A firm has an annual demand of 2000 units for a given part T

A firm has an annual demand of 2000 units for a given part. They can produce the part at a rate of 12 per day with a set up cost of $24. The materials to make the part cost $37.50 per unit. The firm\'s carrying cost is $20 per part per year. Consider there are 250 work days per year. What is the daily production rate? What is the daily usage? What is the optimal production lot size? What is the total annual cost associated with this part?

Solution

Annual Demand D = 2000 units

Set up cost K = $24

carrying cost h = $20

materials to make the part cost P = $37.50 per unit

Optimum production size Q = sqrt(2 * D* K / h) = sqrt(2 * 2000 * 24 / 20) = 69.28 = 70

Total cost = P*Q + D * k/Q + h * Q/2

=37.5 * 70 + 2000 * 24/70 + 20 * 70/2 = $4010.7

Daily production rate = 2000/250 = 8 parts per day

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