On: Minimize your cloud costs with GLPK and Haskell

[yummyfajitas]

It's true, glpk is not part of the haskell standard library. But solving a simple LP problem is easily done in a minute or two:

    lp = execLPM $ do	setDirection Max
			setObjective objFun
			leqTo (varSum ["x1", "x2", "x3"]) 100
			leqTo (10 *^ var "x1" ^+^ 4 *& "x2" ^+^ 5 *^ var "x3") 600
			leqTo (linCombination [(2, "x1"), (2, "x2"), (6, "x3")]) 300
			varGeq "x1" 0
			varBds "x2" 0 50
			varGeq "x3" 0
			setVarKind "x1" IntVar
			setVarKind "x2" ContVar

    main = print =<< glpSolveVars mipDefaults lp

The code in the blog post is just longer and more complicated because it's generating multiple constraints from code.

The only reason my code doesn't look as simple as the above is because it's doing a lot more. For example, this line generates 9 constraints:

    reservationConstraints loadPattern = [ linCombination [ (1.0, "reservation_" ++ k),
                                       (-1.0, "reserved_" ++ k ++ "_" ++ p) ], 0.0  |
                                       p <- (Map.keys loadPattern),
                                       k <- reservationTypes ]

E.g.:

    reservation_heavy - reserved_heavy_morning <= 0
    reservation_heavy - reserved_heavy_afternoon <= 0
    reservation_heavy - reserved_heavy_evening <= 0
    reservation_medium - reserved_medium_evening <= 0
    ....

If Mathematica is so easy, I'd love to see a significantly simpler version of the same problem written in it. But I have absolutely no idea how I'd write that simpler version.

[nukedukem → yummyfajitas]

Maximize[...], Minimize[...], LinearProgramming[...] thats it... But Mathematica costs money.

Example:

Minimize[{x + 2 y, -5 x + y == 7 && x + y >= 26 && x >= 3 && y >= 4}, {x, y}] LinearProgramming[{1, 2}, {{-5, 1}, {1, 1}}, {{7, 0}, {26, 1}}, {{3, Infinity}, {4, Infinity}}]

[yummyfajitas → nukedukem]

The vast majority of the code I wrote is setting up the problem (which has 15 vars and 27 constraints), not solving it. I.e., those list comprehensions are a way of writing 9 constraints on a single line.

To demonstrate mathematica is easier, you need to demonstrate that it's similarly easy to translate the problem from a verbal specification to an LP problem. Solving LP is the easy part.