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E  IIS and SA

It is possible to perform infeasibility and sensitivity analysis with TOMLAB /Xpress. The inputs and outputs are described in detail in Section A.1 and A.2.

E.1  IIS

If TOMLAB /Xpress reports that your problem is infeasible, then you can invoke the TOMLAB /Xpress infeasibility finder to help you analyze the source of the infeasibility. This diagnostic tool computes a set of infeasible constraints and column bounds that would be feasible if one of them (a constraint or variable) were removed. Such a set is known as an irreducibly inconsistent set (IIS).

To work, the infeasibility finder must have a problem that satisfies two conditions:
  • the problem has been optimized by the primal or dual simplex optimizer or by the barrier optimizer with crossover, and

  • the optimizer has terminated with a declaration of infeasibility.
Correcting Multiple Infeasibilities

The infeasibility finder can find several irreducibly inconsistent sets (IIS), however the TOMLAB default is one (controlled by MAXIIS). Consequently, even after you detect and correct one such IIS in your problem, it may still remain infeasible. In such a case, you need to run the infeasibility finder more than once or increase MAXIIS to detect those multiple causes of infeasibility in your problem.

Interpreting IIS Output

The size of the IIS reported by TOMLAB /Xpress depends on many factors in the model. If an IIS contains hundreds of rows and columns, you may find it hard to determine the cause of the infeasibility. Fortunately, there are tactics to help you interpret IIS output:
  • If the problem contains equality constraints, examine the cumulative constraint consisting of the sum of the equality rows.

  • Try preprocessing with the TOMLAB /Xpress presolver. The presolver may even detect infeasibility by itself. If not, running the infeasibility finder on the presolved problem may help by reducing the problem size and removing extraneous constraints that do not directly cause the infeasibility but still appear in the IIS.

  • Other simplifications of the constraints in the IIS, such as combining variables, multiplying constraints by constants, and rearranging sums, may make it easier to interpret the IIS.

E.2  SA

The availability of a basis for an LP allows you to perform sensitivity analysis for your model, if it is an LP. Such analysis tells you by how much you can modify your model without affecting the solution you found. The modifications supported by the sensitivity analysis function include changes of the right hand side vector and changes of the objective function.

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