Bicriteria Robustness versus Cost Optimisation
in the Generation of Aircrew Pairings

The airline crew scheduling problems

Tour of Duty planning (Pairings)

The Set Partitioning optimisation model

The ToD model

The Tour of Duty SPP model

Natural integer properties of the SPP LP

Balanced zero-one matrices

Subsequence

Subsequence

Subsequence

The ToD problem and limited subsequence

The ToD problem and limited subsequence

Some computational techniques for SPP

Fractional Solutions

Constraint branch on flights s and t

Constraint branching strategies for ToD

Summary of minimum cost TOD features

The effect of late aircraft arrival

Tour of Duty planning (Pairings)

Delay data (over 46,000 flights)

How can we introduce robustness into ToD build?

How can we introduce robustness into ToD build?

How can we introduce robustness into ToD build?

A non-robustness measure

Bicriteria optimisation in ToD planning

Bicriteria optimisation in ToD planning

Results of the weighted sum method

Preferred solution approach

Illustration (solution of LP relaxation)

Illustration (solution of integer problem)

Solution of LP Relaxation - trade off curve

Corresponding IP solutions

The SPPLP polytope

The effect of the cost objective cut

The elastic cost constraint

The ESPPLP polytope

Theoretical result

Numerical results

Minimal cost versus robust ToDs flight attendants

From minimal cost to robust ToDs

From minimal cost to robust ToDs

From minimal cost to robust ToDs

Conclusions

Future work