Variables
$X_{\mathit{iwt}}^{\mathit{MN}}\left\{\begin{array}{c}1\hfill \\ 0\hfill \end{array}\right)$	Binary	$\left\{\begin{array}{c}\text{If the manufacturer of vaccine}i\text{is ordered in period}w\text{to receive the vaccine in period}t\\ \text{Otherwise}\\ \end{array}\right)$
$Y_d^{\mathit{DS}}\left\{\begin{array}{c}1\hfill \\ 0\hfill \end{array}\right)$	Binary	$\left\{\begin{array}{c}\text{If distribution center}d\text{is capable of handling vaccines requiring cold refrigeration}\\ \text{Otherwise}\\ \end{array}\right)$
$X_d^{\mathit{DS}}\left\{\begin{array}{c}1\hfill \\ 0\hfill \end{array}\right)$	Binary	$\left\{\begin{array}{c}\text{If distribution center}d\text{is set up for vaccines requiring very cold refrigeration}\\ \text{Otherwise}\\ \end{array}\right)$
$X_d^{\mathit{EX}}\left\{\begin{array}{c}1\hfill \\ 0\hfill \end{array}\right)$	Binary	$\left\{\begin{array}{c}\text{If equipment of ultra - cold refrigeration is added to distribution center}d\\ \text{Otherwise}\\ \end{array}\right)$
$Y_{\mathit{idwt}}$	Integer	The doses of vaccines i ordered in period w by distribution center d received in period t
$u_{\mathit{idt}}$	Integer	The doses of vaccines i allocated to distribution center d in period t
${\mu }_{\mathit{igst}}$	Integer	The doses of vaccines i allocated to group g in state s in period t
${\psi }_{\mathit{ist}}$	Integer	The doses of vaccines i stored in the warehouse of state s in period t
${\theta }_{\mathit{idst}}$	Integer	The doses of vaccines i shipped from distribution center d to warehouse of state s in period t