From: Managing daily surgery schedules in a teaching hospital: a mixed-integer optimization approach
Sets | |
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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 s∈S precedes s'∈Sand is done by the same surgeon k∈K, 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 s∈S |
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 |