Benaco is a large firm sells seeds to farmers. It costs $10 to make each kilogram (kg) of seed. They sell each kg for $55. If they have more seed than demanded by farmers, the remaining seed is sent overseas. They only earn $5 per kg from the overseas market. If demand exceeds their quantity, then the sales are lost. As a forecast for demand they will use a normal distribution with a mean of 250,000 and a standard deviation of 106,000. How many kilograms (in '000) should they have in the warehouse before the next growing season? |
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Solution:
Overage cost (Co) i.e. cost of overbuying is calculated as,
Co = Cost price - Salvage value
Co = $10 - $5
Co = $5
Underage cost (Cu) i.e. cost of underbuying is calculated as,
Cu = Selling price - Cost price
Cu = $55 - $10
Cu = $45
Service level = Cu / (Cu + Co)
Service level = $45 / ($45 + $5)
Service level = 0.90
Using the Z-table, value of Z can be computed. For service level = 0.90,
Z-value = 1.29
Alternatively, Z-value can also be determined using NORMSINV function in Excel.
Z-value = NORMSINV (Service level)
Z-value = NORMSINV (0.90)
Z-value = 1.29
Quantity (Q) to have in the warehouse,
Q = Mean Demand + (Z-value x Standard deviation)
Q = 250,000 + (1.29 x 106,000)
Q = 386,740
Quantity = 386.74 Kilograms (in ‘000)
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