Thanks.
And so thanks for everybody coming this
is a rather small audience compared to
the one I had in in room literally there
was a huge auditorium with a balcony and
I was told there were more than
twelve hundred people at the talk and
three or four hundred in an overflow
room so I was pretty pretty pleased.
Please with that but I was also told that
you know in and asking in being invited
to give a plenary talk that this had to
be a very general talk that the audience
while away the most of the people would
all people would be operations research.
These were not people who would
necessarily know anything
about a new to programming so
on and so forth.
So this had to be a very general talk and
this gave me a great opportunity
because what I decided to do
was to essentially do I'm walking
talk about energy or programming.
OK And so what does that mean.
And so my goal in this talk
is is to convince you and
I know many of you already or or
may be convinced that
the the technique of a war and
some people may may disagree we see some
people from other areas in the room that
the technique of or that by far is had
the biggest impact on solving problems
that industry government military whatever
you want has been in or programming.
In in the last decade.
And so that.
And so that's what I'd like
to to to show you today.
So so we'll do a brief
introduction to energy program and
no mathematics in this talk.
And I.
Mainly emphasize history and
in some applications we see so
good I can see it right here.
Yeah that's good.
And so
basically what we're talking about is
optimization models in which some or
all of the variables are energy or
and most of the time when we talk
about energy of variables not always
goes into a variable or binary and
why binary variables because binary
variables zero one variables are just
just can be used to model not quite
everything but almost anything.
Certainly decisions and
with you do something or
you don't do something all
kinds of nonlinearities
are modeled by zero one variables and
convex cities and so on.
OK So here's what I'm going
to do today talk start with
with a bit of history in the past and
then talk about where we are now and
what I'm going to emphasize in
this talk is real applications and
the key word here is real.
OK applications are something
that you know you might
think somebody writes a paper and says
well here's a model of a given problem.
And and here's an algorithm for
solving it by some technique
a real application is when something
is actually done in practice.
OK that's a big difference between
what you know academic modeling and
real applications and that's what we
really want to demonstrate today and
about and if your program.
Ok going to start with a little
bit of history and for
those who do who take in mind.
My discrete optimization class
you know how much I I love
this particular first thing this and
this is really the beginning of modern
internship programming this one nine
hundred fifty four paper by the answer
focusing on Johnson where
they actually solve a few.
Forty nine city
Traveling Salesman Problem You
all know the Traveling Salesman Problem so
I won't say any more about it but
why forty nine cities.
Well at that time it was forty that
time we had forty eight states in
the US not fifty and had ADD.
Add the one at the one of
the capital Washington D.C.
And that's where the forty nine
cities come from remember for
those you look surprised there are Alaska
and Hawaii we're not we're not states.
At that time.
Did they.
OK Well OK the T.S.P.
would not be interesting.
Remember we're talking about
driving distances and so on.
Yeah OK thanks for that correction.
That's good and and so they should
actually show that you could leave use
linear programming to get a provably
off the most pollution to
this forty nine city problem which had
roughly forty nine square variables.
And they did it all by hand.
They were not a computer use
they did it all by hand.
OK simplex method by hand with all
those variables rather amazing.
And after that but
that was a very specific problem and
they indicated there that you know this is
just some evidence that maybe we can use
linear programming to solve to solve
our energy programming problems and
they very modestly said at the end that's
all we're playing in here we're not
claiming any general algorithms or
anything and it took until one nine
hundred fifty eight when there was
a cutting plan algorithm cutting
planes you know are these things that are
linear inequalities that cut off solutions
to linear programming problems that
don't satisfy in a gravity conditions.
With Godfrey developed a finite algorithm
for for integer programming problems and
that could solve general
energy program problems
that was fifty eight and then following
soon after was this nice paper by.
Landen Dawei and they actually introduced
the notion of solving these energy
programming problems by branch and
bound branch and bound again I'm
not going to go into any details here but
again you use some linear programming but
lots of enumeration to explore
the solution space and
sixty three came another paper
a specialized branch and
bound algorithm for the Traveling
Salesman Problem by John little and
others at MIT and
the neat thing about this paper is it.
It actually coined the name branch and
background.
And so the sixty three paper is where the
term branch unbound was was created and
it just it just shows you how important
I think getting the right name.
For technique is and
I think Branch about is a very cool name.
