Question

Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation Thomas's fastest-moving inventory item has a demand of 6100 units per year. The cost of each unit is $96, and the inventory carrying cost is $9 per unit per year. The average ordering cost is $29 per order. It takes about 5 days for an order to arrive, and the demand for 1 week is 122 units.? (This is a corporate operation, and there are 250 working days per year).

a. what is the EOQ? (round to two decimal places)

b. what is the average inventory if the EOQ is used? (round to two decimal places)

c. what is the optimal number of orders per year?( round to two decimal places)

d. what is the optimal number of days in between any two orders? (round to two decimal places)

e. what is the annual cost of ordering and holding inventory? (round to two decimal places)

f.what is the total annual inventory cost, including the cost of the 6100 units? ( round to two decimal places)

Answer 1

Following data are provided :

Annual demand = D = 6100 units

Ordering cost = Co = $29 / order

Annual unit inventory carrying cost = $9

1. The economic Order quantity ( EOQ )

= square root ( 2 x Co x D/Ch )

= square root ( 2 x 29 x 6100 / 9)

= 198.27 ( 198 rounded to nearest whole number )

1. Average inventory If EOQ is used = EOQ/2 = 198/2 = 99 UNITS

1. Optimal number of orders per year

= Annual demand / EOQ

= 6100 / 198

= 30.80

1. Daily demand = 6100 units / 250 days = 24.4 units/ days

Optimal number of days between two orders

= EOQ/ Daily demand

= 198/24.4

= 8.11 days

1. Annual purchasing cost = $96/ unit x 6100 units = $585600

Annual ordering cost

= Ordering cost x Number of orders

= Ordering cost x annual demand/ EOQ

= $ 29 x 6100/198

= $893.43

Annual holding cost

= Annual unit holding cost x average inventory

=$9 x 198/2

= $891

Therefore total annual cost

= $585600 + $893.43 + $891

= 4587384.43