Scheduling IT Staff at a Bank: A Mathematical Programming Approach

$N_{j k l}:$ the requirement of staff of category $j$ in shift $k$ in day $l$,

$n_{j}$ : the number of employees of category $j$,

$S_{w}: \quad$ the set of days of week $w$,

$S_{\text {off }_{(i, j)}}$ : the preferable set of days off of employee $i$ of category $j$,

$\mathrm{AL}_{i j}$ : the set of annual leave days of employee $i$ of category $j$,

$s_{1 w}$ : the first 5 days of each week $w$,

$s_{2 w}: \quad$ the 2 last days of each week (Thursday and Friday).