Question

Question 13.4 Txt book) Halifax 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 six weeks and a standard deviation of two 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

Question: Halifax 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 six weeks and a standard deviation of two weeks. Demand is also a variable and normally distributed with a mean of 200 cigars per week and a standard deviation of 25 cigars.

Answer:

Given that:

Average weekly demand = 200

Standard deviation of demand (d) = 25

Average lead time in weeks = 6

Standard deviation of lead time (Lt) = 2

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

Given that:

Service level = 90% = Z = 1.28

Now:

Reorder point (ROP) is given by:

ROP = Daily demand x Lead time + Safety Stock

Let us first calculate Safety Stock

Safety Stock = Z x Sqrt( Leadtime x d^2 + Average demand^2 x Lt^2)

Therefore:

Safety Stock = 1.28 x Sqrt(6 x 25^2 + 200^2 x 2^2)

Safety Stock = 1.28 x 404.66

Safety Stock = 517.96

Now:

ROP = 200 x 6 + 517.96

ROP = 1717.96

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

Given that:

Service level = 95% = Z = 1.65

Therefore:

ROP = (200 x 6) + (1.65 x 404.66)

ROP = 1867.689 = 1867.69

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

Service level gives the percentage with which the demand is met, in other words, it is the probability of not hitting the stockout during the next replenishment cycle. A 90% service level signifies the probability of hitting the demand of 90%. Here the service level of 100% is considered optimal but it is usually not feasible in the real-world to attain that percentage, hence higher service level is considered optimal as the probability of achieving the demand is high.