The OP has so many different business cards; there's
some pathos and poignancy there.

What he is talking about has some examples that have
been quite successful:

(1) Oil Refinery Operation. For input to your
refinery, out back have, for each of several
varieties of crude oil, some millions of gallons.
For output, look at the market for the various
possible products and the prices of each. Then your
mission is to decide how to process the different
varieties of crude oil to maximize the profit.

Early on this problem was attacked with linear
programming, and some mainframes were sold. Of
course, the problem is nonlinear, and there has been
a chemical engineering professor at Princeton who
has worked on this problem, and at least one of his
students got a job in Houston.

(2) Airline Scheduling. There's a lot of money to
be saved there, and the OP gives a good high level
description of that problem. At times the problem
has been attacked seriously by groups at least at
MIT and Georgia Tech.

(3) Military. During the cold war, there was a lot
of interest in various topics in applied
mathematics, including operations research, in a
radius of 100 miles of the Washington Monument.
Indeed there was a company, Operations Research, in
Silver Spring that did some 'max-min' game theory
with saddle points, Sion's theorem, combinatorial
optimization, etc. There were applications of
optimization by the Institute for Defense Analysis
for the US DoD Joint Chiefs of Staff.

(4) Feed Mixing. A classic textbook problem in
linear programming is feed mixing, and there have
been rumors that at least one major animal feed
producer takes this work seriously.

(5) Worker Scheduling. Airlines, hospitals, and
maybe even fast food restaurants can get some
significant savings via careful worker scheduling.

But such work encounters some difficulties:

(1) Data and Software. Too often the work requires
some custom input data gathering and some custom
software writing. Weeks or months of such work are
not welcome for some one-shot question.

(2) Algorithm Power. Too often one wishes for an
algorithm that shows that P = NP with a polynomial
of small degree with small coefficients. Of course,
the question of P = NP? remains one of the grand
challenges in pure and applied mathematics. Instead
of such an algorithm, too often one must look for
and exploit special problem structure, write some
custom, one-shot software, and struggle. The people
paying the bills don't like to see the struggle,
even when it is successful. More welcome is just to
push a button, "Optimize" and get a best possible
answer.

(3) Uncertainty. The OP is correct about the role
of uncertainty: E.g., the Dean of Engineering at
MIT, Tom Magnanti, gave a Goldman Lecture at Johns
Hopkins on designing a large IP network, e.g., a big
chunk of the Internet. Yes, it's a big problem in
'combinatorial' optimization as in, say,

George L. Nemhauser and Laurence A. Wolsey, 'Integer
and Combinatorial Optimization', ISBN 0-471-35943-2,
John Wiley & Sons, Inc., New York, 1999.

Yes, these problems are apparently the original
motivations for the question of P versus NP.

At times companies have tried to attack this network
design problem. There was work in PLano, TX
associated with SMU, some early Bell Labs work, and
a Cisco effort to help with multi-protocol label
switching (MPLS).

Well, much of the real challenge of this network
design problem is the uncertainty: That is, we know
that the traffic and network capacity will be
growing quickly and that we will have to continue to
make major changes in the physical network. In
principle if we had a probabilistic description of
the growth, then we could minimize expected
discounted cost over time. Alas, we don't have that
probabilistic description, and if we did mostly
using it would be too difficult for the algorithms
and computing.

More generally for the real world I see three
problems, one need, and one solution:

Three Problems.

(1) Professionalism. Such applied mathematics is a
technical field in part trying to be useful in the
real economy. There are other technical fields
doing this, but often they have a big advantage of
'professionalism', that is, government licensing,
peer review, official continuing education, code of
ethics, and liability. The practice of applied
mathematics has none of these and, thus, is taken
much less seriously.

(2) Interface. Large US organizations, one big
enough to pay for such applied mathematics for their
internal use, are still organized much like Henry
Ford's factory floor 100 years ago where the
supervisor is supposed to know more and the
subordinate is supposed just to add routine effort
to the work of the supervisor.

So, there is a severely awkward interface between a
subordinate working as an applied mathematician and
a supervisor who does not understand the applied
mathematics. And, unless the CEO and COB are such
mathematicians, going up the management chain there
must always be such an awkward interface.

The in-house legal staff solves this problem with
some aspects of their professionalism that the
applied mathematicians don't have.

Further, a norm in such a hierarchy is that the
supervisor's job is just to do what has been
assigned by their superior; making some innovative
application of applied mathematics is not part of
the job description; and pursuing such a project and
failing could ruin the supervisor's career.

Also, no one had their career ruined from failing to
make an innovative application of applied
mathematics. And if a supervisor somehow does make
such an innovative application, then every
non-mathematician up the management chain to the COB
can be afraid of their job.

Really, then, nearly only a secure CEO can sponsor a
project in applied mathematics that is serious for
the company, and only a small fraction of such CEOs
will want to put such a project on their calendar.

(3) Power.

In US business, the top few people have a lot of
power, want to keep it, and don't want it
challenged. To them a project in applied
mathematics can be a nuisance to be swatted down
like a fly.

So how does computing solve the problems (1)-(3)?
Awkwardly. The best situation is that the company
is just a computing company -- Microsoft, Adobe,
Intuit, Google, Facebook, etc. Otherwise usually
the computing is so important that the non-technical
people in the company struggle to work with the
computing people.

The Need.

In broad terms, computing has often programmed what
people did before manually. So, what was to be
programmed was well understood. Now that work is
slowing, and for more progress computing will have
to program work that never was done manually and,
thus, is much less well understood.

Then there is a challenge: Just in computing, as we
move away from what was understood manually, we are
left without means of knowing what the heck we are
doing.

Let's take an example, finding a spacecraft
trajectory to Saturn. That was never done
manually. So, how was it done? Sure, with some
mathematical physics, ordinary differential
equations, and some numerical methods for those
equations. With that work done, the corresponding
software could begin. We were quite sure that the
software, if written as specified by the physics and
math, would work. So, it was the physics and math
that let us know what we were doing.

Then, sure, in part computer science has tried to
move into such applied math and, at times, the
physics.

Here's the need: More progress in applying
computers needs more use of math so that for good
solutions to more real problems, never solved well
manually, we can know what software to write and be
more sure the results will be good. That is, the
math does the logical connection from the real
question to the real answer, and the computing then
implements the data manipulations specified by the
math.

The Solution.

I believe that the solution for computing and
applied math has been presenting itself via some
good examples. The theme is, the CEO needs to be
one of the main technical guys. So, the founders of
Intel, Microsoft, Google, and Facebook were the main
technical guys. For applied mathematicians,
consider J. Simons at Renaissance Technologies and
A. Viterbi at Qualcomm.

So, for both future applications of computing and
for careers of people studying technical fields
without solid professional support, the path forward
is for the technical person to be a company founder
instead of an employee with a stack of many
different business cards.

The opportunity is there, but don't expect the
currently powerful non-technical guys to reach out
with a welcoming hand!

Final point: For an entrepreneur with a valuable
application of some powerful mathematics and with
current attitudes in business, just let the
mathematics be an advantage in getting a better
solution for the real problem but don't mention the
mathematics and, instead, let everyone else just
assume that all the technical work was just routine
software.