Table 1 Model notation Sets i ∈ I Set of...

Table 1

Model notation

Sets
$i \in I$	Set of candidate server locations
$j \in J$	Set of demand points
$n \in N$	Set of servers to be located
$i \in W_{j}$	Set of servers covering demand point j
$B_{a} \in E_{n j}$	Set of states in which server n is the nearest-available for demand point j
$B_{a} \in N_{j}$	Set of states in which no server is available for demand point j
Variables and HQM notations
$y_{j}$	Binary variable, that shows whether demand point j is covered
$C_{N}$	Vertices of the N-dimensional hypercube
$f_{j}$	Fraction of demand point j on the overall demand
$p_{n j}$	Fraction of dispatches server n sends to demand point j
$t_{n j}$	Travel time of server n to demand point j
$λ_{a b}$	Upward transition rate between state a and state b
$μ_{a b}$	Downward transition rate between state a and state b
$B_{a}, B_{b}$	State a and state b of the N-dimensional hypercube
$P {Loss}_{j}$	Loss percentages of incoming demand calls for demand point j
$d_{a b}^{+}, d_{a b}^{-}$	Upward and downward Hamming-distances between states a and b
Decision variable
$x_{i}$	Binary variable, that shows whether candidate server location i is chosen

Sets
$i \in I$	Set of candidate server locations
$j \in J$	Set of demand points
$n \in N$	Set of servers to be located
$i \in W_{j}$	Set of servers covering demand point j
$B_{a} \in E_{n j}$	Set of states in which server n is the nearest-available for demand point j
$B_{a} \in N_{j}$	Set of states in which no server is available for demand point j
Variables and HQM notations
$y_{j}$	Binary variable, that shows whether demand point j is covered
$C_{N}$	Vertices of the N-dimensional hypercube
$f_{j}$	Fraction of demand point j on the overall demand
$p_{n j}$	Fraction of dispatches server n sends to demand point j
$t_{n j}$	Travel time of server n to demand point j
$λ_{a b}$	Upward transition rate between state a and state b
$μ_{a b}$	Downward transition rate between state a and state b
$B_{a}, B_{b}$	State a and state b of the N-dimensional hypercube
$P {Loss}_{j}$	Loss percentages of incoming demand calls for demand point j
$d_{a b}^{+}, d_{a b}^{-}$	Upward and downward Hamming-distances between states a and b
Decision variable
$x_{i}$	Binary variable, that shows whether candidate server location i is chosen

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