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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.

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.

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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