Question

Rich Hotel distributes a mean of 1,000 bath towels per day to guests at the pool and in their rooms. This demand is normally distributed with a standard deviation of 100 towels per day, based on occupancy. The laundry firm that has the linens contract requires a 2-day lead time. The hotel expects a 98% service level to satisfy high guest expectations.

a. What is the safety stock needed to meet this service level?

b. What is the ROP?

c. Suppose the laundry firm negotiates a 3-day lead time with Rich. Now what are the safety stock and reorder point that Rich should use?

d. Suppose that with better housekeeping the standard deviation of towels distributed is reduced to 80 towels. Everything else remains the same as before. With a 2-day lead time, what are the new safety stock and ROP?

e. Rich’s linen manager believes that a 99% service level would be good to stay competitive with other hotels in the area. Assuming a 2-day lead time, what are the new safety stock and ROP?

f. Based on your answers to (c)-(e) clearly describe (5-8 lines) the impact of lead time, standard deviation of demand, and service level on safety stock.

Answer 1

DEMAND = 1000
STDEV DEMAND = 100
SERVICE LEVEL = 98, CORRESPONDING Z VALUE 2.054
LEAD TIME = 2

REORDER POINT = (DEMAND * LT) + SAFETY STOCK
1. SAFETY STOCK = Z * STANDARD DEVIATION OF DEMAND * SQRT(LEAD TIME)

SAFETY STOCK = 2.054 * 100 * SQRT(2) = 290.48

2. ROP = (1000 * 2) + 290.48 = 2290

3. SAFETY STOCK = 2.054 * 100 * SQRT(3) = 355.76
ROP = (1000 * 3) + 355.76 = 3356

4. SAFETY STOCK = 2.054 * 80 * SQRT(2) = 232.38
ROP = (1000 * 2) + 232.38 = 2232

5. SERVICE LEVEL = 99, CORRESPONDING Z VALUE 2.326
SAFETY STOCK = 2.326 * 80 * SQRT(2) = 263.16
ROP = (1000 * 2) + 263.16 = 2263

6. LEAD TIME REPRESENTS THE TIME IT WOULD TAKE FOR THE ORDER TO ARRIVE. THE DAILY DEMAND WOULD NEED TO BE SATISFIED AND THEREFORE, WE WOULD NEED TO HAVE ENOUGH IN INVENTORY TO SATISFY THE DEMAND TILL THE LEAD TIME, WE CALL THIS THE LEAD TIME DEMAND.

A HIGHER LEVEL OF SERVICE LEVEL WOULD MEAN LESS STOCK OUTS BUT WOULD REQUIRE MORE IN INVENTORY LEVEL.

STANDARD DEVIATION CREATES TH EUNDERTSNSINDG OF UNCERTAINTY OF THE NORMAL DISTRIBUTION, WHICH MEANS THAT WITH A LARGER VARIABILITY, THE INVENTORY LEVEL WOULD NEED TO BE RAISED ACCORDINGLY.