Question

Chicago's Hard Rock Hotel distributes a mean of 1,200 bath towels per day to guests at the pool and in their rooms. This demand is normally distributed with a standard deviation of 95 towels per​ day, based on occupancy. The laundry firm that has the linen contract requires a 4​-day lead time. The hotel expects a 99​% service level to satisfy high guest expectations. Refer to the standard normal table for z-values.

​a) What is the reorder​ point? ___towels ​(round your response to the nearest whole​ number).

​b) What is the safety​ stock?____towels ​(round your response to the nearest whole​ number).

Answer 1

Given values:

Mean demand (d) = 1,200 bath towels

Standard deviation, Sigma (d) = 95 towels

Lead time (L) = 4 days

Service level = 99% = 0.99

Solution:

Using standard normal table, value of Z can be determined. For service level = 99%, Z = 2.33

(a) Reorder point (ROP):

ROP = (d x L) + [Z x Sigma (d) x SQRT(L)]

Putting the given values in the above formula, we get,

ROP = (1200 x 4) + [2.33 x 95 x SQRT(4)]

ROP = 4800 + 442.7

ROP = 5242.7 or 5243 (Rounding off to the nearest whole number)

Reorder point = 5243 towels

(b) Safety stock:

Safety stock = [Z x Sigma (d) x SQRT(L)]

Safety stock =  [2.33 x 95 x SQRT(4)]

Safety stock = 442.7 or 443 (Rounding off to the nearest whole number)

Safety stock = 443 towels