And it's something that that I think
helped people pick up on the branch and
bound method and
finally probably earlier than this but but
the notion of you saying local search
to solve it or to programming problems.
This is one of the papers that's
frequently cited where you actually you
know just solve over subsets of variables
and and and continue in that way.
In one nine hundred fifty seven there
was another perhaps important paper
written by George Dance A Who course is
famous for the the simplex method and
then sit in this paper simply
said look we can formulate so
many things by integer programming and so
jumping from Linear Programming limited in
in the models you could deal with going to
programming and now you can you can solve
all kinds of nonlinear problems
scheduling problem so on and so forth but
soon thereafter somebody
published a paper saying hey I I I
just use this finite Comrie algorithm to
to strive to solve a scheduling problem.
And I've I added more
cuts to this problem.
I'm then there were solution.
In the first place I could have
a numerated everything faster then
then having done this algorithm and so
there was some doubt about whether this
cutting plan algorithm could really work.
And now let's start talking
about about applications.
And so
from the dance of paper in fifty seven.
It almost took a decade or more or
a decade or a bit more until
there actually was what I call a real
application somebody actually using it or
to programming problem to demonstrably
software real problem at least
the first ones that that were found
very difficult to find documentation of
early applications.
I spent a lot of time going
through the literature you know
loads of papers on different
models facility location.
Whatever you want loads of different
things like us trying to get something
trying to see a paper or somebody actually
said they solved the problem in practice
there was almost almost nothing in the
literature and so what I tried to do was
contact some people who were involved
with the early commercial codes.
And some of those people
are not living anymore and but
I did finally identify somebody who I had
a great e-mail correspondence with and
I'll tell you what he told me and and and
so the petrochemical industry was
probably first in being the industry
where people started actually
exploring exploring the use
of energy or programming and
it's interesting if you
go back to that one nine hundred sixty
Landon paper the branching man paper.
I hadn't realized this till I went back
and read the paper they actually say
in the first page of the paper that they
were contacted by British Petroleum.
To solve a Marin time
inventory routing problem and
those would be some of you
know here that that's an.
Area that we've been working on at Georgia
Tech Hunter his thesis among others
were were on maritime
inventory routing and land and
the like they say in the in the paper
they they immediately went back to
British Petroleum and said Look in
order to do anything for this problem.
We need to develop an integer
programming algorithm is it OK
if we use your funding to develop in a
general interest programming algorithm and
British Cone said sure.
And that's how they cut this branch and
bound up with them but
they never programmed it.
OK.
So that it never was actually it
never was actually implemented
it took the late sixty's where there were
there was a company called C I R N A.
And they developed the first real inner
programming code that you could actually
use in practice it was called
L P ninety ninety four.
And and it came in the late sixty's and
it was developed by a team led by
a guy the name of more than Beal I
don't know how many of you know that
name but he really is one of the most
influential persons in in
developing into programming
British He was knighted or were sort
of Martin Buell or something like that.
OK.
And one of the people in on Bill's team
was a guy the name of Maque Shaw and
he was the person I've communicated
quite a bit by email and
telling me about some of their
first real applications and so
the first one he mentioned these two for
free they did work for
Philips Electronics on the location
of factories in Spain.
It was a combination.
It was a logistics type type supply
chain type location problem.
And also.
British Petroleum.
I looked for the first public published
application again it came from
the same group and it was a it
was a military application from.
From the United Kingdom and
things really were moving more in Britain.
I would say at the in England at the time
then than in the US or elsewhere.
And so that's takes us through
the sixty's in the seventy's we began to
see a transition to more powerful
mid codes codes that you know
could solve a little bit bigger
problems and so L P ninety ninety four
translated to Empire transition
to Empire which France a.
Trance.
When two psychotic and
psychotic then went to the code that many
of you now know called Express N.P..
And so express M P Has this roots
back to this L P ninety ninety four
which was the first first
developed commercial code I.B.M.
was the other big developer and
they had M.P.'s X. M.P.'s X.
three seven The LS Johnson
was very involved in.
In some of those developments and
from there.
I.B.M. went to zero S. L.
which some of us have have used
here that got incorporated in
the public domain code cone point
zero are but then I.B.M. bought.
Bought I log and
therefore now has a C. plex.
What does that mean nine
hundred ninety four.
