Yes, at FedEx, we considered that
problem for about
three seconds before we noticed
that we also needed:
(1) A suitable, existing airport at
the hub location.
(2) Good weather at the hub location,
e.g., relatively little snow, fog,
or rain.
(3) Access to good ramp space, that
is, where to park and service the
airplanes and sort the packages.
(4) Good labor supply, e.g., for
the sort center.
(5) Relatively low cost of living
to keep down prices.
(6) Friendly regulatory environment.
(7) Candidate airport not too busy,
e.g., don't want arriving planes
to have to circle a long time
before being able to land.
(8) Airport with relatively little
in cross winds and with more than
one runway to pick from in case
of winds.
(9) Runway altitude not too high,
e.g., not high enough to restrict
maximum total gross take off weight,
e.g., rule out Denver.
(10) No tall obstacles, e.g.,
mountains, near the ends of the
runways.
(11) Good supplies of jet fuel.
(12) Good access to roads for
18 wheel trucks for exchange
of packages between trucks
and planes, e.g., so that some
parts could be trucked to the
hub and stored there and
shipped directly via the planes
to customers that place
orders, say, as late as 11 PM
for delivery before 10 AM.
So, there were about three candidate
locations, Memphis and, as I recall, Cincinnati
and Kansas City.
The Memphis airport had some old
WWII hangers next to the
runway that FedEx could use
for the sort center, aircraft
maintenance, and HQ
office space. Deal done --
it was Memphis.
That's how the decision
was really made.
Uh, I was there at the time,
wrote the first software
for scheduling the fleet,
had my office next to that
of founder, COB, CEO F. Smith.
Great reply with interesting details. However to be fair to the author, I don't think he was passing off his mathematics as a realistic business decision matrix. In the The College Mathematics Journal[1], a lot of presentations are of the "assume a spherical cow" type of stuff. It's presenting scenarios for education exploration that are more complicated/interesting than highschool algebra of "two trains leave the station, when do they meet?". That's why the paper's scope is limited to a Euclid geometry exercise.
To model the extra factors you listed, it is a complex multi-constraint optimization NP problem and I suspect the author probably knows that. He just didn't put that disclaimer explicitly because he didn't anticipate that the non-journal audience (e.g. savvy HN readers) would pick it apart.
In the same spirit, the Levenshtein distance can be studied for simple spell checking algorithms. Even though we know the more sophisticated ones can utilize machine learning with massive datasets, we can still explore Levenshtein for teaching purposes.
There is a lot of fun to be had considering the cases for passenger airlines in the US, since the large traditional hub-and-spoke airlines all maintain multiple hubs (in fact, following the most recent round of merger consolidation, each of the big three US airlines has at least seven hubs in the country).
That's a multi-way tradeoff between local population and desirability as a destination (to ensure plenty of profit-making opportunities on direct flights); proximity to other important destinations (to offer short connections to non-hub cities); coastal or northern locations (good for trans-oceanic or long great-circle routes); climate (to ensure your hub doesn't get frequently shut down by adverse weather); congestion (to ensure your hub isn't frequently delayed by the sheer amount of traffic to coordinate); airport layout (to give you maximum efficiency for lots of flights); etc., etc.
When people wonder, for example, why Atlanta is consistently the busiest or second-busiest airport despite not being an obvious first-tier American city (those being New York, Chicago and Los Angeles), the weather, the congestion and the airport layout are huge factors. Atlanta doesn't get a ton of snow or severe thunderstorms like the northeast or upper midwest, it isn't in an overloaded air corridor like the northeast, and the airport's runway and taxiway configuration allow multiple simultaneous takeoffs and landings with much more ease than someplace like O'Hare (which is basically beyond capacity at this point with its configuration).
> a complex multi-constraint optimization
NP problem
There was a day when I thought that!
So, I was thinking non-linear optimization
with, say, some of gradients, steepest
descent, conjugate gradients,
quasi-Newton, Kuhn-Tucker conditions,
maybe some Lagrangian relaxation, etc. and
saw no hope.
And I still remember the day when I got an
explanation and learned better! Can make
the problem 0-1 integer linear programming
but otherwise linear. The
non-linearities, really complicated costs,
say, have a plane step climb when have a
heavy cargo load, and really goofy
constraints, e.g., don't fly over any US
military bases or the White House, don't
fly over residential areas at dinner time,
etc., can handle in a simple way before
the optimization itself.
The technique has some generality and,
thus, is a good tool to have in a 'data
science' tool kit, especially with current
computer hardware, library software, and
practical data availability.
Here's an outline of the technique: For
one period from, say, 5 PM to midnight
(again from 1 AM to, say, 8 AM) set up a
table with one row for each city to be
served, 90 cities, and one column for each
candidate airplane trip, tour, from
Memphis and back.
In this table, for each city and column
put a 1 in the table for that city and
column if the tour for that column serves
that city and put a 0 otherwise. So,
generate all such columns; may have some
thousands of columns.
Considering all fine cost details want to
account for, and taking expectations for
random costs, say, from weather and air
traffic control, find for each of the
candidate tours its cost (first cut,
assume that if a plane goes to a city,
then it completely serves that city).
