Question

COMPLETE ALL PARTS AND ILL LEAVE YOU A THUMBS UP

A retail company is reevaluating its inventory policy for meeting a constant annual demand of 5,200 units

for its top-selling product. The current inventory policy is to order 650 units each time. The company

purchases the product from a manufacturer at a wholesale price of $20 per unit. The company also pays $80 as the ordering cost for each order regardless of the order quantity. The company’s inventory capital is borrowed from a bank at a simple annual interest rate of 10%. In addition, the company must pay a tax of 6% of the annual inventory value and another 3% of the annual inventory value for insurance. The lead time is estimated to be 4 days and the business opens 365 days a year.

ANSWER A-D FOR A THUMBS UP!!

(a) List the given information under the current situation (hint: list both values and units):

A =

Q =

k =

c =

h =

L =

(b) Calculate the total annual holding cost under the current inventory policy:

((c) Calculate the optimal order quantity (Q*) and reorder point (R*):

((d) What will be the reduction in total annual relevant cost (TC) if the company adopts the

optimal inventory policy obtained in (c)?

Answer 1

(a) List the given information under the current situation (hint: list both values and units):

Annual demand, A = 5,200 units
Order quantity, Q = 650 units
Wholesale price per unit, k = $20
Ordering cost for each order, c = $80
Holding cost, h = 10% + 6% + 3% = 19%
Lead time, L = 4 days

(b) Calculate the total annual holding cost under the current inventory policy:

Current Total Holding cost = Ordering cost + Carrying cost
= (A*c)/Q + (Q*h)/2
= (5,200 * 80)/650 + (650*19%)/2
= 640 + 61.75 = $701.75

(c) Calculate the optimal order quantity (Q*) and reorder point (R*)

Q* = (2*A*c/h)^1/2 = (2 * 5,200 * 80 / h)^1/2 = 2093 units
R* = L * A/365 = 4 * 5,200/365 = 57 units

(d) What will be the reduction in total annual relevant cost (TC) if the company adopts the optimal inventory policy obtained in (c)

When the ordering quantity is 2093 units instead of 650 units, the new cost is:

New total cost = Ordering cost + Carrying cost
= (A*c)/Q* + (Q**h)/2
= (5,200 * 80)/2093 + (2093*19%)/2
= 198.75 + 198.75 = $397.5

Reduction in cost = $701.75 - $397.5 = $304.25