Axcelis Technologies, Inc. is a world-leading
provider of equipment and services to the
semiconductor manufacturing industry. For
thirty five years, chipmakers from around the
globe have relied on Axcelis' systems and
process expertise to form the transistors that
power all electronics - from smart phones and
tablets, to laptops, personal music players and
more.
• Their equipment portfolio comprises a
powerful suite of manufacturing technologies
for ion implantation - one of the most critical
and enabling steps in the IC manufacturing
process.
• http://www.youtube.com/watch?NR=1&v=gB
AKXvsaEiw&feature=endscreen
• In addition, they provide extensive
aftermarket service and support, including
spare parts, equipment upgrades,
maintenance services and customer training.
Our customers include all of the 20 largest
semiconductor manufacturers in the world.
More than 3,000 of our products are in use
worldwide.
Competition
• The US Companies in our local area besides
Axcelis include Applied Materials (Varian) and
Ulvac.
• In other words there are job possibililities in
the immediate area. These include business,
sales, finance, as well as manufacturing.
• These companies survive and prosper in the
face of foreign competition because they
utilize smart manufacturing techniques and
innovation.
• This requires not only that their scientist are
on top of their fields but their technicians and
floor managers know what they are doing.
• So How Do They Survive?
• Strong improvements in U.S. manufacturing
productivity and output since 1990 began
with less capital-intensive TQM, Six Sigma,
Kaizan strategies, but evolved into larger
investments in automation which have been
eliminating many routine jobs.
• Most of the 5 million manufacturing workers
displaced in the past decade had a high school
education or less. Less than 40 percent of U.S.
manufacturing employees today are engaged in
actual production. New jobs will look different.
• “Investing in technology, equipment and
automation” is the #1 way that U.S.
manufacturers say they can increase their
competitiveness.
• As U.S. business leaders also discover the innovation
advantage of locating manufacturing in closer
proximity to R&D, it may unexpectedly add to any
technology-driven U.S. manufacturing resurgence.
• Manufacturing is responsible for 69% of private R&D
spending in the U.S. Recent studies show that this R&D
is sometimes more effective when co-located with
manufacturing.
• “We must rebuild the nation’s industrial commons –
the collective R&D, engineering and manufacturing
capabilities that sustain innovation.”
• Manufacturing SMART:
• http://www.flixxy.com/boeing-737-timelapse.htm
• Where is the math?
• Does it matter whether it is a
plane or an ion implanter?
• Is it a place where you could
work and make a career?
• Today Companies expect everyone to be
a Contributor and to be Involved
• You will not find Jobs that pay well
where you are merely a cog
•Machine parts are easily
Replaced
• So what is important and where does math
come in:
• Algebra I
• Geometry
• Algebra II
Algebra I
• How many Units should we manufacture and
at what price?
• What should the marketing/sales department
seek to charge and what should the
manufacturing department make
Algebra I Demand Function
• Suppose that the customers are price sensitive
– That is they will buy less of your equipment the
higher the price.
– Fortunately it is a linear function:
– The units (u) demanded by the customers increase
as the price in thousands of dollars (p) decreases
P = -3.5 (u) + 80 where u< 20
Algebra I Supply Function
• The Units (u) that the manufacturing
department is willing to supply is also a
function of the price
• That is the higher the price in thousands the
more that will be built (as the cost of making
units increase after a certain minimum U (e.g.
4).
So: the Supply function is :
P = 1.5 U – 1 once U > 4
Algebra I
• Thus the question is how many should the
manufacturing department make and can the
sales department sell at a price that justifies
both equations (note that since you cannot
make partial machines but can charge
fractions of P which is in thousands of dollars)
U must be rounded if necessary to a whole
number and P can be rounded to what level?)
Geometry
• As seen in the video and the pictures of the manufacturing
process, efficiency is paramount. One way to ensure
efficiency is to leave adequate room for employees to work
while having appropriate equipment and tools close at
hand.
• The constraints are that the work area is a rectangular
space 10’ by 12” and the Unit frame is 6’ by 4’. The first,
second, and third unit part trays have rectangular bases
3’x4.5’, 2.5’x5’ and 3’x4’. The first (used with the first and
second part tray) and second unit tool tray (used with the
second and third part tray) are cylindrical with radius 2’).
• (Continued Next slide)
Geometry
• Now, as seen in the pictures the outlines for the work
area, the unit frame, tool carts, and part carts are
marked on the manufacturing floor.
• What is the total area used, what is the total area
devoted to the unit frame, and what is the total area
devoted for the carts.
• Only 45% of the work area can be occupied by the unit
and all carts at any one time, please devise your most
efficient manner for the placement and the removal
and replacement of the carts so that movements are
minimized while still maintaining 55% or above clear
floor space during manufacture.
Algebra II
• In Business, the revenue, cost and ultimately
profit drive the sales department and the
manufacturing departments of any business.
• That is a company tries to maximize revenues
(the number of products sold x the price sold),
and minimize the costs of doing business (the
cost of making products, distribution of the
product, the advertising and sales expense, and
general overhead) to yield profit (revenue –
costs)
Algebra II
• The profit as it relates to revenue can be stated as a
quadratic function where a is positive and the profit
function as it relates to cost can also be stated a
quadratic function were a is negative and X is the
number of units sold or manufactured.
• Manufacturing too many units reduces the overall
profit as it costs more to make each additional unit and
because storage costs must be added, while
manufacturing too few reduces the overall profit (lost
revenue). Thus, the number of manufactured units
manufactured and sold on an annual basis should be
approximately equal (one year you may manufacture
an portion to have it for next year).
Algebra II
• Profit (P in thousands of dollars) as a function of
units manufactured is
P = -.5(x²) + 15x – 11.25
• Profit (P in thousands of dollars) as a function of
units sold is
P= .75(x²) - 6x + 8
What is the value of X when the Profit is equal
Graph the functions and write a discussion of what
value(s) of X make the most sense.