Skip to main content
. 2022 Nov 22;175:108821. doi: 10.1016/j.cie.2022.108821
Set of indices
j Index of DCjj=1,,J
i Index of RCWsi=1,,I
p Index of relief items p=1,,P
h Index of THsh=1,,H
k Index of ECsk=1,,K
m Index of AAsm=1,,M
t Index of periods t=1,,T
x Index of periods x=1,,X
s Index of scenarios s=1,,S
f Index of fleet types f=1,,F
Parameters
IHCpj Inventory holding cost at DCj for product p
ICDj Institution cost of DCj
ICHh Institution cost of THh
TCpfts Transportation cost for product p using fleet type f at period t(tomans/(km. kg))in scenario s
PCSpk Penalty cost of shortage of product p in ECk
PCSupk Penalty cost of surplus of product p in ECk
dijfs Distance between RCWi and DCj with fleet type f in scenario s
djkfs Distance between DCj and ECk with fleet type f in scenario s
djhfs Distance between DCj and THh with fleet type f in scenario s
PCS´ph Penalty cost of shortage of product p in THh
PCSuph Penalty cost of surplus of product p in THh
imppk Importance of product p at ECk
imp´ph Importance of product p at THh
CapFf Capacity of fleet type f
CapH´hs Capacity of THh in scenario s
CapDjs Capacity DCj in scenario s
CapECks Capacity of ECk in scenario s
M Big M
Volp Volume of product p
Asf Average speed of fleet type f
αp Consumption coefficient of product p
PSs Probability of occurrence of scenario s
t´mhs Transferring time of patients from AAm to THh in scenario s
tmks Transferring time of patients from AAm to ECk in scenario s
MDCs Maximum number of distribution centers that can be instituted under scenario s
MNFf Maximum number of fleet type f that can be used
P1 infection rate of COVID-19 in AAs
P2 infection rate of COVID-19 in ECs
Opmts Total population in AAm that should be transferred to EC s at period t in scenario s
PCOmts Total population in AAm that should be transferred to THh at period t in scenario s
PAmts Population should be evacuated in AAm at period t in scenario s
Decision variables
Qpjhfts Quantity of delivered product p from DCj to THh using fleet f at period t in scenario s
Qpijfts Quantity of delivered product p from RCLi to DCj using fleet f at period t in scenario s
Qpjkfts Quantity of delivered product p from DCj to ECk using fleet f at period t in scenario s
numFfijts Number of fleet type f from RCLi to DCj at period t in scenario s
numF´fijts Number of fleet type f from DCj to ECk at period t in scenario s
numF´´fijts Number of fleet type f from DCj to THh at period t in scenario s
Ipjts Inventory level of product p in DCj at period t in scenario s
THhs (Binary variable) = 1, if THh is opened in scenario s; ow = 0
ECks (Binary variable) = 1, if ECk is used in scenario s; ow = 0
TDCjs (Binary variable) = 1, if DCj is opened in scenario s;ow = 0
Zphts2 Surplus amount of product p in THh at period t in scenario s
Zphts3 Shortage amount of product p in THh at period t in scenario s
Z´pkts2 Surplus amount of product p in ECk at period t in scenario s
Z´pkts3 Shortage amount of product p in ECk at period t in scenario s
P´mhts Number of symptomatic patients transferred from AAm to THh at period t in scenario s
Pmkts Number of affected people transferred from AAm to ECk at period t in scenario s
p´´khts Number of infected cases in ECk detected by IoT system and transferred to THh at period t in scenario s
Pk´´kxs Number of people entering in ECk at period x in scenario s from AA s
PChxs Number of people entering in THh at period x in scenario s from AA s
RQCpkts Required demand of product p by ECk at period t in scenario s
RQHphts Required demand of product p by THh at period t in scenario s