Yeah I don't know it's a good question.
I'm sorry and I don't know.
OK so
it's sort of political a little bit
of a personal part into this talk.
I'll tell you how I got I got involved in.
In an energy programming so
I was then a faculty member.
This was in the late sixty's
sat at at Johns Hopkins and
there was a park and and
this was the time and
somebody probably correct me
on the date on this one as.
Well but but but this was the time.
Just when the Supreme Court in the US.
Indicated the one man one vote
principle in terms of electing.
Congressmen senator.
But Congressman so on and and.
What's your recognize that
that's the state of Georgia.
And Georgia was absolutely
one of the worst states at
the time in terms of the one
man one vote representation.
The the rural counties controlled
everything and it was something like.
In the Atlanta area there was
one congressman representing
close to a million people and
in some of the rural areas there was one
congressman representing something
like a hundred thousand people.
And so this one man one vote was
really and men tend to want and
that's what the Supreme Court said
had to be changed and so during
this period there was a lot of scrambling
going on and how we had to do this.
And of course and
somebody gave a talk at Hopkins and
I said hey this could be a problem that
we might be able to do something about
with optimization particularly energy or
programming and
Bob Garfinkel was my student then and
we worked on this problem and
so what is the problem.
You've got to come up with
districts equal to the number of.
Congresspeople such that each district
has roughly an equal population and
the District should satisfy other things
like con to get a you know that this
picture would be connected.
Compact natural boundaries and.
And of course once you start doing this
and you start talking to two politicians
the political considerations
become significant as well.
And so we we did formulate this
naturally as a set partitioning
problem each potential district is say.
Is this a considered subset
which might have a cost.
Depending upon how closely it met the
criteria that you you want to satisfy and
the notion was that the two to
find a set of districts such
that each population units of the basic
units are not individual people but
very small things called census tracks or
or population units that that.
That stay together and.
We we developed a an implicit or
numeration algorithm for
solving this problem.
It did not have linear programming.
It was more like what constraint
programming does today doing a new partial
enumeration some branching and
eliminating of solutions and
Garfinkel was a really good programmer and
he wrote Our code in assembly language and
we could solve problems with no
about fifty population units and
maybe putting them into five to ten and
districts.
So even so for the larger states
to make our method work you had
to actually solve sub optimize
solving some problems.
This is what's done now and problems
are solved by an algorithm called Branson
price which I mentioned a little
bit more about later and
I think here's a result we're not
necessarily very you know great technology
always leads to good results and
that we're in a situation now where yes.
One man one vote is achieved but
the party that controls
the power can and can do pretty much what
it wants within the legal rules and.
We wind up in the US having
something like eighty
to ninety percent of our districts now
being the so-called safe districts where.
You know one party totally
controls the situation.
OK Coming back to
New General into program.
I mean now the seventy's the eighty's
was really a transition period and
it was a period where there wasn't much
advanced in the application side but
there were lots of theory developed and
so for
example you know the complexity theory
the notion of the end be harness and so
on came then people talked of
polynomial time out rooms for
linear programming and
leading to a barrier algorithm and
image or program a huge number of papers
on cutting plan specialized cutting plans
knapsack covers flow covers all
this kind of stuff if you've
taken into programming courses you know
about that were were were developed but
but not much change in terms of
the practical practical use.
Still it was basic LP base branch and
bound the algorithm that
was available and that had changed very
much from just simply solving L.P.
relaxations branching and so on.
It was one exception really and and that
and that was the airline industry seemed
to be much more much more
forward looking in terms
of using technology than almost
any other any other industry and
and mainly associated around
the airline crew scheduling problem.
They began to to do some
some very serious work on on
on on energy approaches specialized into
programming problems separate issues and
problems set covering problems with
hundreds of thousands of variables and
hundreds of constraints were were being
solved in the airlines who were probably
the first that I know about that
really did support a lot of
academic academic research and
a lot of that took place right here.
Ellis Johnson joined our
faculty soon after I did and
he through I.B.M.
already had a lot of car.
Back with their alliance and
we then got our young faculty
member Cindy Barnhart involved with us and
we began to work with
with many of the airlines starting with
Delta but also with American and United.
And that time Northwest and
US Air on on on first
on airline crew scheduling but then on
many other airline problems and as well.