Then for the schedule, want to pick no
more than 33 columns (there were 33 planes
in the fleet) from the 1000s so that all
90 cities are served and total cost is
minimized.
So, each column serves, covers, some
cities (each city where the column has a
1), and want to pick columns that cover
all 90 cities -- so have a set covering
problem. Right, it's in NP-complete.
So, in particular, we have a linear
programming problem: We have one variable
for each column. The costs and those
variables form the linear function of the
variables to be minimized. The constraint
matrix is just that table we described.
The constraints are that each city is
served by some one column.
Or in matrix algebra, we have from the
table described above a matrix A with 90
rows and some thousands, say, m, columns.
We have the variables x, m x 1. We have
the m costs, 1 x m c. And we have the
right hand side, 90 x 1 b where each
component of b is 1. Then we want to find
x to minimize cx subject to Ax = b. So,
it's linear programming.
Then in addition we ask that the variables
take on values of only 0 or 1 -- so we
have a 0-1 integer linear programming
problem.
If ignore the 0-1 constraint, then have a
fairly routine linear programming problem
but will likely end up with some
fractional tours allocated.
For honoring the 0-1 constraints, on this
problem likely could do well enough with
branch and bound.
As FedEx grew, the nature of the
scheduling problem changed. The outline
above should have helped save significant
bucks at least in the early years.
Then, of course, that solution technique
could be used to evaluate the few
candidate hub locations.
With some generalization, the solution
technique could also be used to evaluate
airplane types to add to the fleet.
So, here we have 0-1 integer linear
programming set covering; keep it in mind
and see if you can find another good
application.
Thanks for mentioning Gurobi. I
just looked them up! So, they
are headed up by Bixby! Terrific!
After IBM bought ILOG and C-PLEX,
I assumed that Bixby would retire.
Apparently, nope!
Also Bixby has two students from
Georgia Tech so, likely from
George Nemhauser and Ellis
Johnson.
George is the person who explained
0-1 integer linear set covering to
me. That same day he gave me
three words of advice that became
the direction for my Ph.D. dissertation
(in stochastic optimal control)
at Johns Hopkins. I knew Ellis
when we were both at IBM's
Watson lab.
What you mentioned looks like
something quite common for
linear programming software.
E.g., think linear programming
tableaux and appending a new
constraint with its own, new
artificial variable. Then do
elementary row operations to zero
out the row of the new constraint
in the columns of the old basic
variables. Then do elementary row
operations to zero out the new
artificial column in all rows except
the row of the new constraint.
Then do simplex algorithm pivots
to get the new artificial
variable out of the basis.
Changing costs is also easy and
standard in convenient little operations
called post-optimality.
There are more details, but covering
all of those would need much of a
course in linear programming.
E.g., the IBM Optimization Subroutine
Library (OSL) is quite nice work,
likely heavily from Ellis Johnson
when he was still at IBM before he
went to Georgia Tech where George
Nemhauser has long been and does
what you mentioned.
Once I
wrote some 0-1 integer linear programming
software with some Lagrangian relaxation
based on the OSL -- it was nice.
From Bixby, the guy that did C-PLEX,
and two Georgia Tech students,
etc., I would expect more than the usual
or just the OSL! I'd guess that they have
some good results in integer programming,
numerical stability, much larger problems,
exploitation of multi-core processors,
and more.
I read one comment asking if you've considered a book; I've since been reading your comment history which is the next best thing. I'm convinced that A) I want to read that book, B) you don't need a cofounder, C) you could use a co-author. Your book would live on the long tail, yes, but so do these HN comments and at least the book wouldn't have the same limited shelf life. I hope you consider it: perhaps while vacationing after your startup makes you sufficiently wealthy.
I enjoyed all the mentions of weather, as Paul T. at the Memphis GOCC is someone I've had the pleasure of talking to about some of those issues.
I'm the co-founder of a company whose mission is to synchronize climate and commerce. Would love to find out what you're doing these days as you are clearly a SME (almost beyond belief) and I'm guessing I could learn a lot from you.
What do you mean by SME? A quick search didn't help, unless you meant "Small to Medium Enterprise", which I wouldn't quite understand either. My own guess would be "Single Man Enterprise", but please tell us.
When was it clear internally that FedEx was going to be one of the most significant companies of the century? (I'm trying to calibrate how much visibility insiders have into this, vs the public)
When? That was the intention from the
beginning. The first goal was to serve
90 US cities. Broadly there was nothing
seriously wrong with the plan. The idea,
now common in the VC community, that can't
plan such things accurately enough is
absurd.
Once virality started to take hold and
the package volume grew, standing in the
sorting center was an enthralling
experience: The astounding, mind-bending
variety of what the US economy wanted to
ship with high priority was beyond
comprehension and belief. Early on, time
critical legal papers? Sure, there were
plenty of those. Okay.
A cubic foot of some specific small metal
fasteners a big production line needed
ASAP or shut down at some cost of
thousands of dollars an hour. Fine.
But bricks? Yup: A brick oven could send
some samples to an architect, or an
architect could send the samples to a
customer.
Spare parts for computers, etc.? Yup.
But baby chicks? Yup. Medical samples on
the way to a medical testing lab? Yup. A
live baby bear? It happened.
