Question

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.

1. What is the current EOQ?
2. What is the current Reorder point?
3. 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

We know

S = 100

P = 9

H = 25% of 9 = 2.25

L = 8 days or 8/7 week

d = 750 per week

σ = 80 per week

D = 330*750/7 = 35357.14 or 35357

z = 2.32 for 99% service level or 1% stock-out

EOQ = sqrt(2DS/H) = sqrt(2*35357*100/2.25) = 1772.8 or 1773 units

ROP = d*L + z*σ*sqrt(L) = 750*(8/7) + 2.32*80*sqrt(8/7) = 1055.5 or 1055 units

Yes. If the stockout chance is increased to 10% then the service level will drop to 90%. This means the value of z will be 1.28 and the safety stock will reduce. This will reduce the inventory cost.