Question

In: Operations Management

Suppose that sales for a shirt are 900 units per month. It costs $60 to generate...

Suppose that sales for a shirt are 900 units per month. It costs $60 to generate an order. The item to be ordered has a unit cost of $14 and the inventory holding ratio is 8%. Find the answers to the following questions.

1) Calculate the optimal lot size to purchase.

2) How frequently should an order be placed throughout the year?

3) Calculate the annual order cost

4) Calculate the annual carrying cost

5) Find the total cost

Solutions

Expert Solution

Monthly demand = 900 units

Annual demand (D) = Monthly demand × 12 months = 900 × 12 = 10800 units

Ordering cost (S) = $60

Holding cost (H) = 8% of unit cost = 8% of $14 = $1.12

1) Optimal order quantity (Q) = √(2DS/H)

= √[(2 × 10800 × 60)/1.12]

= √(1296000/1.12)

= √1157142.8571

= 1075.71 or rounded to 1076 units

2) Number of orders per year = D/Q = 10800/1076 = 10.04

3) Annual ordering cost = (D/Q)S = (10800/1076)60 = $602.23

4) Annual carrying cost = (Q/2)H = (1076/2)1.12 = $602.56

5) Total cost = Annual ordering cost + Annual carrying cost

= $602.23 + $602.56

= $1204.79

keosha answered 2 years ago
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