Table 1 parameters of the... | Emerald Publishing

Table 1

parameters of the task-assignment decision problem

Problem parameters		Decision variables
$p = 1, \dots, k \in P$	Set of production lots (i.e., recipes)	$s_{j} \in T$	Start time of task j
$j = 1, \dots, n \in F_{p}$	Set of production tasks	$t_{j} \in T$	End time of task j
$r = 1, \dots, k \in R$	Set of resources (i.e. machines)	$T_{j}$	Temperature of a product $p : j \in F_{p} at t_{j}$
$T$	Continuous set of the time horizon	$y_{j r}$	${\begin{array}{l} 1 if task j processed by machine r \\ 0 otherwise \end{array}$
$q_{r j}$	Saturation of task j on machine $r_{j}$	$x_{p}$	${\begin{array}{l} 1 if temperature of product p falls within the temperature danger zone \\ 0 otherwise \end{array}$
$c_{j}$	Processing time of task j
$d_{p}$	Production duedate of lot p
$α_{j r}$	Temperature decay law (°C per unit of time) for task j processed on machine r

Problem parameters		Decision variables
$p = 1, \dots, k \in P$	Set of production lots (i.e., recipes)	$s_{j} \in T$	Start time of task j
$j = 1, \dots, n \in F_{p}$	Set of production tasks	$t_{j} \in T$	End time of task j
$r = 1, \dots, k \in R$	Set of resources (i.e. machines)	$T_{j}$	Temperature of a product $p : j \in F_{p} at t_{j}$
$T$	Continuous set of the time horizon	$y_{j r}$	${\begin{array}{l} 1 if task j processed by machine r \\ 0 otherwise \end{array}$
$q_{r j}$	Saturation of task j on machine $r_{j}$	$x_{p}$	${\begin{array}{l} 1 if temperature of product p falls within the temperature danger zone \\ 0 otherwise \end{array}$
$c_{j}$	Processing time of task j
$d_{p}$	Production duedate of lot p
$α_{j r}$	Temperature decay law (°C per unit of time) for task j processed on machine r