The variety was beyond all belief and
comprehension.
No question about the need, definitely a
must have -- a large fraction of the
customers would have paid nearly anything,
often beyond all reason.
It's so inspiring hearing about people who had unbelievable expectations from the very beginning. I always hear about the opposite – younger Zuckerberg expecting someone bigger like Microsoft/Google/etc to build the "real Facebook" [1], Larry and Sergey thinking they'd never make it to be as big as Shawn Fanning [2], etc.
Those are all extremely interesting, but I'm much more interested in what goes on with people who call it from the beginning. I'd love it if you wrote a book. Do you have a blog?
i can't remember if we used fedex or ups but the most expensive shipping i've purchased was the result of an oversight. booth equipment, about 200 pounds, overnight from LA to denver in order to make a trade show. cost us nearly 2 grand but the cost of not shipping would have been much greater!
graycat: I have spent an amusing half hour reading your back-posts. Many others are suggesting that you write your memoirs. I'm suggesting a possible format: a professional biography told through the formulas and theorems you have used.
Compare with Primo Levi's The Periodic Table. Levi was a chemist and senior manager with a large chemical company who also wrote novels and essays - now known mainly as a writer. His autobiography takes the form of a series of chapters each with the title of an element. Each chapter tells a story that is somehow related to the properties of the element chosen for the title. Levi lived in dire and dangerous times, I think your times were incomparably better but will still provide lessons for those who come later.
My suggestion is a professional biography with each chapter based around a theorem or algorithm that you have used to advantage. A brief exploration of the theorem pitched at undergraduate level (perhaps the explanations could be crowd sourced from many here) coupled with one of your anecdotes. A self-published ebook of this would prove popular I think.
What I've posted to HN in this thread
and otherwise is about the best I
can do for now.
For the history of FedEx, there are several books
already. Roger Frock wrote one.
I've seen none of them, but some
friends found me mentioned in
one of them. I was also mentioned,
with some errors,
in an article in Informs,
the popular magazine on
operations research
and management science.
No time to retire yet!
If I get rich, then I will have several
projects to consider. Sure,
several projects
of the kind *what I wish I'd known
when I was 8, 10, 12, 14, 18,
22, 30, 40" are candidates.
Your experience sounds like you would be an interesting fit for a senior network optimization role at Uber. If you have any interest, drop me a line jmn@uber.com
I am guessing the scheduling has become significantly more complex as the company has grown. The conveyor system in the Memphis facility alone looks to be an interesting problem. Is there stuff you want to have, but just don't have the time to do it?
For the conveyor, and the work from
the time the planes arrived at the hub until they
left, was an issue. We had a guy,
Mike Basch, Senior VP Planning,
from Rapistan, big in conveyor systems.
I got involved for a while: I tried to
do a continuous time, discrete
state space Monte Carlo simulation,
but it got too big to do at all
easily and we dropped it.
So, the hub design was done with just
back of the envelope arithmetic
and engineering. It worked fine
for years.
Over the years, the fleet
scheduling problem went through
various phases.
The first phase that worked
at all well was just my
software.
The last time
I checked (I'd left for my Ph.D.),
the package volume was high
enough that
one of Fred's ideas became the
solution: At noon, have all the
planes at distant cities.
Then, in the evening, loaded up,
all the planes fly to Memphis.
Nearly all the flights are
non-stop -- one plane, one flight,
one city served. So, net, first
cut, no scheduling problem at all.
Maybe there could still be problems
for scheduling maintenance,
considerations for remote sort
hubs and/or international service,
but that was all after I left.
You mean the time FedEx towed
one of its airplanes to the other
side of a hanger to keep it out
of sight of a sheriff with a
lock and a chain sent to
lock down the airplane as
collateral for unpaid fuel bills?
You mean when some angry union
people showed up objecting to
FedEx pilots handling packages?
You mean the time two barrels of
liquids in the shop got confused
and maybe some bad stuff got
pumped by mistake into the
hydraulic systems of some
unknown number of airplanes?
The time I used the differential
equation
y'(t) = k y(t) ( b - y(t) )
to please our two representatives
of Board Member General Dynamics,
have them unpack their bags and
stay after all, and, thus, saved
the company?
The time after midnight
in my office I was practicing
violin and, as I left, noticed
that Fred, in the next office,
had been working late?
The time at a top employee basketball
game, in the locker room
with Fred I asked him if
he would do it again and
got his answer, a
more colorful version of
investors don't like risk.
The time Fred, in the Dassault DA-20
Fanjet Falcon he saved
as the company executive jet,
was flying, kept finding
airports closed, kept flying,
and finally landed but
flamed out from no fuel on the runway --
cutting it close.
How the planning had said that
we could fly the airplanes
half full and print money
but actually flew the airplanes
packed solid, doubled the rates,
and still were losing money --
not good planning.
How Fred wanted to have containers
to fit the inside of the plane,
like regarding the inside of the
cargo part of the
plane as a big sausage and
cutting it into a few identical
slices. Then have ball rollers on
the floor of the plane
for moving the containers.
