Table 4 Indexes, parameters, and variable 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 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