Table 5.

Notations used in model.

$I$	Forecast horizon.
$N$	Time period for which inventory model is valid.
$V$	Node set in a supply chain network.
$\left|V\right|$	Cardinality of the set $V$.
$n$	Time period such that $n\in N$.
$F_n(n+i)$	Demand forecast in period $n$ for the period $n+i$.
${\widehat{d}}_n$	Estimated demand in the period $n$.
$v$	Node in supply chain network.
$\Delta F_n(n+i)$	Forecast deviation in the period $n$ for period $n+i$.
$E\left[\Delta F_n\left(n^{\prime }\right)\right]$	Expected value forecast deviation over forecast horizon $I$$\forall n^{\prime }\ge n$.
$t_v$	Node processing lead time.
${\omega }_{v,v^{\prime }}$	Service time of the node $v$ for node $v^{\prime }$.
${\lambda }_{v,[v^{\prime },v^{″}]}$	Inventory replenishment time of node $v$ when node $v^{\prime }$ and node $v^{″}$ are its predecessor node and successor node respectively on a specific path.
$v_s$	NVS node.
$v_d$	PHC node.
$V_d$	Set of demand node such that $v_d\in V_d$.
$p_{v_d}$	Path connecting the demand node $v_d$ .
$l_v^{p_{v_d}}$	Lead time for the node $v$ for the path $p_{v_d}$.
${\widehat{d}}_v^{n{p}_{v_d}}$	Estimated demand at the node $v^{th}$ at time $n$ due to lead time along the path $p_{v_d}$.
$P$	Set of all valid path in the supply chain network.
${\widehat{d}}_v^{\Omega n{p}_{v_d}}$	Estimated demand at the node $v^{th}$ at time $n$ due to lead time along the path $p_{v_d}$ in disruption scenario $\Omega$.
${\widehat{D}}_v^n$	Cumulative demand at the node $v$ in the $n^{th}$ time period.
${\widehat{D}}_v^{\Omega n}$	Cumulative demand at the node $v$ in the$n^{th}$ time period in disruption scenario $\Omega$.
$in\left(v\right)$	Set of nodes in the higher echelon connected to node $v$ .
$out\left(v\right)$	Set of nodes in the lower echelon connected to node $v$ .
$Q_v^{{}^{\prime }z}$	Maximum order that can be placed by node $v$ at node $z$ such that $z\in in\left(v\right)$
$Q_{vn}^z$	Actual order size by the node $v$ to the node $z$ at $n^{th}$time period.
$j_v$	Age of the inventory when at the node $v$.
$Su$	Set of initial supply nodes.
$I{n}_v^{j_{v}n}$	Number of $j_v$ aged inventory at the node $v$ at $n^{th}$ time period.
$I{N}_v^n$	Total inventory at the node $v$ at $n^{th}$ time period of all ages.
$I{N}_v^{\Omega n}$	Total inventory at the node $v$ at $n^{th}$ time period of all ages in disruption scenario $\Omega$.
$q_{zv}^{j_{v}n}$	Number of $j_v$ age inventories in the order $Q_{vn}^z$.
${\rho }_v$	Ordering cost of the node $v$.
$IN{*}_v^{\Omega n}$	Total inventory at the node $v$ at $n^{th}$ time period of all ages when all the nodes place maximum orders after the initiation of disruption scenario $\Omega$.
$h_v$	Inventory holding cost at the node $v$.
$h{}_v^{\prime }$	Excess inventory holding cost at the node $v$.
$O_{vn}^z$	Binary variable whose value depends on whether an order is placed by node $v$ to the node $v$ such that $z\in in\left(v\right)$.
$S{p}_v$	Space available for inventory storage at node $v$.
$Sp{}_v^{\prime }$	Total additional space available at node $v$ by incurring extra cost for allocating strategic inventory reserves.
$b_{vn}^{z{j}_v{p}_{v_d}}$	Binary value variable whose value depend on whether any $j_v$ age inventories supplied by node $z$ to node $v$ in time period $n$ has been allocated to path $p_{v_d}$ such that $z\in in\left(v\right)$.
$\Psi$	Expiration constant in terms of number of time periods.
$S$	Disruption scenario set.
$S^{\prime }$	Set of critical disruption scenarios.
$\Omega$	Disruption scenario such that $\Omega \in S$.
${\delta }_v^{\Omega }$	Disruption recovery time for the node $v$ for the disruption scenario $\Omega$.
$l_v^{\Omega p_{v_d}}$	Lead time of the node $v$ for the path $p_{v_d}$ in disruption scenario $\Omega$.
${\Omega }^{\prime }$	No disruption scenario.
$T^{\Omega }$	Time period at which disruption$\Omega$ is initiated.
$y_v^{\Omega }$	Binary variable (0,1) whose value depends on whether a node $v$ has been disrupted in scenario $\Omega$.
$q_v$	Total strategic inventory reserve allocated at node $v$.
$q{*}_{v_d}$	Maximum strategic inventory reserve to be allocated on the path connecting$v_d$.
$l_v^{\Omega p_{v_d}}$	Lead time of the node $v$ for the path$p_{v_d}$ in disruption scenario $\Omega$.
$C_v$	Fixed cost of creating an excess fixed inventory space from $S{p}_v$ to $Sp{}_v^{\prime }$.
$\alpha$	Design parameter for service level.
$M$	Large number (Model constant).
$K_{v_d}^v$	Maximum service level loss at the demand node $v_d$ due to disruption at the node $v$.
${\eta }_{H1}$	Efficiency of heuristic H1.
${\Phi }_v^z$	Transportation cost per unit from $z^{th}$ node to $v^{th}$ node