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 successfu

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.