Table 13.

Decision variables.

Notations	Description
$x_{\mathit{ij}}^{\mathit{ht}}$	1 if dose i of vial j is used at hospital h at time slot t, 0 otherwise
$y_j^{\mathit{ht}}$	A binary indicator whether the vial j is opened at hospital h at time slot t
$in{v}^{h,t}$	Number of vials at hospital h at time slot t, $in{v}^{h,t}\in {\mathbf{Z}}^{+}\cup \{0\}$
$R^{h,t}$	Number of vials to reorder for hospital h at time slot t, $R^{h,t}\in {\mathbf{Z}}^{+}\cup \{0\}$
$z_{(h^{+},h^{-})}^t$	Direction of transshipment from $h^{+}$ to $h^{-}$ at time slot t when transshipment is implemented 1, 0 otherwise.
$T{R}_{(h^{+},h^{-})}^t$	Number of vials to transship from hospital $h^{+}$ to $h^{-}$ at time slot t
$o_{h,t}$	Overaged dose at hospital h at time slot t
$u_{h,t}$	Underaged dose at hospital h at time slot t
Profit	Total profit by vaccinating customers
$Cos{t}_R$	Total reorder cost of reordered vials
$Cos{t}_T$	Total lateral transshipment cost of transshipped vials
$Cos{t}_o$	Total overage cost of left doses after operation hours
$Cos{t}_u$	Underage cost cost of unvaccinated doses (people) after an hour