Question

Daily demand for a certain product is normally distributed with a mean of 138 and a standard deviation of 13. The supplier is reliable and maintains a constant lead time of 7 days. The cost of placing an order is $17 and the cost of holding inventory is $0.40 per unit per year. There are no stock-out costs, and unfilled orders are filled as soon as the order arrives. Assume sales occur over 358 days of the year.
Your goal here is to find the order quantity and reorder point to satisfy a 73 percent probability of not stocking out during the lead time.
a. To manage inventory, the company is using
Continuous review system
Periodic review system
b. Find the order quantity. (Round your answer to the nearest whole number.)
Order quantity books
c. Find the reorder point. (Use Excel's NORMSINV() function to find the correct critical value for the given α-level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.)
Reorder point

Answer 1

Answer:

A. Continuous review system

B. Order quantity = 2,049 Books

C. Reorder point=987

Explanation:

a. To manage inventory, the company is using CONTINUOUS REVIEW SYSTEM

b. Calculation to find the order quality

Using this formula

Order quantity = √((2DS)/H)

Let plug in the morning

Order quantity=√ ((2 x 49,404 x 17)/0.40)

Order quantity = 2,049 Books

Calculation for annual demand

Annual demand=138*358 days

Annual demand=49,404

C. Calculation for reorder point

First step is to find the σL

73 % S.L. - z = 0.613

Using this formula to find the σL

σL = (Lσ^2)

Let plug in the formula

σL=√(7(13)^2)

σL= 34.39

Second step is to find the Reorder point using this formula

Reorder point = d bar(L) + zσL

Let plug in the formula

Reorder point = (138)(7) + 0.613(34.39)

Reorder point = 966+21

Reorder point=987