So I see modern modern age of programming
really starting as it as we see it now in
the one nine hundred ninety S.
And here is what caused the big change.
And so to me.
These are just an amazing set of
numbers and so see plex code that
probably you all know I don't know if
you know the development of C. plex C.
plex was developed by by
Bob Bixby at the time.
Bob was a faculty member in math sciences
at Rice University and he had the saw it.
Id he decided to write just for
fun for his class decided to write
a simplex code I've known Bart for
many many years he was a Ph D.
student at Cornell was when I
was on the faculty there and
Bob just one of the most incredibly
meticulous people I've I've ever known and
just just get so
involved in details and his link.
He wrote this linear programming code and
then sent it to a few other
colleagues around the country people
said gee this is a quite nice.
Cody and want to think about about you
know seeing if industry centers that and
he did and he he got some he
got some good good response and
but then people said hey we really need
energy programming at that time at
Georgia Tech Martin salvos Berg who had
first come to George Itzhak in one nine
hundred eighty eight as a as a postdoc and
another graduate student and
I started working on Minto which
was a research code for an.
Programming and it was a code that.
You had to have another LP software but
with that LP solver.
Now you could get to any part of
the code add any cuts you wanted
any kind of branching rules so
on and so forth.
And they speak knew about our
work with mental illness and
we got involved with him and mental
really really was the start of the C.
plex energy or programming code
which of course then took on
developed quite a bit since then and
here here roughly from experiments
that picks me and so on have goop.
Who was a Ph D.
student here as well have done over
the years have shown the improvement in
the speed in the algorithmic speed not
the computer speed computers fixed here.
Here's the algorithmic improvement
of about thirty thousand in in C.
plex to two thousand and seven and
at the end of roughly at this time
was when Bixby and goo and Rosberg.
Let's see plex move to Groby and
started Groby which let's say Groby two
thousand and nine was about the same.
Same speed as C.
plex eleven in two thousand and
seven and synced up to two thousand and
thirteen that I've had a another
twenty speed up algorithm speed up.
OK just average.
Together.
There's the number you see.
One of the coin a war movement start.
Then a minute and a minute.
OK I don't know and so this week.
What we see is this two hundred
fifty thousand or so speed up over
over what little bit more than twenty
years algorithmically and now.
Just take a modest one
thousand speed up in computers
on the hardware side and so you put those
two together and now now now look at that.
Look at the effect and and so
which you can solve in one second.
In two thousand and
seven took great as it would have
taken greater than four months and
in the early ninety's.
What we can solve in one second.
Now would have taken great More than
seven years in the early ninety's.
So you know this is what really has made
it possible to do all this kind of stuff.
And and how did this happen early on
the code seemed to focus in one direction
or another we had this gummy cutting
playing cards that didn't work very well
we had branch and band which is used.
You used LP.
And the LP codes.
You know part of this big improvement is
is in the speed of solving Lidia programs
and the LP codes were not
really all that good and
but now you add to this all this work
that's been done on cutting plains and
pre-processing meaning that you
should clean up these problems.
First of all with some very
simple rules before you
get into the sophisticated stuff
reducing the size of a problem.
A lot also heuristics for finding good
feasible solutions quickly put this all
together and as the slide comes for
Rudolfo storing it all up in
and and and
you get this this this ultimate result.
Sort.
They are but
that's not really they're not you so
much for
energy program because interior
point codes which on and so.
Classes of problems a certainly
better than the simplex method
don't have a good restart capability.
The whole idea of branch unbalanced
is you know you solve an LP and
you add a constraint and you want to
resolve the LP you need to use the current
solution and and so what I'm really
talking about here is the linear algebra
enormous enormous improvements in
the linear algebra the numerical aspects
of just a sense are going to mean
something linear equations right.
So here I list a whole bunch of
the stuff that that that that
that made B.S.
these improvements possible.
Just figuring out what's the right
in orders simplex method is
really not a single algorithm
right you've got prime and
rhythms steeper said means how you choose
the entering variable and so on but
all of these things put together was
what really really is possible and
and and so here we go with perhaps
answering David's question a little bit
on the commercial side now of course
there's a lot more than this but
the three codes that are known
to be the ones that are or or
are codes that can really
solve big problems quickly and
these are the three main
commercial computing codes or C.
plex which is I.B.M. Express and P. now
owned by the get the which which company.