Then to move the containers
on/off the plane, have a truck
with a platform in front,
about the right size for one container,
able to be raised and lowered
with hydraulics, drive up,
next to the opening for the
cargo door, and on/off the
containers.
Well, Fred
described all this on the phone
to a guy in CA who got a
truck chassis, did the welding
and hydraulics,
and drove the thing, chassis, no body,
to Memphis.
Actually, at least as a prototype,
it was okay. And the basic
idea was important in production.
Still, that the thing had been
designed in a phone conversation
upset some on the Board.
There were a lot of such war stories.
But, in total the experience
was a good lesson in
doing a startup.
You mean the time FedEx towed one of its airplanes to the other side of a hanger to keep it out of sight of a sheriff with a lock and a chain sent to lock down the airplane as collateral for unpaid fuel bills?
Apocryphally, this is similar to the reason alleged for American Airlines not offering service to Israel.
When TWA went into bankruptcy, it simply abruptly terminated employees at outstations. The former employees in Israel went to court, alleged the proper severance procedures had not been followed, and won, getting a pretty significant award from the court. But since TWA was no longer flying there (or anywhere), they had no way to collect on that judgment.
The remnants of TWA were acquired out of bankruptcy by AA, and allegedly Israeli courts have held that AA thus inherited TWA's obligation to the former employees, but AA has not paid it off. Thus, the implicit threat is that any AA aircraft which lands in Israel is subject to seizure either as collateral or to simply be sold to pay the judgment.
At the moment US Airways flies PHL-TLV, but it remains to be seen whether that route will survive the final stages of their merger with AA.
My cousin flew for FedEx for many years. He lived in southern California but was "based" in Memphis so he had to commute to work (jumpseat).
One thing he said was pilots enjoyed flying freight as they were able to takeoff, land, and generally maneuver much more aggressively than they could to with passengers.
My first work for FedEx, writing
the software to schedule the fleet,
I did from our living room in Maryland.
My wife was in her Ph.D. program
at Johns Hopkins in Baltimore.
To write the code,
I had a time sharing terminal and
wrote the code in PL/I on a CP67/CMS
system in Stamford, CT. Nice setup.
I really liked the data structures
and string manipulations in PL/I.
And, yes,
for the great circle calculation, that's
just the law of cosines for spherical
triangles!
Well, for writing the code,
I wanted the basic PL/I manuals
so called the local IBM office to order
them. Soon the manuals came, hand delivered,
complete
with a very interested and attentive
IBM marketing representative! I'm
not sure we ever paid for the manuals!
So, sure, sitting there in our living room,
I explained to the IBM guy what I was
doing. So, sure, he and his branch
office had guessed that anyone who wanted
PL/I manuals was likely up to something
significant and, thus, might also want
a few million bucks worth of hardware, too.
Their guess was correct: Eventually FedEx
did go with IBM (there's a story there, too).
When I got the software written, in six weeks,
also finishing teaching computer science
at Georgetown U., I drove to Memphis and
rented a room.
But I wanted to get home as often as possible.
So, since my work had to do with airplane
operations, FedEx talked the FAA into
letting me ride jump seat as an observer.
It was just I did all my observing
commuting to/from home in Maryland!
Yes, the pilots sometimes flew
somewhat less gracefully than they
would have with a passenger plane.
A lot of the pilots were fresh
from Viet Nam, maybe as fighter
pilots. The pilots were the most
competent, serious, effective,
and professional part of FedEx.
So, one time when I was observing
the pilots for some
reason on the way to landing
wanted to descend quickly.
So, they went down at 6000 feet
per minute. Going down that fast,
in the little jump seat
I was hanging by my seat belt!
Going down that fast also had the
outside of the
plane, still cold from cruise
altitude, suddenly in much warmer and
very humid air. So, we got
a layer of ice over the
front windows and could see nothing.
The pilots
were not concerned at all but
just flew via instruments.
As an engineer, programmer, and human being I would be thrilled to hear these sorts of war stories. If you've a book or lecture series, I'm all ears (err, eyes, as the case goes). This is a great, fascinating look - thanks for continuing to weigh in!
(And, incidentally, cruel to just skim over this stuff; some of this is Surely You're Joking Mr. Feynman material :)
Agree with the aside: if you want more detail view his comment history and you'll see at least some of these stories spelled out in more detail—though still less detail than I want.
As others have said, please write a book if you have the time and interest. This stuff is so fascinating and an amazing way to learn how businesses are really built from the inside.
But actually FedEx (Federal Express)
was started in Little Rock. Fred
had bought Little Rock Airmotive,
a corporate aircraft interior decorating,
customizing,
repair, and lube and tune shop.
He dreamed of FedEx, and in a back room
got a Dassault DA-20 Fanjet Falcon,
popular executive jet, 28,660 pound
max take off weight, two GE aft-fan
turbo jet engines (originally designed
for drones; used in the F-5; but with
an aft-fan), a relatively rugged
airplane, e.g., no frame fatigue life,
worked on the modifications
to make it into a suitable cargo
plane, rewrote the official flight
manual for the modifications, and
got the FAA to approve the modifications
and issue the appropriate certificate.
FedEx rushed to 33 such Fanjet Falcons;
that was the initial plan for the
full fleet, serving 90 US cities.
