Item X is a standard item stocked in a company\'s inventory of component parts.

Question

Item X is a standard item stocked in a company's inventory of component parts. Each year the firm, on a random basis, uses about 1,600 of item X, which costs $25 each. Storage costs, which include insurance and cost of capital, amount to $7 per unit of average inventory. Every time an order is placed for more item X, it costs $14 a. Whenever item X is ordered, what should the order size be? (Round your answer to the nearest whole number.) Order size b. What is the annual cost for ordering item X? (Round your answer to 2 decimal places.) Ordering cost c. What is the annual cost for storing item X? (Round your answer to 2 decimal places.) Holding cost

Explanation / Answer

Given values

Annual demand (D) = 1,600 units

Item cost (C) = $25 each

Storage cost / Holding cost (H) = $7 per unit

Ordering cost (Co) = $14

Solution

(a) Order size (Q*) is calculated as,

Q* = SQRT [(2 x D x Co) / H]

Putting the given values in the above formula, we get,

Q* = SQRT [(2 x 1600 x $14) / $7]

Q* = 80

Order size = 80 units

(b) Ordering cost is calculated as,

Ordering cost = (Annual demand / Order size) x Ordering cost per order

Ordering cost = (1600 / 80) x $14

Ordering cost = $280

(c) Holding cost is calculated as,

Holding cost = (Order size / 2) x Holding cost

Holding cost = (80 / 2) x $7

Holding cost = $280

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