Question

The Textile Company sells 175 units per month of a certain large bath towel. The unit cost of a towel to the store is $2.50 and the cost of placing an order has been estimated to be $12.00. The store uses an inventory carrying charge of 27% per year. Compute: i. The optimal order quantity [] ii. Order frequency [] iii. The annual cost of inventory management [] iv. If, through automation of the purchasing process, the ordering cost can be cut to $4.00, what will be the new economic order quantity [] v. Order frequency [] vi. Annual inventory management cost? [] vii. Explain these results.

Answer 1

Demand = 175 units per month = 175*12 = 2100 units per year

Unit cost = $2.50

Ordering cost = $12 per order

Holding cost = 0.27 * 2.5 = 0.675 = 0.68

i) Optimal order quantity

ii) Order frequency

iii) Annual cost of inventory management = Annual Holding cost + Annual ordering cost

Economic order quantity =

Order Frequency =

Annual cost of inventory =

D - Annual demand

S - Cost of ordering per order

H - Holding cost per unit per annum

CASE I

Economic order quantity =

=

= (74117.65)^1/2

= 272.25

= 272

Order Frequency =

= 2100/272

= 7.72

= 8

Annual cost of inventory management = Annual Holding cost + Annual ordering cost

=  H * Q/2 + S * D/Q

= 0.68*272/2 + 12 * 2100/272

= 92.48 + 96

= 188.48

CASE II

Ordering cost = $4 per order

Economic order quantity =

= (2*2100*4/0.68)^1/2

= (24705.88)^1/2

= 157.18

= 157

Order Frequency =

= 2100/157

= 13.38

= 14

Annual cost of inventory management = Annual Holding cost + Annual ordering cost

=  H * Q/2 + S * D/Q

= 0.68*157/2 + 4 * 2100/157

= 53.38 + 56

= 109.38

Explanation:

In case I, order should be given 8 times in a year in a lot of 272 to cater to the demand. The total annual cost of inventory management is $188.82.

In case II, order should be given 14 times in a year in a lot of 157 to cater to the demand. The total annual cost of inventory management is $109.38.