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# Decimal places and significant figures in solutions

When solving problems and quoting solutions, the accuracy of your solutions is really only as good as the accuracy of your problem data. Hence, if you have problem data to 5 decimal places (dp) or 4 significant figures (sf) you solution should have 5dp or 4sf respectively. However, most software works to machine precision, so you will have to round your solutions. You need to be careful when rounding that you don't cause your solution to become infeasible or cause your objective function to deteriorate so that another solution become better.

-- MichaelOSullivan - 19 Mar 2008

The most accurate way of determing a solution to a specified number of dp is to solve an integer programme to the specified accuracy, e.g., if 2dp are required then solve an integer programme with variables = 100 x the original variables values and then divide by 100 once the solution is obtained. However, this may be too complex for many problems.

-- MichaelOSullivan - 19 Mar 2008

Another way to check that rounding is ok is to perform some sensitivity analysis or parametric analyis on the data to see if rounding changes the optimal solution.

-- MichaelOSullivan - 19 Mar 2008

Best practice is probably to check with the client regarding accuracy. However, DO NOT just round your solution values without recalculating the objective function value and checking feasibility!

-- MichaelOSullivan - 19 Mar 2008

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Title | Decimal places and significant figures in solutions |

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Topic revision: r1 - 2008-03-19 - MichaelOSullivan

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