  This paper focuses on the problem of minimizing the outages due to extreme
events on the power grid equitably among all customers of the grid. The paper
presents two ways of incorporating fairness into the existing formulations that
seek to minimize the total outage in the power grid. The first method is
motivated by existing literature on incorporating fairness in optimization
problems and this is done by modifying the problem's objective function. The
second method introduces a novel notion of fairness, termed
$\varepsilon$-fairness, that can be incorporated into existing problem
formulations through a single second-order cone constraint. Both these methods
are very general and can be used to incorporate fairness in existing planning
and operational optimization problems in the power grid and beyond. Extensive
computational case studies that examine the effectiveness of both these methods
to characterize fairness is presented followed by conclusions and ways forward.
