Table A1 Notation guide (in order of...

Table A1

Notation guide (in order of appearance within category)

	Sets
K	set of helicopter teams
N^k	set of AMRs assigned to helicopter team k, $N^{k} = {i_{1}^{k}, \dots, i_{\| N^{k} \|}^{k}}$
$S_{N^{k}}^{k}$	set of complete feasible routes for helicopter team k
$H$	set of HLZs
	Indices
i	index for AMRs, e.g., $i \in {i_{1}^{k}, \dots, i_{\| N^{k} \|}^{k}}$ ⁠, in Algorithm 1
$j, j^{'} \in H$	indices for nodes in the HLZ network, j′ ≠ j
k ∈ K	index for helicopter teams
s	index for route, $s \in S_{\| N^{k} \|}^{k}$
	Parameters
n	number of AMRs
β^k	utilization penalty for aircraft team k, $β^{k} = α B^{(9 - p_{i})} = α b_{i}$
$ζ \in Z^{+}$	initial AMR assignment quantity
η ∈ [0, 100]	unrestricted assignment percent parameter
θ ∈ [0, 1]	assignment improvement quantity ratio
α	unsupported AMR penalty
γ^k	flight hour penalty for helicopter team k
B	base for exponential transformation of doctrinal AMR priority level
L	maximum ride time (hours)
	Computational variables
y	number of assignments to attempt to improve, y = ⌊θζ⌋
τ	number of feasible routes after each AMR insertion iteration to carry forward to the next iteration
r = (r₁, …, r_m)	routing sequence
f_TOF(r)	time of flight (TOF) for route sequence r
f_TST(r)	total slack time (TST) for route sequence r
f_MST(r)	minimum slack time (MST) for route sequence r
l_j	latest arrival time for AMR j
$t_{j, j^{'}}^{k}$	time between nodes j and j′ for helicopter team k
$A_{j}^{k} (r)$	calculated time of arrival at node j
b_i	transformed AMR priority for AMR i, $b_{i} = B^{(9 - p_{i})}$
Π_i	binary variable with value 1 if AMR i is unsupported and 0 otherwise
ϒ^k	binary variable with value 1 if helicopter team k is assigned one or more AMRs and 0 otherwise
Φ^k	total flight hours for helicopter team k
p_i	doctrinal AMR priority level from Table A2

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	Sets
K	set of helicopter teams
N^k	set of AMRs assigned to helicopter team k, $N^{k} = {i_{1}^{k}, \dots, i_{\| N^{k} \|}^{k}}$
$S_{N^{k}}^{k}$	set of complete feasible routes for helicopter team k
$H$	set of HLZs
	Indices
i	index for AMRs, e.g., $i \in {i_{1}^{k}, \dots, i_{\| N^{k} \|}^{k}}$ , in Algorithm 1
$j, j^{'} \in H$	indices for nodes in the HLZ network, j′ ≠ j
k ∈ K	index for helicopter teams
s	index for route, $s \in S_{\| N^{k} \|}^{k}$
	Parameters
n	number of AMRs
β^k	utilization penalty for aircraft team k, $β^{k} = α B^{(9 - p_{i})} = α b_{i}$
$ζ \in Z^{+}$	initial AMR assignment quantity
η ∈ [0, 100]	unrestricted assignment percent parameter
θ ∈ [0, 1]	assignment improvement quantity ratio
α	unsupported AMR penalty
γ^k	flight hour penalty for helicopter team k
B	base for exponential transformation of doctrinal AMR priority level
L	maximum ride time (hours)
	Computational variables
y	number of assignments to attempt to improve, y = ⌊θζ⌋
τ	number of feasible routes after each AMR insertion iteration to carry forward to the next iteration
r = (r₁, …, r_m)	routing sequence
f_TOF(r)	time of flight (TOF) for route sequence r
f_TST(r)	total slack time (TST) for route sequence r
f_MST(r)	minimum slack time (MST) for route sequence r
l_j	latest arrival time for AMR j
$t_{j, j^{'}}^{k}$	time between nodes j and j′ for helicopter team k
$A_{j}^{k} (r)$	calculated time of arrival at node j
b_i	transformed AMR priority for AMR i, $b_{i} = B^{(9 - p_{i})}$
Π_i	binary variable with value 1 if AMR i is unsupported and 0 otherwise
ϒ^k	binary variable with value 1 if helicopter team k is assigned one or more AMRs and 0 otherwise
Φ^k	total flight hours for helicopter team k
p_i	doctrinal AMR priority level from Table A2

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