Can you please help me solve this?

Jettisoning Surplus Stock

Scarlett Windermere cautiously approaches the expansive gray factory building and experiences a mixture of fear and excitement. The first day of a new consulting assignment always leaves her fighting conflicting emotions. She takes a deep breath, clutches her briefcase, and marches into the small, stuffy reception area of American Aerospace.

"Scarlett Windermere here to see Bryan Zimmerman," she says to the bored security guard behind the reception desk.

The security guard eyes Scarlett suspiciously and says, "Ya don't belong here, do ya? Of course ya don't. Then ya gotta fill out this paper work for a temporary security pass."

As Scarlett completes the necessary paper work, Bryan exits through the heavy door leading to the factory floor and enters the reception area. His eyes roam the reception area and rest upon Scarlett. He approaches Scarlett booming, "So you must be the inventory expert Scarlett Windermere. So glad to finally meet you face to face! They already got you pouring out your life story, huh? Well, there will be enough time for that.Right now, let's get you back to the factory floor to help me solve my inventory problem!"

And with that, Bryan stuffs a pair of safety glasses in Scarlett's right hand, stuffs the incomplete security forms in her left hand, and hustles her through the heavy security door.

As Scarlett walks through the security door, she feels as though she has entered another world.Machines twice the size of humans line the aisles as far as the eye can see. These monsters make high-pitched squeals or low, horrifying rumbles as they cut and grind metal. Surrounding these machines are shelves piled with metal pieces.

As Bryan leads Scarlett down the aisles of the factory, he yells to her over the machines, "As you well know from the proposal stage of this project, this factory produces the stationary parts for the military jet engines American Aerospace sells.Most people think the aerospace industry is real high-tech. Well, not this factory. This factory is as dirty as they come. Jet engines are made out of a lot of solid metal parts, and this factory cuts, grinds, and welds those parts."

"This factory produces over 200 different stationary parts for jet engines. Each jet engine model requires different parts. And each part requires different raw materials.Hence, the factory's current inventory problem."

"We hold all kinds of raw materials from rivets to steel sheets here on the factory floor, and we currently mismanage our raw materials inventory. We order enough raw materials to produce a year's worth of some stationary parts, but only enough raw materials to produce a week's worth of others. We waste a ton of money stocking raw materials that are not needed and lose a ton of money dealing with late deliveries of orders. We need you to tell us how to control the inventory how many raw materials we need to stock for each part, how often we need to order additional raw materials, and how many we should order."

As she walks down the aisle, Scarlett studies the shelves and shelves of inventory. She has quite a mission to accomplish in this factory!

Bryan continues, "Let me tell you how we receive orders for this factory. Whenever the American Aerospace sales department gets an order for a particular jet engine, the order is transferred to its assembly plant here on the site. The assembly plant then submits an order to this factory here for the stationary parts required to assemble the engine. Unfortunately, because this factory is frequently running out of raw materials, it takes us an average of a month between the time we receive an order and the time we deliver the finished order to the assembly plant. The finished order includes all the stationary parts needed to assemble that particular jet engine. BUT and that's a big but the delivery time really depends upon which stationary parts are included in the order."

Scarlett interrupts Bryan and says, "Then I guess now would be as good a time as any to start collecting the details of the orders and solving your inventory problem!"

Bryan smiles and says, "That's the attitude I like to see chomping at the bit to solve the problem!Well, I'll show you to your computer.We just had another consulting firm complete a data warehouse started by American Aerospace three years ago, so you can access any of the data you need right from your desktop!" And with a flurry, Bryan heads back down the aisle.

Scarlett realizes that the inventory system is quite complicated. She remembers a golden rule from her consulting firm: break down a complex system into simple parts. She therefore decides to analyze the control of inventory for each stationary part independently. But with 200 different stationary parts, where should she begin?

