Applied Mathematical Programming (1977)

Do you think not learning math would have helped you understand people at a younger age? It sounds like you just needed time to grow socially and in practicality. For most people on this forum, that’s a challenge regardless.

I never wanted the Ph.D., what I learned there, the research I did there, to be the basis of a career. Instead, before the Ph.D. I had a good career going with computing and, at times a crucial help, some math, and went for the Ph.D. ONLY to do better at THAT career. For my career, the day I entered the Ph.D. program was a BIG step down, and what I'd learned about optimization was, in a word, WORTHLESS.

My main point here is on the word "applied" for optimization: I was well qualified, and happened to publish some research in optimization, but discovered that "applied" optimization was not the basis of a good career. Here I'm just reporting that fact. I doubt that there is still any real career opportunity in "applied" optimization.

So, a book title with "Applied" Optimization is to me a outrage.

I wasn't stuck on "optimization". For a while worked in the first wave of AI (artificial intelligence via the Rete algorithm). Then published in mathematical statistics. I was perfectly willing to mow grass, shine shoes, ..., do anything that would support me financially, be reasonably safe, and not seriously illegal but discovered that "Ph.D." on the resume blocked any such. Thought about taking "Ph.D." off the resume but was afraid that I'd get into trouble due to the gap in time.

Here my point, complaint, warning, contribution to others, is: My long experience was that there is nearly no career in "applied" optimization. A second point could be, outside of academics, a Ph.D. can hurt your career. Try leaving it off your resume. A Ph.D. might be worse for your career than a felony conviction; no joke (my legal history is totally clean).

In life, we are forced to make important decisions without good information. In my career, at times I did well, and at times I didn't.

E.g., by middle school it seemed accepted and true that education helps, more education helps more, education in the STEM fields is the best, a Ph.D. is the best education, and, thus, a Ph.D. in a STEM field should be really good, e.g., easily enough to buy a house and support a family.

Truth: Nope, too simple. I couldn't take care of my wife, kitty cats, get a job, any job, at all, ANY job, got run out of the house by the Sheriff with guns.

With a BS "With Honors" in math, I got strongly recruited. With a Ph.D. in applied math, including optimization, I got strongly rejected.

Yup, it hurt. I was manipulated, lied to, and hurt.

"psychological burden": Maybe those are the right words. But millions of people have suffered worse, e.g., The Great Depression, wars, Covid in the family, and much more, and still did well.

Don't know the solution in general.

For me, now, still good in math and computing, with .NET, etc. got a Web site, with some math at the core, running easily enough, and intending to go live, get some viewers, run simple ads (standard sized rectangles), and make some money. In this, want to remain anonymous and not be a public person.

And want to OWN the business. Have someone list what papers I need to file for a business, an LLC, etc. Get an accountant. Get and receive revenue. In simple terms, add up the expenses and keep the rest. Eventually sell the business and pursue, say, mathematical physics.

> From your anecdotes you were the one tasked with clarifying things to them. From the sound of it, you didn't accomplished that, and it was unclear to stakeholders whether your output even provided any value worth keeping.

First, for any application, there has to be some practical interest. My view, there isn't much. The schools of math, engineering, and business have given optimization a big push, back at least to Dantzig, but from my long experience the interest was and is still just too low for "applied" optimization to have much in applications.

Cases: Sure, there has been a professor at Princeton who applied optimization to oil refining: What mixture of crude oil to mix into the refinery and what mixture of refined products to take out. Maybe a few, large livestock operations actually do run some diet problem solutions. And can use 0-1 optimization for Sudoku problems? What path for picking orders in a big warehouse, for Amazon or Walmart? A simple traveling salesman problem, and for a good enough solution build a minimum spanning tree and walk around that -- maybe they are doing that already. Assembly line balancing: Assign workers to positions to maximize the speed of the slowest worker assignment. Is anyone actually doing that? Even if they are, the solution is quite simple. Yes, a start on P vs NP was at Bell Labs designing networks. So, maybe with the Internet there are still valuable applications? Considered that. Got an interview at a company trying that. They were impressed by what I'd done at FedEx, but they were nearly dead and, I suspect, soon died. Maybe with big logistics, ocean, rail, trucks, warehouses, there are some big logistics problems where optimization could save a lot -- applications enough for careers? Better than grass mowing? When I got my Ph.D., the Chair of my dissertation orals committee was a big name in logistics -- saw no evidence of significant interest in applications. No ones in the halls. Phone not ringing. No suggestions of contacts for me.

