Off-by-one error when solving integer linear program

[Matthew Keeter]

Hi folks,

I used GLPK to solve a problem in this year’s Advent of Code [1], and noticed
that it produces a very slightly wrong answer for one of the examples.

It’s an integer linear programming problem, pasted below the fold in CPLEX LP 
format.

The correct answer is 82892753, and I’m getting 82892752.

I’ve pasted my glpsol output at [2]

Strangely, other folks have gotten the correct answer with the same input;
there’s a reddit thread discussing it at [1].  I'm on a Mac OS 10.13.6,
GLPK 4.65, GMP 6.1.2, compiled with Apple LLVM version 10.0.0
(clang-1000.11.45.5)

Any ideas?

Regards,
Matt Keeter

[1] https://adventofcode.com/2019/day/14
[2] 
https://www.reddit.com/r/adventofcode/comments/eafj32/2019_day_14_solutions/fawjrgr/
[3] https://gist.github.com/mkeeter/1b4f5a5a89014fdc9e80f43187788436

--------------------------------------------------------------------------------

Maximize out: produced_fuel

Subject to
 NZVS: 5 equation1 -29 equation3 -7 equation9 >= 0
 ORE: -157 equation1 -165 equation2 -179 equation5 -177 equation6 -165 
equation8 +1 consumed_ore >= 0
 DCFZ: 6 equation2 -7 equation7 -3 equation9 >= 0
 FUEL: 1 equation3 -1 produced_fuel >= 0
 XJWVT: -44 equation3 +2 equation7 >= 0
 KHKGT: -5 equation3 +8 equation9 >= 0
 QDVJ: -1 equation3 +9 equation4 >= 0
 GPVTF: -9 equation3 -1 equation4 +2 equation8 >= 0
 HKGWZ: -48 equation3 -12 equation4 +5 equation6 -5 equation9 >= 0
 PSHF: -8 equation4 +7 equation5 -7 equation7 -10 equation9 >= 0
 ore_consumption: consumed_ore <= 1000000000000

Integer
 produced_fuel
 consumed_ore
 equation1
 equation2
 equation3
 equation4
 equation5
 equation6
 equation7
 equation8
 equation9

end