Identifying FX Arbitrage as a linear programming problem using COIN-OR Linear Program Solver (CLP).

fx_arbitrage.lp

max D
subject to
  D + DE + DP + DY - 0.8706 ED - 1.4279 PD - 0.00750 YD = 1
      ED + EP + EY - 1.1486 DE - 1.6401 PE - 0.00861 YE = 0
      PD + PE + PY - 0.7003 DP - 0.6097 EP - 0.00525 YP = 0
      YD + YP + YE - 133.33 DY - 116.14 EY -  190.48 PY = 0
bounds
  D <= 10000
end

fx_solver.cpp

#include <ClpSimplex.hpp>
#include <vector>
#include <iostream>
#include <string>

int main( int argc, const char *argv[])
{
  ClpSimplex model;
  int status;

  // Read the linear program description
  if (argc < 2) {
    status = model.readLp( "fx_arbitrage.lp");
  } else {
    status = model.readLp( argv[1] );
  }

  if ( !status ) {
    // Perform the optimization
    model.primal();
  }

  // Print the solution
  auto nCol = model.numberColumns();
  auto colSolution = model.getColSolution();
  for(int i=0; i<nCol; i++ ) {
    std::cout << model.getColumnName(i) 
              << ": " << colSolution[i] << std::endl;
  }
  
  return 0;
}

Makefile

all: fx_solver

fx_solver: fx_solver.cpp
	clang++ -std=c++0x -I/usr/include/coin -o fx_solver fx_solver.cpp -lClp

# Install CLP:
# sudo apt-get install coinor-libclp0 coinor-libclp-doc

output.txt

### WARNING: CoinLpIO::readLp(): Maximization problem reformulated as minimization
Clp0006I 0  Obj 0 Primal inf 0.700329 (1) Dual inf 4e+10 (4)
Clp0006I 7  Obj -10000
Clp0000I Optimal - objective value -10000
D: 10000
DE: 2.04885e+07
DP: 0
DY: 0
ED: -1.64009e-12
PD: -1e-12
YD: 2.73313e+09
EP: 0
EY: 2.35331e+07
PE: 0
YE: 0
PY: 1e-12
YP: 0

This is awesome!
Thanks for demo-ing this.

Quick question,
When I do this with all other currencies except for Euros, the results make sense. However, if I do Euros, I get the following:

{ 
  'DOLLARS -> EUROS': 0.8706251088281078,
  'DOLLARS -> POUNDS': 1940.846914326005,
  'POUNDS -> YEN': 1359.1750941025014,
  'YEN -> DOLLARS': 258895.67192464444
  }

Which, when I plug the information into a spreadsheet ; balances. However, the results don't make sense as its telling you to go

Dollars->Euros;
Dollars->Pounds->Yen->Dollars;

Leaving you $0.87 in Euros. Is this correct?
If so, is there a way to prevent this?