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 5 weeks and a standard deviation of 3 weeks. Demand is also a variable and normally distributed with a mean of 175 cigars per week and a standard deviation of 25 cigars. Refer to the standard normal table LOADING... for? z-values. This exercise contains only parts a and b. ?a) For a 90?% service? level, what is the? ROP? The reorder point is nothing cigars ?(round your response to the nearest whole? number). For a 95?% service? level, what is the? ROP? The reorder point is nothing cigars ?(round your response to the nearest whole? number).

Answer 1

average demand (d) = 175

standard deviation of demand (s) = 25

lead time (L) = 5

standard deviatio of lead time (lt) = 3

a) service level = 90%

z score using standard normal table for 90% = 1.28

ROP = d*L + z*(L*s² + d² * lt²)

ROP = 175*5 + 1.28*(5*25² + 175² * 3²)

= 875 + 1.28*(3125 + 275625)

= 875+1.28*528

= 875+675.84

= 1550.84 = 1551 is the ROP

b) service level 95%

z = 1.645

ROP = d*L + z*(L*s² + d² * lt²)

ROP = 175*5 + 1.645*(5*25² + 175² * 3²)

= 875 + 1.645*(3125 + 275625)

= 875+1.645*528

= 875+868.56

= 1743.56 = 1744 is the ROP