Question

A resort hotel is planning to install a computerized inventory system to manage complementary guest items such as soap and shampoo. The daily demand for bars of soap appears to be distributed normally, with mean = 16 and standard deviation = 3. Assume there are 365 days considered for this inventory system. Once an order is placed, it takes seven days before delivery is made. The effort for the staff person to place an order is $10. The annual holding cost of a bar of soap is $0.05. The hotel is concerned about stock-outs of such a basic item and, thus, desires a 99.9% service level.

a. Recommend an order quantity and reorder point for this inventory system.
b. What is the total annual cost for this inventory system?

Answer 1

Mean daily demand = 16

SD of daily demand = 3

No of days = 365

LT = 7 days

Cost = 0.1 dollar

Order cost = $10

Holding cost = $0.05

Service level = 99.9%

Optimal order quantity:

Order quantity = √(2*D*S)/H

Order quantity = √(2*16*365*10) / 0.05

Order quantity = √(116800)/0.05

Order quantity = √2336000

Order quantity = 1528.40 units

Reorder level:

Reorder level = dL + zб

Reorder level = 16*7 + 1.55*3

Reorder level = 112 + 4.65

Reorder level = 116.65 units

Total annual cost:

TC = ((16*365)*0.1) + ((16*365)*10 / 1528.40) + (1528.40/2 * 0.05)

TC = 584 + 38.21 + 38.21

TC = $660.42