Question

Gainesville Cigar stocks Cuban cigars that have variable lead times because of the difficulty in importing the product: lead time is normally distributed with an average of 6 weeks and a standard deviation of 2 weeks. Demand is also a variable and normally distributed with a mean of 200 cigars per week and a standard deviation of 25 cigars. 

a) For a 90% service level, what is the ROP? 

b) What is the ROP for a 95% service level? 

c) Explain what these two service levels mean. Which is preferable?

Answer 1

a)

Both demand and lead time are variable

Average weekly demand = 200 cigars

Standard deviation of demand = 25 cigars

Average lead time in weeks = 6 weeks

Standard deviation of lead time = 2 weeks

Service level = 90%, so Z = 1.64

ROP = ( 200 6 ) + 1.64 404.66

ROP = 1863.6 cigars 1864 cigars

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b)

When the service level is 95% , Z = 1.96

ROP = ( 200 6 ) + 1.96 404.66

ROP = 1993.1 1993 cigars

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c)

Service level refers to the probability of meeting the demand hence a service level of 90% signifies that the firm can meet the demand 90% of the time or having stock out only 10% of the time.

Service level of 95% signifies that the firm can meet the demand 95% of the time or having stock out only 5% of the time.

Hence a higher service level is preferable as the probability of meeting the demand is high.