Question

My Manufacturing is involved in the production of machine parts. The company uses​ 600,000 pounds of steel annually. The current purchasing cost for steel is​ $3.20 per pound. The carrying cost for inventory is 10 percent of the purchase price. The cost of ordering steel is​ $800 per order. The company has decided to maintain a safety stock of​ 15,000 pounds. The delivery time per order is 6 days. The company works 365 days a year.

​A) What is the optimal​ EOQ?

​B) How many orders will be placed​ annually?

​C) What is the average​ inventory?

​D) What is the inventory order​ point? (That​ is, at what level of inventory should a new order be​ placed?)

​E) What is the​ company's total inventory cost for the​ year?

Answer 1

A)

2 X AD X OC E0Q=V2 CC

Where,
EOQ = Economic Order Quantity
AD = Annual Demand
OC = Ordering Cost per order
CC = Carrying Cost per unit per annum

Substituting the values in the formula, we get:

$EOQ = \sqrt{\frac{2\times 600000\times 800}{3.2 \times 10\%}}$

$= \sqrt{\frac{\textup{ 960,000,000 }}{0.32}}$

$= \sqrt{ \textup{3,000,000,000}}$

$= \textup{54,772.26 Pounds of steel}$

B)

Number of Orders per year = Annual Demand / EOQ
= 600,000 / 54,772.26
= 10.9545 ...(note that it is practically not possible to order in decimals, but for the sake of calculations we use it)
or
= 11 orders

C)

Average Inventory = EOQ / 2
=  27,386.13 pounds

D)

Usage per day = Annual demand / No of days in a year
= 600,000 / 365
=1,643.84 pounds

Inventory Order point = Safety Stock + (Usage per day * No of days for delivery)
=15000 + (1,643.84 * 6)
= 24,863.04 pounds

E)

Total Inventory Cost = (Carrying Cost * Average Inventory) + ( Ordering Cost * No of orders)
= (0.32 * 27,386.13) + (800 * 10.9545)
= 8763.56 + 8763.60
=  $17,527.16