FICA which is mainly a company that that
that you don't think about
optimization that they do credit card.
Now it's the stuff I think it's
a FACT that but they are they.
They bought express from the British
people who would have it
that the new code started
up after Bixby and
doing Rothberg left see plex Groby
on the noncommercial saw I had.
The.
Escape code which was developed by
Tobias Och the bird who's who now is
also works for c plex but it probably
is the code that's most advanced
among the codes that are or
are or are free but
it does make you close.
Yes yes yes yes but but October been fact
gave a talk at some meeting recently so
many what the differences are and
you know it's.
It's quite reasonable.
It's certainly an excellent research code.
It's open source but you cannot use it for
promotional purposes without signing
some agreement with them but for
research purposes completely open source
and and a quite good code and end and
end when I.B.M. decided that O S L was not
something they really wanted to pursue
commercially they moved all their
stuff over to what became queen or
which is which is another set of
codes that are open source and
we really started this open
source stuff with with mint And
it's apparently still available but
I don't know if anybody uses it anymore.
OK so I promised them a title something
about impact and so the let me go there.
OK so I thought about how am I
going to measure impact right.
How am I going to do it
in a broad sense and
I decided what I would do is
there's this Edelman contest
that takes place every year
sponsored by informs where you
can submit sort of a case study of
problems that you've solved and and
then they have a serious judging process
that that pick six finalists each year.
I think they get they get many many.
You know.
Ten times as many or
more entries each year and
and they look at the innovation in
the financial impact is very important
in how they choose these and so.
There were therefore we went
back to two thousand and
we looked at all the six finalists
in each of those years so.
And so it's roughly.
I think through two thousand and twelve.
So.
Maybe seventy two finalists
took place in those years and
more than half more than half of those
finalists in describing their application.
Actually used some form
of discrete optimization.
I think that's very
impressive that you know
more than half of them actually use this.
OK And so in the next few slides
here just to just to give you
some idea of the roughly fifty three
percent of how many there were here.
Here were the titles and the winners we're
not going to go through all of these
starting with the early ones the ones
in red were actually winners.
So they had six finalists each year and
then I pick a winner and
sort of ones in Reds were winners and
if you look at the early ones you can see
the airline stuff really really being very
very significant not exclusive but
but very significant.
And again and
again you see a lot of supply
chain a lot of a lot of things related to
transportation but it starts to move away.
It starts to move away from from this.
Let me point out here.
This one.
Was a winner operation research and
advances cancer therapeutics and
that was work done.
Partly here by by evil lead.
Actually comment on this further on.
But she was part of a group that that.
That actually won.
If you see here.
You don't see names of people you see
companies because because the way this
process works is the submission is not buy
it is by a company saying you know here's
what here's where it whether they did
it themselves or not it's not relevant.
But here's our application and
here the improvements we've got.
And you know.
Different kinds of things.
Now you see here and
I won't spend more time on this.
OK but I thought I would take in the last.
In the last fifteen minutes or so
I would take some of some of these
application areas and give you some more
detail about about where things are and
in many of these cases since these
some of these areas I don't.
Some want some of them.
I know something about others.
I don't know a lot about I actually
contacted people in the industries and
asked them to give me information on
on how things were being used and
and and so that's when the material
comes from and the end.
All site who they were.
We start with transportation and
I'll do a citation already it is nice
pictures all come from about phone.
OK And and so we talked about airline
optimization a little bit but
and these were the people who really got a
lot of stuff started the pioneers in using
optimisation and and their work really
had a huge impact on the development of
initial Proma get programming methodology
and a whole bunch of different problems.
The network planning problem.
The one that says OK what should you or
what should your network
actually be where should you fly.
Two for example.
Fleet assignment that will come
back to that one is as well.
Fleet assignment means.
Now that you have a flight at a given
time from A to B. The question is
what size airplane should you put on
that flight that's fleet assignment crew
planning is is setting up schedules for
pilots gate assignment.
You know is what we what Gates.
How do you patted you man.
Matt Matt your gates to your flights and
and
finally at the end then probably
the problem that still is a huge one is
how you really plan robustly and
recover after you know bad weather
snowstorms are things like that.
