Question

Inventory Models 4. (HINT: Refer to the inventory problem being faced by A to Z Carpets Inc. in the chapter) TP Inc. is a small company specializes in supplying toilet paper to small businesses, offices, universities, restaurants, and other similar establishments in the city of San Antonio. TP Inc. purchases their stock from brand-name toilet paper manufacturers and has significant limitations on its ability to carry an exceptionally large inventory. Despite the small business style, the company is immensely popular and gets enough clients that the demand is not deterministic in nature, but instead, follows a probabilistic pattern. The Manager of TP Inc. would like a recommendation on how many packages of toilet paper to order and when to order in an effort to minimize the inventory costs. You are provided the following pertinent information regarding the company and costs. Answer questions (a.), (b.) and (c.) given below

• Ordering Cost is $100.00 per order

• Cost of each package of toilet paper is $9.00 per box for TP Inc.

• The company uses a 25% annual holding cost rate for its inventory

• The lead time for a new order of toilet paper is 8 days

• Sales data indicate that the demand during 8-day lead time follows a normal probability distribution with a weekly mean of 750 boxes and a standard deviation per week of 80 boxes.

• The number of working days per year is 330

• Acceptable probability of a stock-out is 1% or 0.01.

a. What is the current EOQ?

b. What is the current Reorder point?

c. The manager is also considering increasing the risk of stockouts from 1% to 10%. Do you think that would help him reduce costs? Explain why.

Answer 1

It is given that mean weekly demand = 750

Therefore, total demand in a year = D = 750 /7 x 330 = 35357.14 ( 35357 rounded to nearest whole number )

Annual unit inventory holding cost = I = 25% OF $9 = $2.25

Ordering Cost = C = $100 per order

Current EOQ = Square root ( 2 x D x C/I) = = Square root ( 2 x 35357 x 100/2.25) = 1772.80 ( 1773 boxes rounded to nearest whole number)

Z value for 1 % stock out = NORMSINV ( 0.99) = 2.326

Current reorder point

= Average demand during lead time + Z value x Standard deviation of demand during lead time

= 750 + 2.326 x 80

= 750 + 186.08

= 936.08 ( 936 rounded to nearest whole number)

In the above case, safety stock = 186.08

Z value of 10% of risk of stockout

Corresponding Z value = NORMSINV ( 0.90) = 1.2815

Safety stock requirement = Z value x Standard deviation of demand during lead time

= 1.2815 x 80

= 102.52

It can be clearly seen that safety stock requirement will reduce from 186,08 to 102.52 wcih will help him to reduce cost in terms of inventory carrying cst of safety stock