The fleet schedule I did
with my software and Roger Frock
one night was for the 33 and 90.
That schedule overcame some Board
objections that were blocking
some crucial equity funding,
pleased the Board, "Solved the
most important problem facing
the start of Federal Express"
(Fred, at a senior staff meeting),
enabled the funding, and saved the
company.
When I joined, the company was still in
Little Rock.
Yes, the fact that Fred knew Memphis
well was likely also relevant. But fully
likely FedEx would have been in Little
Rock if it had had a suitable airport.
There were some concerns about the
Ohio valley: The whole place could
get socked in with fog, quickly,
nearly unpredictably.
For the hub location,
I observed the decision making;
the description I gave here is
accurate enough;
my criticism that the site selection
was not just a geometry problem
is fully correct; but I was not
involved in the decision itself.
Can you verify what I was told in business school in the late 70's (Wharton). I remember reading a case study that said that Smith was considering flying passengers on the deadhead by installing seats between freight runs. Was there any discussion of that?
When I was there, there wasn't much of a
'deadhead' problem, and I doubt that there
ever has been:
Or it's roughly 8 PM in Seattle, SF, LA,
Denver, Chicago, Cleveland, NYC, DC,
Atlanta, Miami, etc., and the planes are
all at such cities. Packages from those
cities are loaded, and the planes fly to
Memphis, getting there ballpark at
midnight. The packages are sorted and the
planes loaded. The planes fly back to the
cities and get there ballpark 6 AM or so.
So, so far no deadhead flights.
Well, might have a lot of lower priority
packages didn't move from the origin
cities, so load those on, fly to Memphis,
sort near noon, load the sorted packages,
and fly back to the remote cities. Still
no deadhead flights.
At times, for some extra revenue, FedEx
did some airmail flights for the USPS
and/or some cargo charter flights, and,
then, sure, there could be some deadhead
flights, but such flights were so rare and
unpredictable that getting human
passengers would not have been promising.
FedEx tried off-peak passenger carriage in the early 1980s when they received their first 737s. The seats were on pallets installed through the cargo doors.
UPS tried the same idea with 727s in the early 2000s but in both cases it proved too disruptive to normal operations.
However several European airlines today operate the inverse service with quick-changers, primarily passenger service and remove the seats at night for mail carriage.
It's also a great example of how a well-trained human brain can take in a large amount of information, crunch it together, and spit out a solution that closely approximates a detailed analysis, all in a few seconds.
That kind of clarity and intuition is what drives so much technical decision making, because you rarely have the time and information you would want to make a decision.
I agree completely with it resonating. I saw it less as get shit done and more of just a perfect example of how things work in the real world. The model mentioned in the article is great, but it means shit when you bring it into the real world and find a huge list of problems like graycat mentioned.
As others mentioned, such a great comment. Thanks for sharing graycat.
I did after once flying out of Denver, and the luggage had to be removed because the airplane was overweight for the altitude and air temperature.
Next time you're flying out of Denver, notice how long the takeoff roll is. When my father flew jets out of Denver, he'd hang the tailpipe over the back edge of the runway so he'd have every last foot of runway to get airborne.
The difference in Denver is so significant that United actually swapped all the Houston-based 737s that came over from Continental in the merger with the Denver-based A320s from United. The 737 base moved to Denver and the A320 base moved to Houston.
The 737 has better performance with high-altitude takeoffs.
Checked luggage is weighed when you drop it off, so presumably the exact weights are available to the pilots. For passengers themselves and their carry-on baggage, accurate weights aren't available so statistical averages are used, based on the number of passengers and their baggage allowances.
Airliners do have "squat sensors" in the landing gear, but they're not capable of accurately measuring the aircraft's weight. They're just binary-valued sensors that check whether the gear struts are under stress, to prevent the gear from accidentally being raised while the plane is on the ground.
I wonder if gluing strain gauges to the landing gear struts would be accurate enough once calibrated.
There has been at least one crash due to mis-estimating the weight of the passengers + luggage + cargo. A strain gauge on the struts, even if inaccurate, could provide a backup sanity check for the weights.
As I joined FedEx, I was told that
they had already worked out sensors,
of some kind (I never saw details),
on the landing gear that would give
the data needed for knowing and
controlling
weight and balance.
For balance, right, e.g., don't want all the
weight near the tail and, instead, want
the weight more evenly distributed
in the cargo area along the length of
the plane, that is, want the
load in balance.
So, yes, FedEx did think of having
sensors, of some kind, in the
landing gear.
But I never heard more about
such sensors, and, for the times I
rode the jump seat in the planes,
I never saw pilots working
with weight and balance from
data from the landing gear.
Maybe later, after I went to
grad school, FedEx did do something
with such sensors.
So, right, the sensors are a good idea
and were considered and, maybe, eventually
implemented.
They could put something in the ground - a weigh station - that the plane travels over before getting to the runway. That avoids the need for modifying airside equipment which is a bureaucratic nightmare.
I don't know what happens in the USA, but in Australia each piece of luggage is weighed before it can be checked in. For various reasons: heavy bags (over ~20kg) must have warning labels attached, very heavy bags (over 32kg) are disallowed with no exceptions, and it means a total can be provided to the pilot.
