Cost of carrying 1 unit is $1.2 per year. The shop has 360 working days per year. The lead time is usually 12 working days. Determine the annual total relevant, including ordering and carrying, cost.

I. Annual ordering cost = $240

II. Annual carrying cost = $240

III. Total annual inventory cost = $480

Explanation:

We begin by listing out the data we were given, we have:

annual demand (D) = 1200, ordering cost (S) = $80 per order,

per unit cost (H) = $ 1.20, number of working days = 360 days,

lead time = 12 days

To calculate the economic order quantity we use the formula

economic order quantity = square root of [(2 * annual demand * the ordering cost) ÷ (per unit cost)]

Mathematically,

EOQ =  

where:

D = annual demand, S = ordering cost, H = unit cost

Substite the variables into the formula, we have:

EOQ =

EOQ = = 400

EOQ = 400 units

I. Annual ordering cost = annual demand * ordering cost ÷ order size

number of orders (Q) = annual demand ÷ order size = 1200/400 = 3 orders

Annual ordering cost = ordering cost * number of orders

Annual ordering cost = S * Q ⇒ 80 * 3

Annual ordering cost = $240

II. Annual carrying cost = average inventory * per unit cost

average inventory = EOQ ÷ 2

Annual carrying cost = (EOQ * H) ÷ 2

Annual carrying cost = 400 * 1.2  ÷ 2 = 240

Annual carrying cost = $240

Total annual inventory cost = Annual ordering cost + Annual carrying cost

Total annual inventory cost = $ (240 + 240)

Total annual inventory cost = $480

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