Applied Mathematical Programming (1977)
This book is comparatively old, but the authors are experts, and likely the material is still surprisingly current.<p>But I will insert another point, call it the &quot;Dirty Little Secrets of Optimization Your Books and Professors Don&#x27;t Tell You.&quot;<p>Here is a bottom line, bold, summary fact of life about such <i>optimization</i>, <i>mathematical programming</i>, <i>operations research</i>:  It&#x27;s super tough to find real world problems where can apply such material, do well on the problems, please the customers, and get paid well enough to have a career.  Trying such work either as a consultant or an employee is tough.<p>There are exceptions, but they are rare.  If you can find an exception, terrific, but, did I mention, they are rare.  Nearly anything else you can do with a BS, MS, or Ph.D. in a STEM field will be an easier way to make a living.<p>In practice, the field has a bad reputation:  Early on there was a lot of hype and a lot of projects that failed.  Leading reasons for project failure were (1) the basic data was too difficult to collect, (2) some custom software was needed, and it was too difficult to write, (3) the available optimization software was not powerful enough, (4) the mathematical techniques were not powerful enough, at least not without a lot of special work unique to the particular practical problem, (5) the computer run times were too long, too often days or weeks.<p>In addition there were various <i>social</i> problems:  So, the optimization people were seen as wizards with tall, conical black hats decorated with stars and moons and were not really welcome, were not understood, were threatening, etc.<p>Here is a larger problem:  The optimization people did not have a recognized profession.  Lawyers, physicians, insurance actuaries, and more do have a recognized profession, maybe with government licensing, a code of ethics, professional peer review, legal liability, graduate education which is not just academic but also professional, likely with practical apprenticeship, a serious professional society, professional certification, etc.  That way, a generalist line manager can hire a respected professional, as an employee or consultant, with relatively low risk to his career.  Without professional status, such a line manager is reluctant and for good reason.<p>Then there&#x27;s another secret:  Early on, when there was a lot of optimism, there were two ideas, maybe just implicit but, still, powerful:<p>The first idea was that such optimization would, to borrow a more recent phrase, &quot;eat the world&quot;.  That is, essentially every economic activity in the world would be directed by such optimization.<p>The second idea was that the <i>optimal solution</i> was the absolute goal.  Accepting a solution that was 10 cents away from optimal was seen as a moral lapse.  The word <i>optimal</i> was a stick used to beat up on everything and everyone else.<p>Then reality set in:  The applied math available was nowhere nearly powerful enough to solve just any practical problems that could be found in routine operations.  And that was just the clouds before the hurricane:<p>The hurricane happened when the question P versus NP was formulated and, then, it was seen that large, practical problems in NP-complete were 
as common as pebbles in a stream bed.  Darned near every problem in scheduling, routing, logistics, resource allocation, and more could want at least something as difficult as integer linear programming, but that problem is in NP-complete.  Then considering non-linear aspects gave a storm that made a hurricane look like a gentle rain.  Then it got worse:  A lot of real problems had a lot of randomness.  Okay, a lot of those problems can be formulated as stochastic optimal control problems, maybe continuous time, maybe discrete time, but then get bad news right away:  First don&#x27;t have enough data on either the system <i>dynamics</i> or the probability distributions of the random effects.  Second on realistic problems, stochastic optimal control can eat super computer time by the months per problem.<p>The worst of the chuckholes in the road was the struggle of P versus NP.  And with the moral attitude that <i>optimal</i> was to be obtained made the P versus NP challenge much worse.  Indeed the US economy went for decades declining to implement solutions that could save 15% of operating costs because saving 16% for an optimal solution was too difficult for the math and the computing.  That is, commonly saving that last 10 cents is by far the hardest.  Or there might be millions of dollars to be saved, but still could not save the last 10 cents, and people gave up due to the difficulty of that last 10 cents.<p>And there was a huge cultural problem:  Various universities set up professorships, sometimes departments, concentrating on optimization.  Well, there the professors concentrated on publishing papers and largely ignored real problems.  And anything like professional education was pushed out as inferior to the research agenda.  Then, sure, the students got relatively little benefit in non-academic careers -- e.g., they were not in a profession.<p>For a while, there was an eager customer who did put up with a lot of the hype and poor or failed projects -- the US DoD.<p>So, bottom line:  A lot of very good applied math has been done for optimization.  And there is a lot of high quality software.  But real problems that can be attacked successfully with these tools and where the benefits are really worth the <i>botheration</i>, time, money, and effort are rare.<p>If you can find suitable real problems and make a living, you will be very rare, but good for you.<p>What will likely happen is that occasionally some optimization will become part of some software that is sold as, say, SaaS.  And, in some fields where optimization is known to be effective, say, feed mixing, we can expect that optimization is an accepted tool in that field.<p>So, what was the biggest result of the academic research?  Sure, they identified the problem of P versus NP.  Gads, I should have started a pizza shop!