OK So
crew scheduling we partition
a set of flights by crews and
you know you got a zero one variable for
every possible possible routing
a crew could take over a four or
five day period and
in the sixty's the airlines began to
the really the first major
developed exploring IP to solve
this problem and it still is a very
large problem through the eighty's
the the the algorithms
that were used in practice could
not solve the whole problem.
They're more like the your wrist except
today they would get a solution and
then fix a whole bunch of that solution
optimizing little pieces in iterations.
But but not able to solve the whole
problem but in the ninety's
there was a big breakthrough for
using column generation to try to directly
deal with billions of variables in
an injured programming setting and
this led to this branching price algorithm
which you know a lot of the work was was
done here by and by Ellis and
Cindy Boren Horton MARTIN So.
And what they can do today.
Now is they actually solve
the O.P.'s with we've you
know ten to the twelfth
number of variables.
I mean and and.
And you know maybe a thousand constraints.
They still can't solve my piece
with that size problem but but but
what they can do is they solve the LP
with all those variables then they can
extract something like twenty or
thirty thousand.
Variables and now you've got an IP
problem with twenty to thirty thousand
variables thousand constraints
that you can actually optimize and
that's what technology is today.
And the fleet assignment that deals
with you know what size of planes
used you assign to two given flights and
this is this is a very important revenue
problem in that you know if you use planes
that are too small you going to lose you.
You get spill in other words
you'll have full flights but
but you'll lose lots of passengers
perhaps two competing airline
on the other hand that
plane is next flight.
If you use a plane that's too big.
Of course you can have empty seats but
maybe you need it for the next flight.
So managing managing
the fleet is is difficult.
The the first mix image problem
again to use there actually by Delta
in the early ninety's and that was
worked on done here by name by Ellis and
Cindy and I and Roy Morrison.
And we could still only solve daily models
we couldn't expanded to a whole week but
now they are able to solve
weekly models with five to
six six thousand daily flights over
thirty five thousand flights and
you have a constraint for
each one of them manage in.
In today's models they
still have challenges and
and so for example the older models
just use the individual flights.
You know what is the demand for
this flight and then you map
the airplane size on to the flight but
the reality reality is people
don't book individual flight legs.
They book I ten or as I want to go from
A to A to see and I may need be as
an intermediary stop and so what you
really got to do is figure do this.
Fleet assignment based upon I ten or is.
And there's still lots
of challenges there.
Here's here's the problem and
I think here's what we're seeing in
all areas of application of discrete
optimization the notion of
trying to do robust planning and
recovery because of uncertainty and
of course anybody Bligh's knows that
it's a big problem in in
the airline industry and
still implementation here is just
just just really really started.
Well there has been a lot of academic
work over the last many years but
when you look at trying to
model the robustness here and
you've got you know you've
got five hundred planes.
You have five thousand
planes in the air and
any one of them could have some problems.
Think of all the.
If you try to put
a probability distribution and
on on all possible outcomes here.
You can't possibly deal with that.
OK supply chain.
Again I thought here what I do is just
mention an area that we've been working on
at tac.
Martin Salisbury we're going to I and
more recently Sokol and
other projects and
sponsored by by Exxon Mobil and
this is maritime inventory routing and
maritime inventory routing.
Is is much much heart
harder than standard routing problems
like the travelling salesman problem.
Why because here you're trying to put
together routing and inventory management.
And and and and
this creates much more complex problems.
And and and and so the oil and
gas is a huge part of this but but
but these large ships are used.
You know agriculturally to for
agricultural products like wheat and so
on and look quite a few different
kinds of ships and here you see some
an interesting slide that that shows
you how important this industry is.
And so look at maritime and and
this is the mobile split by
buy tons of product and
as you see here only it's almost a haul.
It's almost all Marathon there's
of course some overland and
you know that there's an airborne
in here you can't see it.
OK.
I mean when you get to the metric
tons it's just just just there and
what's the reason.
Let's look at the cost per ton mile.
OK And you see why why with the global
you know global globalization and so
many products going all around the world
the impact of Maritime Transportation.
These are the size of
models that that that for
example a company like Exxon Mobil
would like us to solve.
That's mix the nature programs
five hundred thousand constraints
two million variables.
They do they do all their
planning by contracts and
all these a yearly contracts and
these contracts deal with periods or days.
And so and so
it makes these models so hard.