Significant. I'd have to go upstairs,
find the right box, get out the flight
manual (Fred had a guy send me while I was
doing my Ph.D.), and learn how to use it
again to answer.
But, yes, hot air at high altitude hurts
jet engine thrust, a LOT.
I believe that pilots refer to this as density altitude. It factors greatly into allowable takeoff weight, takeoff distance and ability to climb over obstacles in the takeoff path. Pilots are or should be very aware of the density altitude on very hot days especially at high altitude.
There's a leg connecting Tokyo and Mexico City. The Tokyo flight goes direct to Mexico City however the Mexico City flight stops in Hermasillo on the way to Tokyo.
Due to the higher altitude of Mexico City, it takes more fuel to get off the ground and requires a pit stop in hermasillo to get all the way to Tokyo.
Disclaimer I'm only partially sure that I'm remembering the whole story correctly.
Every couple of years, there'll be a day or two in summer when temperatures at the airport in Phoenix get above the maximum takeoff temperature for a lot of the smaller regional jets, and chaos ensues as all those flights (it's a US Airways hub) delay or cancel.
My offer (from Art Bass, then head of
Flight Operations in part because he was,
as the FAA required, a pilot) and offer
letter said that (A) there would be a
stock plan, (B) I would be part of the
stock plan, (C) the plan would be based on
salary in which case I would be quite high
up, (D) the Board was considering the
stock plan now and results were expected
in two weeks, (E) if the plan were not
equitable then the first plane out of
Memphis would be full of ex-Federal
Express employees.
With that, I joined, kept teaching my
courses in computer science at Georgetown
until the courses were over, at home got a
time sharing terminal, a CP67/CMS account,
etc., and dug into writing the software to
schedule the fleet.
Some Board Members, including one with a
lot of experience at American Airlines,
doubted there could be a schedule. So,
the Board wanted to see a schedule, say,
for the full, planned fleet of 33 planes
serving the full, planned list of 90 US
cities. Some crucial funding, some
equity, some loans on the planes, were
being held up waiting for the schedule.
The company was at risk.
I wrote the software, finished my
teaching, drove to Memphis, and rented a
room.
So, with the Board having doubts and the
company at risk, one evening Roger Frock
and I used my software to develop a
schedule for the 33 planes and 90 cities.
We printed out the schedule, had copies
made, and handed them around.
Board Member General Dynamics had sent two
representatives, one an aeronautical
engineer and one a finance guy, to
provide, say, adult supervision; those
two guys went over the schedule fairly
carefully and announced "It's a little
tight in a few places but it's flyable"
(pretty good from just a little fast work
from Roger and I); CEO Fred Smith's
reaction at the next senior staff meeting
was "Amazing document. Solves the most
important problem facing the start of
Federal Express.". The funding was
enabled. FedEx was saved. Pretty good
from typing in 6000 lines of PL/I in six
weeks while also teaching two courses!
PL/I is a nice language -- good on data
types, data manipulations, data
conversions, data structures, scope of
names, exceptional condition handling,
storage management, debugging, etc. E.g.,
its Based structures, can serve as a
poor-man's classes in object oriented
programming.
Later the Board wanted to see some revenue
projections. I didn't want to get
involved, but no one had more than wishes,
hopes, dreams, intentions, etc. So, I
started with the common high school
question, what do we know? Well, we knew
the present revenue or, if you will,
number of packages per day. From our
initial long term planning, we knew what
revenue we expected with 33 full airplanes
serving 90 US cities. So, in some at
least a somewhat meaningful sense the
desired projections were an
interpolation between those two facts we
did know.
Then the question was, how will the
interpolation go? Well, why will the
revenue grow? Sure: The revenue will
grow as it has been so far, customers to
be hearing about FedEx from current happy
FedEx customers. E.g., maybe a customer
to be gets a package via FedEx. So, we're
talking word of mouth advertising or
viral growth.
So, the rate of growth in revenue per day
or packages per day should be directly
proportional to (A) the number of current
customers and (B) the number of customers
to be. That is, the rate of growth should
be proportional to both (A) and (B), that
is, to their product.
So, all downhill from there: At time t,
let y(t) be the revenue, say, per day, at
time t. Let t = 0 correspond to the
present. So, we know y(0). Let b be the
revenue per day with a full system, that
is, 33 full airplanes and 90 US cities.
That is, we know both y(t) and b.
So, from freshman calculus, the rate of
growth is the first derivative of y(t),
that is, d/dt y(t) = y'(t). So, from the
proportionality, we have that there must
exist some constant k so that
y'(t) = k y(t) ( b - y(t) )
So, we have an initial value problem (we
know y(0)) for a first order, linear
ordinary differential equation.
Okay, how to get a solution? Easy, just
need freshman calculus, not even a course
in differential equations. And, yes,
there is a closed form solution, right,
with some exponentials.
Right, the solution is the famous
logistics curve sometimes seen as doing
well tracking, say, the growth of TV set
ownership in the early years of TV. So,
my derivation, as just above, can be seen
as an axiomatic derivation (maybe
rediscovery, maybe original) of the
logistic curve. The solution may remain
an okay, first-cut approach to
understanding viral growth.