Look, when there is a big need, ESPECIALLY when there is big money involved, it soon gets obvious, and the US economy gets to it right away. In that, "applied" optimization is not hot, warm, or much above freezing.

Right, you are mentioning formulation:

(1) They had already formulated a 0-1 optimization problem. It had 40,000 constraints and 600,000 variables. They had tried the then popular simulated annealing, ran for days, and quit. So, the formulation was done and not mine.

I worked hard, with the IBM OSL (optimization subroutine library), did 900 primal-dual iterations, Lagrangian relaxation, got a feasible solution within 0.025% of optimality, within two weeks, for free, a free sample, and never heard from them again. They resented and were afraid of my success.

(2) Another company was working a little more generally in optimization. Had a crude heuristic running. On some of their problems, 0-1, linear, again was successful with the OSL, and got only insults and resentment. Continued on, gave them a nice formulation, better than their heuristic, and path through optimization, and got fired. They'd hired me and wanted to fire me before 6 months was up. They were not very good with linear programming at all, and I was a LOT better at what they were doing in the formulation, math, and computing, and their reaction was they didn't want me for competition.

(3) In a military group, did well with some non-linear optimization (their formulation). Then they had a challenging strategic problem. I did a formulation of a Monte-Carlo solution and wrote and ran the code (used an Oak Ridge random number generator I'd programmed in assembler). They called in a famous probability professor for a review. His remark was that there was no way the Monte-Carlo could "fathom" the tree. He was right; the tree was huge. But each trial of my Monte-Carlo yielded at each point in time a random variable on 0-15, and the law of large numbers applied right away. It wasn't D-day, but suppose it was: The tree of possibilities was enormous, but the, say, number of Allied soldiers killed was, what, 0-200,000. So, each trial give a random variable value at, say, each second, for, say, 48 hours -- the law of large numbers applies and could tell Ike the distribution of number of deaths, the expected values, the median, the variance for each second of the 48 hours. Passed the review. One guy there used my random number generator on one of his old problems, got significantly different results, was afraid, said "I don't want you in the center of all my projects", and I got ignored on the way to being fired.

(4) At FedEx, had written a program that showed the BOD that the program made the fleet scheduling easy enough and saved the company. So, to do better, formulated a set covering direction. Savings? 1% would have been $millions a year. The founder, COB, CEO wrote a memo making that my project, but my boss, a Senior VP, said that there was no money in the budget for me; I'd been commuting between Memphis and Maryland where my wife was in her Ph.D. program; the stock promised in three weeks was very late; and I went for a Ph.D.

Actually another student at another school ran with my set covering formulation for his dissertation.

The high level, overview, simple fact of life, is as I described: There just is no real career in "applied" optimization. That horse is nearly dead and should not be further flogged. Millions of US families have a house, stable marriage, and healthy children, and I'd believe that fewer than 20 of those families are supported by careers in "applied" optimization -- maybe 0 families.

I was naive, manipulated, and fooled. Now on the OP, there is a book title with "Applied Optimization", and I'm outraged.

So: "Always look for the hidden agenda."

„Learning how to formulate problems as integer/linear programming ones“, as another commenter put it, works great if it‘s a natural fit and sure is fun for idk 7th grade math text problems I guess but OTOH squeezing realistic problems into systems of hundreds of equations (or more if dealing with linearizations of inherently non-linear/concave/multi-step problems) to satisfy tool idiosyncracies calls for additional tools in your arsenal.