Table 2 Scheduling problem indices,... | Emerald Publishing

Table 2

Scheduling problem indices, sets, parameters and decision variables

Indices
$d = {1,2, \dots n}$	Days on which clinical services will be performed
$s = {1,2, \dots m}$	Clinical services, where m corresponds to the final visit with the referring doctor
Sets
$D$	Set of days in the planning horizon, indexed d
$S$	Set of clinical services, indexed s
$S^{'} \subseteq S$	Set of the requested clinical services
Parameters
$A_{s_{i}, d_{f}}$	$= {\begin{matrix} 1, if service s_{i} \in S is available on day d_{f} \in D \\ 0, otherwise \end{matrix}$
$P_{s_{i}, s_{j}}$	$= {\begin{matrix} 1, if service s_{i} \in S^{'} must precede service s_{j} \in S^{'} \\ 0, otherwise \end{matrix}$
$S_{s_{i}, s_{j}}$	$= {\begin{matrix} 1, if s_{i} \in S^{'} must be provided on the same day as s_{j} \in S^{'} \\ 0, otherwise \end{matrix}$
$L \geq 0$	Minimum number of days between the last clinical service and the final visit m
$N \geq 0$	Maximum number of days permitted on which a patient must come to the hospital (maximum visits)
$M > 0$	Large number
Variables
$x_{s_{i}, d_{f}}$	$= {\begin{matrix} 1, if service s_{i} \in S^{'} is scheduled on day d_{f} \in D \\ 0, otherwise \end{matrix}$
$y_{d_{f}}$	$= {\begin{matrix} 1, if at least one service has been scheduled on day d_{f} \in D \\ 0, otherwise \end{matrix}$

Source(s): Author's own creation/work