A manufacturer of lawn care equipment has introduced a new product. The anticipated demand is normally distributed with a mean of ? = 100 and a standard deviation of ? = 50
Each unit costs $75 to manufacture and the introductory price is to be $125 to achieve this level of sales. Any unsold units at the end of the season are unlikely to be very valuable and will be disposed of in a fire sale for $25 each. It costs $10 to hold a unit in inventory for the entire season. What is the cost of overstocking? What is the cost of understocking? What is the optimal cycle service level? How many units should be manufactured for sale?
What will be an ideal response?
Answer:
Co = c - s
= $75 - $15
= $60
Cu = p - c
= $125 - $75
= $50
CSL* = Cu/(Cu + Co)
= 50/(50 + 60)
= .4545 ≈ .45
O* = NORMINV(CSL*, μ, σ)
= NORMINV(0.45, 100, 50)
= 93.71693 ≈ 94
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