So, I showed my work to Senior Vice
President Mike Basch, likely the one most
responsible for getting the projections
for the Board, and he liked my work. So,
on a Friday afternoon we picked several
candidate values for the constant k and
drew the corresponding graphs of the
revenue projections. We used my HP
calculator, reverse Polish notation, stack
machine, etc. -- HP should run an ad! We
picked a value of k that gave what seemed
to be reasonable projections and declared
the problem solved.
The HP? It's still in my center desk
drawer. Checking, right, it's an HP-35.
My wife and I paid $400 for it.
The next day, a Saturday, at about noon, I
was in my office likely working on fleet
scheduling and got a call from Roger Frock
asking if I knew anything about the
revenue projections. Saying I did, he
asked if I could come over to the HQ and
explain.
So, I got into my Camaro hot rod (396 big
block, etc.), and drove over. Yes, I
brought my HP-35.
As I arrived, at one of the old WWII
wooden hanger buildings, people were
standing around and not happy. Our two
guys from General Dynamics were standing
in the hall with their bags packed and not
happy.
Roger led me to a table with the graph,
picked a point in time, and asked me to
calculate the value on the graph. So,
with my HP-35, I punched the buttons,
stopped, slowed down, cleared the HP-35,
started again, slowly and carefully
punched the buttons again, and got the
value on the graph. I did that for
several points for the graph, and then
everyone started to get happy.
It turned out that the Board meeting had
been that morning; Mike Basch was
traveling; I'd not been invited to the
Board meeting; the graph had been
presented; the two guys from General
Dynamics (GD) had asked how the graph had
been calculated; and everyone else at the
meeting dug in trying to answer. They
worked for hours with no results. Finally
the two guys from GD lost patience with
FedEx, returned to their rented rooms,
packed their bags, got plane reservations
back to Texas, and as a last chance
returned, with their packed bags, to the
FedEx HQ to see if anyone could explain
the projections.
Somehow Roger Frock had guessed that I'd
done the projections, called me, and got
me to the Board meeting just in time.
It was close, but I'd saved FedEx a second
time.
Right: Some people in FedEx would rather
have seen FedEx go under than invite me to
the Board meeting. We're talking some
severe cases of jealousy, bureaucratic
infighting, attacking the guy down the
hall instead of the competition outside of
the building, goal subordination as in
organizational behavior, etc., right?
Bummer.
Right: Apparently I was the only person
at FedEx who still understood freshman
calculus. Gads. And I never even took
freshman calculus, taught it to myself
from a book, and started with sophomore
calculus.
I never got any thanks for saving the
company the second time.
I'd been at FedEx for over a year. I had
been commuting every few weeks home to
Maryland for a few days at a time -- not
good. There had been no more about the
stock that had been supposed to come in
"two weeks". The company had some
problems, e.g., had nearly gone out of
business due to not inviting me to the
Board meeting. Also the basic planning
was way off -- the planning said that we
could fly the planes around half full and
nearly print money, but we were flying the
planes packed solid, had doubled the
rates, and still were losing money --
bummer.
So that I could be a good bread winner in
my marriage and for our kids if we could
have some, as we hoped, I wanted something
valuable no one could take away from me, a
Ph.D. for my career and/or stock.
So, I'd gotten accepted for an appropriate
Ph.D. at Brown (Division of Applied
Mathematics), Cornell, Princeton, and
Johns Hopkins.
The oil crisis hit. Saving money,
especially on jet fuel, became a biggie.
So, I was working on that. I was getting
a lot of flack from others, especially my
manager.
Finally I called a meeting to explain what
I was working on, three projects. My
manager said I couldn't do that because he
was busy and couldn't come. I told him,
fine, then don't come.
He came. So did Fred, Roger Frock, Art
Bass, the top 15 or so people in FedEx.
My manager was sitting next to Fred and
kept objecting to what I was saying until
Fred told him to cool it.
One of my problems was to use
deterministic optimal control theory to
say how to climb, cruise, and descend the
planes.
A second problem was to use 0-1 integer
linear programming set covering to develop
schedules that would save on OpEx and
maybe also CapEx.
A third problem was how to buy fuel during
a trip from Memphis and back. So, broadly
the idea was to buy extra fuel where it
was cheap and carry it to the next stop or
two where fuel was more expensive. We
were getting fuel for $0.16 a gallon in
Memphis but paying up to $0.55 cents a
gallon (in Nashville). So, that's a case
of what has long been known as fuel
tankering. But doing that interacts with
how to climb, cruise, and descend the
airplane, not being late in the schedule,
loads, weather, air traffic control, etc.
And typically a lot of the cheap fuel gets
burned off just from trying to carry it,
and how much gets burned off has a lot to
do with the flight plan. And any such
decision to buy extra fuel is a bet on
the future of the trip back to Memphis,
that is, a bet against the random
package loads, weather, air traffic, etc.
So, how the heck to solve that? And, for
various reasons, couldn't get a solution
from carrying a computer on the plane and,
really, not even from using a computer on
the ground after landing. I'd found a
way!
So, Fred put me under Senior VP of
Planning Mike Basch and, thus, made me
Director of Operations Research.