Is that is that you centrally repeat
over three hundred sixty five days
an individual belly problem.
And you've got to you've you've
got to optimize You really
need to look at at the whole problem and
deliveries are complicated you
don't necessarily go to a place and
deliver all of your product the product
may may maybe you deliver some here it
may be in to another place and and so
these models are very complicated.
The kinds of problems that are solved now
for a large oil company again deal with
three hundred sixty five periods maybe
just five ports and fifteen ships but
even for these problems they cannot
get close to proving optimality and
these are very small compared to
the real problems like the song.
Here's an area I don't know much
about I know other people like Andy
if he's I think and he's here and
others have worked on but
I think this is the area in which
the biggest possible impact can be made
because of the size of the problem and
this is an energy management and so
the unit commitment problem solving
the economic dispatch of power.
This is the the world gross production in
two thousand and nine of terawatt hours
whatever they are but the point is here
that the total cost is something like.
Two thousand billion dollars per year.
And so
if you can get a one percent savings here.
You're looking at twenty billion dollars
And so this is why this optimization
problem I think as has the potential
bigger biggest impact of all and
still not yet
really dealt with and so the U.S.
system is operated by by something
like ten reasonal organizations and
they coordinate control and
monitor transmission why but by so.
And price is at nodes and the important
thing about electricity management makes
it different any other kind of product
management is you can't store it.
You produce it and
you use it you can't store energy.
Unlike you know almost anything
else we deal with and and
so it's got to be managed
very carefully and.
And it's done by auctions and so
it is a real time there's a real
time option for efficient dispatch.
But then you've got to plan what
you're going to produce and so
that's this is just the Bay Head model.
And and and
these are the sizes of these problems.
And before roughly two thousand.
You couldn't use in your program
to solve these problems but
now in a practical way into
programming is used to recklessly
to solve these problems on
your mystically I'm sure but.
But it's been a recent report by the U.S.
Energy Department indicates that that MIT
peer is created a savings of five hundred
million dollars annually in the U.S.
and with much greater savings possible.
I am I doing running out of time here.
Let's go.
OK.
One more or maybe two more of these and
then and we'll quit and I couldn't
do this without talking about this and
and so you know sports casually and
I'm just about energy and
Matt this really important.
Well.
The sports industry.
Here's the amount of money
spent annually sports industry.
This means television and
whenever you want three hundred billion
dollars annually in the sports industry
that's twice the amount of
the total automobile industry.
OK.
And for example seven times the amount
of the movie industry and and
and and what drives this revenue
more than anything else is T.V.
scheduling you've got all this
what they call inventory of games
which games that you do and
which times do you do them.
And so on and so forth.
Creates a huge problem.
And so let me just say a few words
about Major League Baseball in the US
together with my trick at at at
Carnegie Mellon and my former
student Kelly Easton we have a company
called The Sports scheduling group and
reduce the schedule for Major League
Baseball and we do the football and
basketball schedules for most of
the major college leagues and as well.
Baseball scheduling is about
one of the hardest problems.
I've ever worked on even
though it's deterministic.
And so
there's not an issue here of uncertainty.
But we've got thirty teams two leagues
of fifteen each usually sixteen
fourteen until recently we did a lot of
work we did about three years of work for
Major League Baseball trying to trying
to help them decide where they want
to go from sixteen fourteen
to fifteen fifteen.
And they finally did go to fifteen fifteen
and so the size of the problem is huge.
Each team plays one hundred sixty two
games over one hundred eighty days and
you've got the side who plays who
on on every day and the thing that
makes these sports scheduling problems
really different from most of the other
optimization problems that I've dealt
with is it is a ton of soft constraints.
In other words you really cannot
get the client's tour peculation
what they want they tell you they
they want everything and what they.
They want is always infeasible and it's.
It's impossible for
them to understand that and
and so you asked them to prioritize.
And they try but
then they look at a solution.
So you.
And so it really becomes almost impossible
to construct an objective function
because they look at a solution
after they prioritize and they said.
We didn't get any of this.
And you say Well that was you know
remember you put a low priority on that.
We've changed our minds and and
and so we know of no other way but
to iterate An interesting
to you know one or
both sides get exhausted be for
you can actually
say we've we have a solution that we're
ready to live with and it is it seems
to me that there's a big challenge of how
you deal of course the way we do it is.
