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. 2021 Jul 28;112:107725. doi: 10.1016/j.asoc.2021.107725
Indices
b,bεB Blood types bb=B
jεJ The candidate location for establishing blood collection centers
hεH Hospitals
iεI Permanent blood centers
kεK Temporary blood centers
tεT Time periods
Parameters
bri Blood holding cost at permanent blood center i
bkk Blood holding cost at temporary blood center k
bhh Blood holding cost at hospital h
Dbht Demand for blood type b in hospital h at period t ood holding cost at h
Icbj Available inventory of blood type b in collection center j
Itbk Available inventory of blood type b in temporary blood center k
qkjk Travel time from collection centers j to temporary blood center k
qqkh Travel time from temporary blood center k to hospital h
qrji Travel time from collection centers j to permanent blood center i
qpih Travel time from permanent blood center i to hospital h
qcki Travel time from temporary blood center k to permanent blood center i
cmkh Transportation cost from temporary blood center k to hospital h
cbjk Transportation cost from collection center j to temporary blood center k
cnih Transportation cost from permanent blood center i to hospital h
cdji Transportation cost from collection center j to permanent blood center i
cfki Transportation cost from temporary blood center k to permanent blood center i
otk The operation cost of a unit of blood in a temporary blood center k
opi The operation cost of a unit of blood in a permanent blood center i
tc Operation time per unit of blood in all collection centers
cf Fixed cost for establishing a collection center
RD Rate at which process is redirected from temporary blood centers to permanent centers
ttbbh The time required to substitute a unit of blood type b with blood type b at hospital h
mc Maximum capacity for transportation between centers
oc Operation cost of a unit of blood in a collection center
ptk Operation time per unit of blood at temporary blood center k
ppi Operation time per unit of blood at permanent blood center i
rbk Blood storage capacity of temporary blood center k
rri Blood storage capacity of permanent blood center i
rhh Blood storage capacity of hospital h
N Maximum number of collection centers to be opened
npbb Substitution priority for using blood type b instead of blood type b
nbbb 1 if blood type b can substituted by blood type b, 0 otherwise
M A big number
bl Blood lifespan
Decision Variables
gbht Amount of blood type b expired in hospital h at period t
obkt Amount of blood type b expired in temporary center k at period t
kbit Amount of blood type b expired in permanent center i at period t
abkit Amount of blood type b transferred from temporary center k to permanent center i at period t
qbkht Amount of blood type b transferred from temporary center k to hospital h at period t
hbiht Amount of blood type b transferred from permanent center i to hospital h at period t
jbkt Amount of blood type b processed at temporary center k at period t
ubit Amount of blood type b tested at permanent center i at period t
zbit Amount of blood type b stored at permanent center i at period t
ebkt Amount of blood type b stored at temporary center k at period t
αbht Amount of blood type b stored at hospital h at period t
rbbht Amount of blood type b substituted with blood type b at hospital h at period t
siht 1 if blood transfer is opened from permanent center i to hospital h at period t, 0 otherwise
wjkt 1 if collection center j is allocated to temporary center k at period t, 0 otherwise
vjit 1 if collection center j is allocated to permanent center i at period t, 0 otherwise
xjt 1 if a collection center is opened in location j at period t, 0 otherwise
fkht 1 if blood transfer is opened from temporary center k to hospital h at period t, 0 otherwise
ykit 1 if blood transfer is opened from temporary center k to permanent center i at period t, 0 otherwise