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So I've taken Linear Programming 101.

I've read my textbook, took the test and all that, and - besides all the theory, the nice algebraic interpretations, etc - I've encountered a lot of textbook examples of linear programming problems.

You know, the usual, the diet problem, the transportation problem, the usual "a factory makes 300 screws and 400 bolts a day, McGyver is trapped in the factory and..." problem.

I wonder if there is some interesting example beyond that from real life or puzzles/card/board games that can be interpreted/modelled as a nice, elegant, perhaps even beautiful (but still nice and simple) linear programming problem.

I can't think of any, can you?

Bonus points if it uses duality.

I don't think I want to see the complete model, unless a lot of thought is required, though - you could as well leave me the fun of that or maybe just throw me a clue :)

Thanks!

Tobia Tesan
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  • I'm not sure what you are looking for in an answer. I'm giving you a couple of really neat cutting edge problems concerning transportation, but it is sometimes _surprising_ that linear programming can handle such large problems in practice. – Hooked Feb 14 '15 at 00:26
  • You know - when I stumbled upon this, I went "A-AH!": http://en.wikipedia.org/wiki/Shortest_path_problem#Linear_programming_formulation Something relatively familiar has a simple linear programming model. Who whould have thought. Now - I wonder if I can "A-AH!" again :) – Tobia Tesan Feb 14 '15 at 08:25

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Linear programming is widely used in all sorts of fun transportation problems. These problems are not simple, but they are useful and interesting. An example off the top of my head: how do you effectively allocate bikes or cars as a public resource?

Publicly available papers:

Balancing Bike Sharing Systems with Constraint Programming

Decision support for tactical resource allocation in bike sharing systems

Locating Stations for Bicycle-Sharing Schemes

Balancing Bicycle Sharing Systems: A Variable Neighborhood Search Approach?

The vehicle relocation problem for the one-way electric vehicle sharing

Optimizing Locations for a Vehicle Sharing System

Hooked
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  • Hah, nice! I find it hardly "pretty" or suprising (maybe because I pass by a bike sharing station every day on my way home and I always guessed they did some LP on that), but the papers themselves are pretty interesting. Thanks! – Tobia Tesan Feb 14 '15 at 08:01
  • BTW - upvoted but not accepted because it isn't quite what I'm looking for (see comment for my OP) - but it's cool nonetheless :) – Tobia Tesan Feb 14 '15 at 08:26