal to

= Annual demand ÷ economic order quantity

= $20,000 ÷ 864 units

= 23.14 orders

The average inventory would equal to

= Economic order quantity ÷ 2

= 864 units ÷ 2

= 432 units

c. The total cost of ordering cost and carrying cost equals to

Ordering cost = Number of orders × ordering cost per order

= 23.14 orders × $4 5

= $1,041.30

Carrying cost = average inventory × carrying cost per unit

= 432 units × $2.409

= $1040.688

So, the total would be

= $1,041.30+ $1,040.688

= $2,081

d. The number of days would be

= Economic order quantity ÷ daily demand

= 864 units ÷ 80 days

= 10.8 days

e. The reorder point would be

= Number of orders × demand level

= 4 days × 80

= 320

f. The total cost would be

= Annual demand × cost of each unit + total cost of ordering and carrying cost

= 20,000 × $10.95 + 2,081

= $221,081