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. 2021 Oct 7;312(2):761–825. doi: 10.1007/s10479-021-04238-2
DmSHt Demand of medicine m from warehouse S by hospitals H at the period t
DmSWt Demand of medicine m from warehouse S by pharmacies W at the period t
DmWHt Demand of medicine m from pharmacies W by hospitals H at the period t
DmDPt Demand of medicine m from DC D by MP P at the period t
DmDPt Demand of medicine m from DC D by LP P at the period t
DmDSt Demand of medicine m from DC D by warehouse S at the period t
DmPPt Demand of medicine m from MP P by LP P at the period t
σDt Operating cost at the DC D at the period t
σSt Operating cost at the warehouse S at the period t
IHmPt Inventory holding cost of medicines m at the MP P at the period t
IHmPt Inventory holding cost of medicines m at the LP P at the period t
IHmSt Inventory holding cost of medicines m at the warehouse S at the period t
IHmDt Inventory holding cost of medicines m at the DC D at the period t
IHmWt Inventory holding cost of medicines m at the pharmacy W at the period t
IHmHt Inventory holding cost of medicines m at the hospital H at the period t
TmPDt Transportation cost of medicines m from MP P to DC D at the period t
TmPDt Transportation cost of medicines m from LP P to DC D at the period t
TmPPt Transportation cost of medicines m from MP P to LP P at the period t
TmDSt Transportation cost of medicines m from DC D to warehouses S at the period t
TmSWt Transportation cost of medicines m from warehouse S to pharmacy W at the period t
TmSHt Transportation cost of medicines m from warehouse S to hospitals H at the period t
TmWHt Transportation cost of medicines m from pharmacy W to hospitals H at the period t
φoSt The fixed cost of opening warehouse with capacity level o at location S at the period t
φuDt The fixed cost of opening DC with capacity level u at location D at the period t
PCmPt Production cost of medicine m in the MP P at the period t
PCmPt Production cost of medicine m in the LP P at the period t
FmP Fixed emissions based on transportation of medicines m related to COVID-19 patients from MP P
VmP Variable emissions based on transportation of medicines m related to COVID-19 patients from MP P
FmP Fixed emissions based on transportation of medicines m related to COVID-19 patients from LP P
VmP Fixed emissions based on transportation of medicines m related to COVID-19 patients from LP P
FmS Fixed emissions based on transportation of medicines m related to COVID-19 patients from warehouse S
VmS Variable emissions based on transportation of medicines m related to COVID-19 patients from warehouse S
FmW Fixed emissions based on transportation of medicines m related to COVID-19 patients from pharmacy W
VmW Variable emissions based on transportation of medicines m related to COVID-19 patients from pharmacy W
FmD Fixed emissions based on transportation of medicines m related to COVID-19 patients from DC D
VmD Variable emissions based on transportation of medicines m related to COVID-19 patients from DC D
dPD Distance between MP P and DC D
dPD Distance between LP P and DC D
dPP Distance between MP P and LP P
dDS Distance between DC D and warehouse S
dSH Distance between warehouse S and hospital H
dSW Distance between warehouse S and pharmacy W
dWH Distance between pharmacy W and hospital H
ES Emissions based on inventory at the warehouse S
EP Emissions based on inventory at the MP P
EP Emissions based on inventory at the LP P
ED Emissions based on inventory at the DC D-
EH Emissions based on inventory at the hospital H
EW Emissions based on inventory at the pharmacy W
BmDSV The released CO2 emission of transported medicines m from DC D to warehouse S by vehicle V
BmPDV The released CO2 emission of transported medicines m from MP P to DC D by vehicle V
BmPDV The released CO2 emission of transported medicines m from LP P to DC D by vehicle V
BmPPV The released CO2 emission of transported medicines m from MP P to LP P by vehicle V
BmSHV The released CO2 emission of transported medicines m from warehouse S to hospital H by vehicle V
BmSWV The released CO2 emission of transported medicines m from warehouse S to pharmacy W by vehicle V
BmWHV The released CO2 emission of transported medicines m from pharmacy W to hospital H by vehicle V
EoSt The environmental aspect of opening a warehouse with capacity level o at location S at period t
EuDt The environmental aspect of opening a DC with capacity level u at location D at period t
ImPt The environmental aspect of holding medicines m at MP P at period t
ImPt The environmental aspect of holding medicines m at LP P at period t
ImSt The environmental aspect of holding medicines m at warehouse S at period t
ImDt The environmental aspect of holding medicines m at DC D at period t
ImWt The environmental aspect of holding medicines m at pharmacy W at period t
ImHt The environmental aspect of holding medicines m at hospital H at period t
KoS The number of job opportunities created by opening a warehouse with capacity level o at location S
KuD The number of job opportunities created by opening a DC with capacity level u at location D
RS The rate of unemployment at warehouse S
RD The rate of unemployment at DC D
LS The regional of developed level at warehouse S
LD The regional of developed level at DC D
ϖmax The maximum of social aspect relevant to the balanced service of COVID-19 patients
ξmax The maximum of social aspect relevant to the balanced economic development
ϖmin The minimum of social aspect relevant to the balanced service of COVID-19 patients
ξmin The minimum of social aspect relevant to the balanced economic development
α The weight of social aspect relevant to the balanced service of COVID-19 patients
β The weight of social aspect relevant to the balanced economic development
CP The rate of minimum capacity utilization of MP P
CP The rate of minimum capacity utilization of LP P
CD The rate of minimum capacity utilization of DC D
CS The rate of minimum capacity utilization of warehouse S
CW The rate of minimum capacity utilization of pharmacy W
CH The rate of minimum capacity utilization of hospital H
CPPt The capacity of maximum medicine of MP P with capacity level at period t (ton)
CPPt The capacity of maximum medicine of LP P with capacity level at period t (ton)
CDuDt The capacity of maximum medicine of DC D with capacity level u at period t (ton)
CSoSt The capacity of maximum medicine of warehouse S with capacity level o at period t (ton)
CWμWt The capacity of maximum medicine of pharmacy W with capacity level μ at period t (ton)
CHεHt The capacity of maximum medicine of hospital H with capacity level ε at period t (ton)
Ω The released NO through transport
π The released C6H6 through car exhaust
Q The released CO through car exhaust and the opening of the medicine warehouses, DCs
Λ The released SO2 through fuel burning
ϑ The released PM2,5 through exhaust gases, transport, mechanical processes, biological processes
GSo The economic value of warehouse S with capacity level o
GDu The economic value of DC D with capacity level u
λS Efficiency of warehouse S
λD Efficiency of DC D
YSW The coefficient of penalty for the first metrics of resilience among warehouse S and pharmacy W
YSH The coefficient of penalty for the first metrics of resilience among warehouse S and hospital H
YDS The coefficient of penalty for the first metrics of resilience among DC D and warehouse S
YPD The coefficient of penalty for the first metrics of resilience among MP P and DC D
YPD The coefficient of penalty for the first metrics of resilience among LP P and DC D
ΦD The coefficient of penalty for the second metrics of resilience of DCs D
ΦS The coefficient of penalty for the second metrics of resilience of warehouses S
τD The coefficient of penalty for the third metrics of resilience of DCs D
τS The coefficient of penalty for the third metrics of resilience of warehouses S