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Roll No Name

112 Movin Crasto

a. What is the sample mean and sample variance of the set?Ans:

b. What is the inventory policy that American Aerospace should implement for part 10003487?Ans: As per the case , we are of the opinion that American Aerospace should implement theRe-

order Point , Order-Quantity Policy ( R,Q) Model , because of the following assumptions :-

1) Part 10003487 inventory appears to be a stable/critical product and is under continuousreview.

Month

Number Of MX332

ordered

June 25

July 31

August 18September 22

October 40

November 19

December 38

January 21

February 25

March 36

April 34

May 28

June 27Mean 28

Variance 53.16666667

Std. Dev 7.291547618

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2) No lead time for Part 10003487 by itself , however the lead time of one and a half months andthe corresponding delay is due to that of the other steel parts. This lead time is considered in

our workings below.

3) The demand ofPart 10003487 is equal to the demand of MX332 jet engines , since it isexclusively used for this type of jet engines. Therefore the assumption is that the part is

normally distributed with a mean and Variance of 28 & 53.1667 as per answer a.

4) Fixed set up cost K = 5,800 and holding cost h= 750 and shortage cost p = 3,250

Average Demand Yearly = Mean * 12 months

D = 28 * 12 = 336

There for Average Demand for Lead time of One & Half Months = Mean * 1.5 months

D = 28 * 1.5 = 42

& Standard Deviation = 7.29154761807579 * 1.5 = 10.9373214271137

Average Demand per Unit Time D 336

Set Up Cost K 5800

Unit Holding Cost h 750

unit Shortage Cost p 3250

Service Level L 0.85

From the above : Order Quantity (Q ) = Sqrt of ( 2*D*K) / h) * Sqrt of ( ( p+h)/p) = 79.97538

Re-order Point ( R ) = a + L (b-a) = 53.3358

To Summarise American Aero space should implement the (R,Q) model withrounded off values

ofQ = 80 & R=53

c. What are the average annual holding costs and set up costs as associated with this inventorypolicy.

Average inventory Cost before Order Arrives = R -Average Demand for Lead time = 53-42 = 11

Average inventory Cost After Order has Arrived = Average inventory Cost before Order Arrives + Q

= 11+80 = 91

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Therefore Average Inventory Level = (11+91)/2 = 51

Hence Average Yearly Holding Cost = 51 * Unit Holding Cost = 51 * 750 = 38,250

Average number of set ups per year = Average Demand Yearly / Q = 336 / 80= 4.2

Hence Average Yearly Set Up Cost = 4.2 * Set Up Cost = 4.2 * 5800 = 24,360

d. How do the average annual holding costs and set up costs change if the desired probability thata shortage will not occur between the time an order is placed and the time the order is

delivered is increased to 0.95

New L = 0.95 and hence the revised table below and revised values ofQ & R

Average Demand per Unit Time D 336

Set Up Cost K 5800

Unit Holding Cost h 750

unit Shortage Cost p 3250

Service Level L 0.95

Using similar formulas as used in solution to question c : Q = 80 & R = 60 ( Rounded Off )

Average inventory Cost before Order Arrives = 60-42 =18

Average inventory Cost After Order has Arrived = 18+80 =98

Therefore Average Inventory Level = (18+98)/2 = 58

Hence Average Yearly Holding Cost = 58 * Unit Holding Cost = 58 * 750 = 43,500

Average number of set ups per year = 336 / 80 = 4.2

Hence Average Yearly Set Up Cost = 4.2 * Set Up Cost = 4.2 * 5800 = 24,360

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No Change in Average Yearly Set Up Cost while there is an increase in Average Yearly Holding Cost

e. Do you think Scarletts independent analysis of each stationary part could generate inaccurateinventory policies ? Why or Why Not

Scarletts independent analysis of stationary part 10003487 is justified since only a single jet engine that

needs this part and this part is the one causing the lead time in the process .

However in most cases stationary parts would be used for multiple jets and the lead time due to this

stationary part affects the demand for other parts as well . Hence the interdependency cannot be

analyzed correctly performing an independent analysis of each stationary part. Hence it can be said that

Scarletts approach of independent part analysis may be inaccurate for other stationary parts.

f . Scarlett knows that the aerospace industry is very cyclical the industry experiences several years of

high sales , several years of mediocre sales and several years of low sales . How would you recommend

incorporating this fact into the analysis.

Ans: Forcasting method could be used.