All the soft constraints wind up
pretty much in the objective function.
And that's done with weights and
then we're constantly adjusting the
weights as we get reactions to solutions.
So the whole process warrants a picking
us about about three to six months
the pending upon and and
this is running you know just laptops.
Maybe about eight of them
pretty much steadily for for
that period of time for
the baseball schedule.
So here are some of the issues balancing
home and away games things as easily but
but but the thing that really drives
it is the television schedule and
and which makes things so complicated.
It's a feasibility problem it's
over constrained as I said.
Here's the full problem as as we try
to write it down even even you know
with our understanding of say here's
the priorities on the soft constraints.
This is the size of a problem with it
has roughly one hundred thousand binary
variables two hundred
thousand constraints and so
the only way that we know to solve it.
Now the way we do it now we sub
optimize we break it into time
periods of the first part of the season
and there's interleague play well now and
really play goes on all the time but
we have to break into some problems and
try to connect the edges of the sub
problems because they're there done over
time which is essentially again what
you do in the maritime around it.
And you know I keep
on asking myself how can we do this
with one map and I don't do that yet.
I am running out of time
I want to say something perhaps we get
evil e some time to give a talk and
she knows much more NY do about this nice
MIT way of solving problems in radiation
oncology and
in the CD I'm using using seeds but
I think I'm running out of
time I had this topic and
a little bit about about the use of energy
or programming in the finance industry but
I'll skip those and now and
ask you about that take some questions.
With the numbers you know.
Well OK.
Wow.
Yeah and end up.
I should've put up my own my
closing slides by the way I asked.
I asked Zang how guru of
Groby I said in the last year.
Is there a new area that
we haven't covered.
So for him in which you're
actually getting you know
commercial applications and
he said social networks.
So maybe that's not surprising.
I did but I didn't think of that so
much in terms of energy programming but of
course you know when you think of some of
these problems of the of privacy and
so on.
You can see where in your program would
come in the future dealing with and
certainly the large models
solving them faster.
What possibilities do we have
parallel is is is one possibility.
And so should Bill and
I have actually had a a project with
Exxon Mobil over the last two years and
in seeing what we could do with
with parallel of course the power
parlance now used already but
it's small power or
right now
that you can
get
in that country.
For that
matter that right back
here I want to argue with
you is a good article.
It was whatever I don't get your
overhaul your pact in
the broader world that
it was George.
This story that
is going general I think you know
the whole operation is research he has has
you know worried over the years you know
how do we how do we project ourselves
in terms of the general public.
Knowing that a lot of these things are due
to do things like optimization and
I think we've not done well at all but
I think this analytics
thing is starting is
stored into two to have
some some some impact and and
is likely to have some impact but
but the question is who you read and
read typically have said all or
stuff is really complicated.
Stuff not easy to explain.
We don't we don't do do very
well an example of that is
you know one code I didn't list here on
this list of either open source codes or
the commercial codes was.
You know I forgot the name of it.
Line a shrug.
The letter.
Linda Linda.
Yeah that's more than that.
And so you know when they started
their code is never their cards have
never been been very good
from a technical sense but they were
giving out their stuff free to M.B.A.
courses you know going
back thirty years ago.
And so I NEVER BE A would graduate
you got caught with M.B.A.
go to some company had
an optimization problem.
What code did you know window and so
Lindo it has very widespread
use even though it's in so
that's what you've got to you've you've
gotta make it happen right we've
got to get our students after taking our
own more courses to to go out there and
associate in their companies and
stuff but the challenge right.
These problems that you
would have while in the book on yeah but
I but I never used IP I mean this was
the start of my interest in writing.
What was your process like.
Because I really thought
Hunter That once I started working on
this at the application scope of this
technique was huge and therefore it would
have much bigger impact and if the time.
Very little was known and so
there was lots of opportunity also and.
And I peer There was tons of
things that you could think about
the try to work on right.
And so yeah that's how I get started.
With that will.
It's happening isn't it.
I mean even know.
Airline recovery is now
being done starting to
be done in this way and I think we're
starting now to achieve the speeds.
Where where we were where we are seeing.
We are seeing things that
are done in almost real time.
So I think you know I
think that will be there.
I still think how to deal with
robustness as you seem to see.
You know OK at.