But the fall came, and I had to decide
actually to leave for graduate school or
not. With no stock, not a lot of thanks,
with a lot of scars from being attacked,
still away from my wife, the company still
at risk, I decided to go to graduate
school. I liked FedEx, the challenges,
the work, etc., but making the
stockholders rich, with me not one of the
stockholders, while wrecking my marriage
and passing up the chance for a Ph.D. that
might help my career and that no one could
take away from me looked not good. If I
couldn't get stock with the company still
at risk and worked to make the company
valuable, then what hope would I have of
getting stock in the company I'd helped
make valuable before getting any stock?
I went home to Maryland. At the last
moment, Fred wanted me back in Memphis.
He and I met with Mike Basch, and Fred
said, "You know, if you stay, then you are
in line for $500,000 in Federal Express
stock?". Heck no; I didn't "know" any
such thing; I had had and accepted such
promises before, "two weeks", and after 18
months, saving the company twice, and with
three projects to do much more for the
company, all there was were more such
promises, not on paper that a lawyer could
do something with, no thanks -- "Fool me
once, shame on you. Fool me twice, shame
on me.".
Sure, that $500,000 would be ballpark $50
million to $500 million today. And
apparently some people did get some stock.
But there that last day, Fred still was
just not putting it down on paper.
Since then I ran all this past a lawyer
who concluded, "Legally FedEx owes you
nothing. Morally they owe you
everything.".
So, here on HN, maybe I definitely should
tell this story as I have so that others
can benefit so that more promises of stock
can become ownership of stock.
Of course, there is a lot more to getting
wealthy from stock in a startup than what
I've outlined here.
Broad Lesson: The broad lesson for people
in startups with promises of stock, become
very well informed and be very careful.
My reaction: Do my own startup. Doing
it. Need to get back to it. It'd be fun
to make more money than Fred! I have a
shot! Back to it!
I'm in love /w this post! Not only is it informative but it clearly expresses the differences between decision making in real-world scenarios and delving deep into the data for an 'on-paper' optimal decision.
Optimization, e.g., from
operations research can
at times make a good contribution,
but such work is not always easy, and
typically the first challenging
step is problem formulation
where address considerations such
as I listed.
Indeed, at one point I was starting
to address the fleet scheduling
problem with integer linear programming
set covering, talking with
G. Nemhauser, now at Georgia Tech,
then at Cornell, etc. With
current software and computers,
what I was trying to do, for just
the 33 Falcon airplanes and 90 US
cities, should be nicely easy to do.
Another problem, though, could
be the mix of aircraft types:
Early on FAA and CAB rules boiled
down to the Dassault DA-20 Fanjet
Falcon with Fred's cargo modifications.
Why? Because, e.g., wanting to be
able to operate both airplanes and trucks,
FedEx was flying
as an unscheduled air-taxi,
maybe intended for little Mom and Pop
operations, but then could
not fly planes with max gross
takeoff weight (GTOW) over 25,000 pounds.
Fred went to Congress and got his
28,660 GTOW approved as an exception.
Later Alfred Kahn deregulated
airfreight and, thus, let
FedEx fly nearly anything
they wanted. At that point,
there would be an issue of
what mix of airplanes?
But that was after I had
gone for my Ph.D.
graycat, my dad was one of those first pilots. Thanks for posting about this; makes me nostalgic. (Did you have stacks and stacks of those styrofoam punch-out planes around the house, too?)
Since the New Madrid fault hasn't had a major quake since 1812 (or arguable 1895) and other places have quakes far more frequently (e.g. California) I imagine the risk would be considered lower than a lot of other places in the country.
According to Wikipedia, seismic monitoring in the area wasn't installed until 1974, so at the time of FedEx's creation in 1971 it probably wasn't on their radar.
(1) A suitable, existing airport at the hub location.
(2) Good weather at the hub location, e.g., relatively little snow, fog, or rain.
(3) Access to good ramp space, that is, where to park and service the airplanes and sort the packages.
(4) Good labor supply, e.g., for the sort center.
(5) Relatively low cost of living to keep down prices.
(6) Friendly regulatory environment.
(7) Candidate airport not too busy, e.g., don't want arriving planes to have to circle a long time before being able to land.
(8) Airport with relatively little in cross winds and with more than one runway to pick from in case of winds.
(9) Runway altitude not too high, e.g., not high enough to restrict maximum total gross take off weight, e.g., rule out Denver.
(10) No tall obstacles, e.g., mountains, near the ends of the runways.
(11) Good supplies of jet fuel.
(12) Good access to roads for 18 wheel trucks for exchange of packages between trucks and planes, e.g., so that some parts could be trucked to the hub and stored there and shipped directly via the planes to customers that place orders, say, as late as 11 PM for delivery before 10 AM.
So, there were about three candidate locations, Memphis and, as I recall, Cincinnati and Kansas City.
The Memphis airport had some old WWII hangers next to the runway that FedEx could use for the sort center, aircraft maintenance, and HQ office space. Deal done -- it was Memphis.
That's how the decision was really made.
Uh, I was there at the time, wrote the first software for scheduling the fleet, had my office next to that of founder, COB, CEO F. Smith.