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Table 4 Indexes, parameters, and variable sets

From: Managing daily surgery schedules in a teaching hospital: a mixed-integer optimization approach

Sets
S Set of surgeries s to be scheduled in a surgical day
S k Subset of surgeries (S) that can be performed by surgeon k
S r Subset of surgeries (S) that can be performed in room r
R Set of operating rooms r
K Set of surgeons k
Parameters
TP s Preparation time (preincision time) of the surgery s
TS sk Surgery time (incision time) of the surgery s by surgeon k
TC s Cleanup time (postincision time) of the surgery s
CV Cost per minute of having an OR vacant
CW Cost per minute of having the surgeon waiting
CO Cost per minute of using an OR beyond the normal shift length T
T Shift length
PT Pause between surgeries done by the same surgeon
MOT Maximum overtime
MaxS Maximum number of surgeries performed by a surgeon
M A large scalar value
Variables
x sr Binary variable; 1 if surgery s S is done in room r R, 0 otherwise
y ss’k Binary variable; 1 if sS precedes s'Sand is done by the same surgeon kK, 0 otherwise
z ss’kk’ Binary variable; 1 if s precede s'S and it is done by different surgeon k and k'K, 0 otherwise
q sk Binary variable; 1 if surgery s S is done by surgeon k K, 0 otherwise
msR r Non negative variable equal to the make span of room r R
msS k Non negative variable equal to the make span of surgeon k K
ts s Non negative variable equal to the start time of the surgery sS
tsS k Non negative variable equal to the start time of the surgeon k K
vt Non negative variable equal to the vacant time
ot r Non negative variable equal to the overtime of room r R
wt k Non negative variable equal to the waiting time of a surgeon k K
tc Total cost