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| Set | Description | | Plasma storage capacity in permanent center m′ in period t |
| K | Set of regular donors | | Blood storage capacity in permanent center m in period t |
| k′ | Set of donors recovered from COVID-19 | | Cost of testing each unit of blood and plasma in laboratory l |
| M | Blood donation of set of permanent centers | | Amount of blood demands in health care medical center n in period t |
| M′ | Set of permanent plasma donation centers | | Plasma demand in hospital n′ in period t |
| J | Set of temporary blood donation centers | d kt | Maximum blood donation from donors k at time t |
| T | Set of time periods | d′ k′t | Maximum plasma donation from a donor recovered from COVID-19 K′ at time t |
| L | Set of laboratories | Decision variables | Description | Type of variables |
| N | Set of hospitals requesting blood | Q jkt | The amount of blood collected in interim center j from donors k in period t | Continuous |
| n′ | Set of hospitals requesting plasma | | The amount of blood independent of center j to permanent blood center m in period t | Continuous |
| Parameter | Description | | The amount of blood collected in blood center m from donors k in period t | Continuous |
| Cost of transferring a unit of blood from laboratory l to demand points n in period t | | The amount of blood independent of permanent blood center m to laboratory center l in period t | Continuous |
| Cost of transferring a unit of COVID-19 plasma from laboratory l to demand points n in period t | | The amount of blood moved from laboratory l to demand points n in period t | Continuous |
| Cost of transferring a unit of blood from temporary center j to permanent center m in period t | | The amount of plasma collected in blood center m′ from donors k′ in period t | Continuous |
| Cost of transferring a unit of blood from permanent center m to a laboratory l in period t | | The amount of plasma transferred from blood center m′ to laboratory l in period t | Continuous |
| Cost of transferring a plasma unit from permanent center m′ to laboratory l in period t | | The amount of plasma transferred from laboratory l to demand points n in period t | Continuous |
| Fixed cost to build blood center m | | Number of interim facilities required in period t | Continuous |
| Fixed cost to build plasma center m′ | | If the temporary facility in location j in period t-1 in location j1 is in period t, it is one; otherwise, it is zero. | Binary |
| FU | Fixed cost to establish a temporary blood center | XR m | If a permanent blood center is created in location m, it is one; otherwise, it is zero | Binary |
| Operating cost for blood collection in blood center m from a donor of group k | XR m′ | If a permanent plasma center is created in location m′, it is one, and otherwise, it is zero | Binary |
| Operating cost for plasma collection in blood center m′ from a donor of group k′ | yu jkt | If donor k is assigned to interim facility j in period t, it is one, and otherwise, it is zero | Binary |
| Operating cost for blood collection in interim facility j from a donor of group k | M | A very large number | Continuous |
| Blood storage capacity in laboratory l in period t | YR mkt | If donor k is assigned to permanent blood center m in period t, it is one, and otherwise, zero | Binary |
| Plasma storage capacity in laboratory l in period t | YR′ m′k′t | If donor k′ is assigned to plasma permanent center m′ in period t, it is one, and otherwise, zero | Binary |
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