Question

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?

Selected Answer: 386.74 How did they computethis

Answer 1

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)