She remembers that when the assembly plant receives an order for a particular jet engine, it places an order with the factory for the stationary parts required to assemble the engine. The factory delivers an order to the assembly plant when all stationary parts for that order have been completed. The stationary part that takes the longest to complete in a given order therefore determines the delivery date of the order.

Scarlett decides to begin her analysis with the most time-intensive stationary part required to assemble the most popular jet engine. She types a command into the computer to determine the most popular jet engine. She learns that the MX332 has received the largest number of orders over the past year.She types another command to generate the following printout of the monthly orders for the MX332.

Month Number of MX332 ordered

June 25

July 31

August 18

September 22

October 40

November 19

December 38

January 21

February 25

March 36

April 34

May 28

June 27

She enters the monthly order quantities for the MX332 into a computerized statistical program to estimate the underlying distribution. She learns that the orders roughly follow a normal distribution. It appears to Scarlett that the number of orders in a particular month does not depend on the number of orders in the previous or following months.

(a) What is the sample mean and sample variance of the set of monthly orders for the MX332?

Scarlett next researches the most time-intensive stationary part required to assemble the MX332. She types a command into the computer to generate a list of parts required to assemble the MX332. She then types a command to list the average delivery time for each part. She learns that part 10003487 typically requires the longest time to complete, and that this part is only used for the MX332. She investigates the pattern for the part further and learns that over the past year, part 10003487 has taken an average of three fourths (3/4) of month or 22.5 days (assume 1 month = 30 days) to complete once an order is placed. She also learns that the factory can produce the part almost immediately if all the necessary raw materials for the production process are on hand. So the completion time actually depends on how long it takes to obtain these raw materials from the supplier. On those unusual occasions when all the raw materials already are available in inventory, the completion time for the part is essentially zero. But sometimes the completion time can be as high as one and a half months. For the lack of a better estimate Scarlett assumes that this completion time also follows a normal distribution.

(b) What is an estimate of the mean and variance of the delivery time for part 10003487?

Scarlett performs further analysis on the computer and learns that each MX332 jet engine requires two parts numbered 10003487. Each part 10003487 accepts one solid steel part molded into a cylindrical shape as its main raw material input. The data shows that several times the delivery of all the stationary parts for the MX332 to the assembly plant got delayed for up to one and a half months only because a part 10003487 was not completed. And why wasn't it completed? The factory had run out of those steel parts and had to wait for another shipment from its supplier! It takes the supplier one and a half months to produce and deliver the steel parts after receiving an order from the factory. Once an order of steel parts arrives, the factory quickly sets up and executes a production run to use all the steel parts for producing parts 10003487. Apparently the production problems in the factory are mainly due to the inventory management for those unassuming steel parts. And that inventory management appears to be completely out of whack. The only good news is that there is no significant administrative cost associated with placing an order for the steel parts with the supplier.

After Scarlett has finished her work on the computer, she heads to Bryan's office to obtain the financials needed to complete her analysis. A short meeting with Bryan yields the following financial information.

Setup cost for a production run

to produce part 10003487: $5,800

Holding cost for machine part 10003487: $750 per part per year

Shortage cost for part 10003487 (includes

outsourcing cost, cost of production

delay, and cost of the loss of

future orders): $3,250 per part per year

Desired probability that a shortage for

machine part 10003487 will not occur

between the time an order for the steel

parts is placed and the time the order is

delivered: 0.85

Now Scarlett has all of the information necessary to perform her inventory analysis for part 10003487!

(c) What is the inventory policy that American Aerospace should implement for the steel part required to produce part 10003487?

(d) What are the average annual holding costs, shortage costs, and setup costs associated with this inventory policy?

(e) How do the average annual holding costs, shortage costs, and setup costs change if the desired probability that a shortage will not occur between the time an order is placed and the time the order is delivered is increased to 0.95?

(f) Do you think Scarlett's independent analysis of each stationary part could generate inaccurate inventory policies?Why or why not?

(g) 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?