Sets and indicators DC Potential DC...

Sets and indicators
DC	Potential DC locations set	L	DNs set
G	Nodes set	PROD	Relief commodities set
PRODNC	Non-emergency commodities set	PRODC	Emergency commodities set
$R_{i, j}$	Roads between two nodes set	TV	Available vehicles set
i,j	Nodes indicator	q	Potential DCs' location indicator
P	Relief commodity indicator	r	Road indicator
v	Vehicle indicator	h	DC location factors indicator
Parameters
K	Maximum number of DCs	$M_{i, j}$	Time upper bound
Inf	Upper bound of non-emergency relief commodities that can be sent to one DN	${Cap}_{q p}$	DC q's capacity of product type p
${Cp}_{v p}$	Vehicle type v's capacity of product p	$D_{j p}$	DN j's demand for product p (⁠ $P \in PRODC$ ⁠)
$\tilde{D_{j p}}$	DN j's uncertain demand for product p (⁠ $P \in PRODNC$ ⁠)	$t_{i, j}^{r}$	The time interval between nodes i and j through road r
$U_{i, j}^{r}$	A binary parameter, determining whether road r between two nodes i and j is available or not	$C_{i, j}^{r, v}$	Cost of going from node i to node j through road r and vehicle type v
$b_{i}$	Upper bound of the service time window of DN i	${Start}_{q, v}$	Emergency operation start time from DC q through vehicle v
$ρ_{j}$	Disaster severity rate at DN j	${Dis}_{q, j}$	Distance between DC q and DN j
${saf}_{q}$	Safety rate of DC q	${Tech}_{q}$	The technological level of DC q
${Roads}_{q}$	Road availability of DC q	$w_{h}$	Weight of location criteria h
$\tilde{Budget}$	Total uncertain available budget	$f_{q}$	Fixed cost of opening DC q
Decision variables
$y_{q}$	Binary variable to determine whether DC q is chosen or not	$O_{q}^{v}$	Binary variable to determine whether vehicle v is allocated to DC q or not
$X_{i, j}^{r, v}$	Binary variable to determine if the distance between nods i and j is traveled through road r and by vehicle v	${qu}_{i}^{v, p}$	Number of non-emergency relief commodity p which is sent to DN i by vehicle v
$S_{j, v}$	Arrival time at DN j by vehicle v	${End}_{q}$	Return time to DC q

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Sets and indicators
DC	Potential DC locations set	L	DNs set
G	Nodes set	PROD	Relief commodities set
PRODNC	Non-emergency commodities set	PRODC	Emergency commodities set
$R_{i, j}$	Roads between two nodes set	TV	Available vehicles set
i,j	Nodes indicator	q	Potential DCs' location indicator
P	Relief commodity indicator	r	Road indicator
v	Vehicle indicator	h	DC location factors indicator
Parameters
K	Maximum number of DCs	$M_{i, j}$	Time upper bound
Inf	Upper bound of non-emergency relief commodities that can be sent to one DN	${Cap}_{q p}$	DC q's capacity of product type p
${Cp}_{v p}$	Vehicle type v's capacity of product p	$D_{j p}$	DN j's demand for product p ( $P \in PRODC$ )
$\tilde{D_{j p}}$	DN j's uncertain demand for product p ( $P \in PRODNC$ )	$t_{i, j}^{r}$	The time interval between nodes i and j through road r
$U_{i, j}^{r}$	A binary parameter, determining whether road r between two nodes i and j is available or not	$C_{i, j}^{r, v}$	Cost of going from node i to node j through road r and vehicle type v
$b_{i}$	Upper bound of the service time window of DN i	${Start}_{q, v}$	Emergency operation start time from DC q through vehicle v
$ρ_{j}$	Disaster severity rate at DN j	${Dis}_{q, j}$	Distance between DC q and DN j
${saf}_{q}$	Safety rate of DC q	${Tech}_{q}$	The technological level of DC q
${Roads}_{q}$	Road availability of DC q	$w_{h}$	Weight of location criteria h
$\tilde{Budget}$	Total uncertain available budget	$f_{q}$	Fixed cost of opening DC q
Decision variables
$y_{q}$	Binary variable to determine whether DC q is chosen or not	$O_{q}^{v}$	Binary variable to determine whether vehicle v is allocated to DC q or not
$X_{i, j}^{r, v}$	Binary variable to determine if the distance between nods i and j is traveled through road r and by vehicle v	${qu}_{i}^{v, p}$	Number of non-emergency relief commodity p which is sent to DN i by vehicle v
$S_{j, v}$	Arrival time at DN j by vehicle v	${End}_{q}$	Return time to DC q

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