Table 3.

Notation for shift scheduling problem.

Notation for shift scheduling problem
Sets
$T$	Number of time epochs
$I$	Number of qualification levels
$K_i$	Total number of shift types of care workers with QL $i$
Parameters
$a_{itk}$	1 if shift type $k$ with QL $i$ works interval $t$, $0$ otherwise
$C_i^{min}$	Minimum number of care workers with QL $i$ or higher
${\bar{C}}_i$	Maximum number of care worker hours of QL $i$ available
$L_{it}$	Number of resident requiring activity of QL $i$ at time $t$
Decision variables
$x_{ik}$	Number of care workers with QL $i$ for shift type $k$
$c_{it}$	Staffing level of care workers with QL $i$ during time interval $t$
$c_{it}^{\ast }$	Number of care workers working at QL $i$ during time interval $t$
$q_{it}$	Backlog of work requiring QL $i$ at the start of time interval $t$