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Medical School internships. Jacques A. Ferland, Dept. Inf. Rech. Oper., Univ. de Montréal, Canada Soumia Ichoua, Dept. Inf. Rech. Oper., Univ. de Montréal, Canada Alain Lavoie, Dept. Inf. Rech. Oper., Univ. de Montréal, Canada Eric Gagné, Dept. Inf. Rech. Oper., Univ. de Montréal, Canada. - PowerPoint PPT Presentation
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Medical School internships
Jacques A. Ferland, Dept. Inf. Rech. Oper., Univ. de Montréal, Canada
Soumia Ichoua, Dept. Inf. Rech. Oper., Univ. de Montréal, Canada
Alain Lavoie, Dept. Inf. Rech. Oper., Univ. de Montréal, Canada
Eric Gagné, Dept. Inf. Rech. Oper., Univ. de Montréal, Canada
Problem description
• Medical School students complete several internships before coming full members of their guild.
• The number of internships, their subject area, their length, depend of the student specialization.
• The internships have to be completed in different hospitals.
• Medical school has to schedule these internships every year subject to several constraints in order to maximize the overall satisfaction of the students.
set of students
set of internship types
set of internships to be completed by student
set of students having to complete internship
set of hospitals o
N
f
otati
fering internship of t
on :
s
t
t
S
T
T s S
S t T
H
ype
set of periods 1, ,13 included in the planning horizon
13 periods of 4 weeks during a planning horizon of 52 weeks
the length (number of periods) of internship of student st s
t T
P
d t T s S
1 if intership of student is initiated in period at hospital
0 otherwise
Decision var
for all , ,
iable
, 3
s
1 1
:
sthp
s t st
t s p hy
s S t T h H p d
Problem formulation
set of students
set of internship types
set of internships to be completed by student
set of students having to complete internship
set of hospitals o
N
f
otati
fering intership of ty
on :
s
t
t
S
T
T s S
S t T
H
pe
set of periods 1, ,13 included in the planning horizon
13 periods of 4 weeks during a planning horizon of 52 weeks
the length (number of periods) of internship of student st s
t T
P
d t T s S
1 if intership of student is initiated in period at hospital
0 otherwise
Decision var
for all , ,
iable
, 3
s
1 1
:
sthp
s t st
t s p hy
s S t T h H p d
13 1
1
Each internship of each student must be assigned
Assi
1
for all
gnment constrain
,
ts:
std
sthph H p
s
y
s S t T
set of students
set of internship types
set of internships to be completed by student
set of students having to complete internship
set of hospital of
N
f
otati
ering intership of typ
on :
s
t
t
S
T
T s S
S t T
H
e
set of periods 1, ,13 included in the planning horizon
13 periods of 4 weeks during a planning horizon of 53 weeks
the length (number of periods) of internship of student st s
t T
P
d t T s S
1 if intership of student is initiated in period at hospital
0 otherwise
Decision var
for all , ,
iable
, 3
s
1 1
:
sthp
s t st
t s p hy
s S t T h H p d
Coefficient indicate if internship of student initiated
in period is still going on in period
1 if 0 1
Dura
0 otherwise
for a
tion of internship:
ll ,
stpp
ststpp
L t s
p p
p p dL
s S t T
, ,p p P
set of students
set of internship types
set of internships to be completed by student
set of students having to complete internship
set of hospital of
N
f
otati
ering internship of ty
on :
s
t
t
S
T
T s S
S t T
H
pe
set of periods 1, ,13 included in the planning horizon
13 periods of 4 weeks during a planning horizon of 53 weeks
the length (number of periods) of internship of student st s
t T
P
d t T s S
1 if intership of student is initiated in period at hospital
0 otherwise
Decision var
for all , ,
iable
, 3
s
1 1
:
sthp
s t st
t s p hy
s S t T h H p d
Coefficient indicate if internship of student initiated
in period is still going on in period
1 if 0 1
Dura
0 otherwise
for a
tion of internship:
ll ,
stpp
ststpp
L t s
p p
p p dL
s S t T
, ,p p P
Follow from the hospitals capacity to supervise internships
For all , ,
lower bound on the
Bound constra
number of int
ints specified by hos
ernships of type that hospital
pitals:
t
thp
t T h H p P
l t
h
can supervise during period
upper bound on the number of internships of type that hospital
can supervise during period
t
thp
thp stpp sthp ths S p P
p
u t
h p
l L y u
, ,p tt T h H p P
For some , , too
large to allow feasible solution, and
hence modify the bound constraints
t
thph H
t T p P l
or 0t t
thp stpp sthp thp stpp sthps S p P s S p P
l L y u L y
set of students
set of internship types
set of internships to be completed by student
set of students having to complete internship
set of hospital of
N
f
otati
ering internship of ty
on :
s
t
t
S
T
T s S
S t T
H
pe
set of periods 1, ,13 included in the planning horizon
13 periods of 4 weeks during a planning horizon of 53 weeks
the length (number of periods) of internship of student st s
t T
P
d t T s S
1 if intership of student is initiated in period at hospital
0 otherwise
Decision var
for all , ,
iable
, 3
s
1 1
:
sthp
s t st
t s p hy
s S t T h H p d
Coefficient indicate if internship of student initiated
in period is still going on in period
1 if 0 1
Dura
0 otherwise
for a
tion of internship:
ll ,
stpp
ststpp
L t s
p p
p p dL
s S t T
, ,p p P
13 1
1
No student has more than one internship scheduled during any period
For all ,
Student co
nflict constraints:
1std
stpp thpt T h H p
s S p P
L y
set of students
set of internship types
set of internships to be completed by student
set of students having to complete internship
set of hospital of
N
f
otati
ering internship of ty
on :
s
t
t
S
T
T s S
S t T
H
pe
set of periods 1, ,13 included in the planning horizon
13 periods of 4 weeks during a planning horizon of 53 weeks
the length (number of periods) of internship of student st s
t T
P
d t T s S
1 if intership of student is initiated in period at hospital
0 otherwise
Decision var
for all , ,
iable
, 3
s
1 1
:
sthp
s t st
t s p hy
s S t T h H p d
Linear objective function
For each of his (her) internship, student specifies in increasing
order of preference, a subset of period and a subset
of hospitals where the
Objective funct
ion:
st st
s S
P P H H
internship should be completed.
Furthermore, he (she) indicates if the period choice is more important
than the hospital choice.
Coefficient of pairs (internship, hospital) regret from best choice
13 1
1
13 1
1
Min
Subject to 1 ,
Assignment Type Problem (AT
1 ,
Model:
P)
st
st
d
sthph H p
d
stpp thpt T h H p
thp stppp P
y
y s S t T
L y s S p P
l L
, ,
or , ,
t
t
t
sthp thp ts S
thp stpp sthp thps S p P
t
stpps S p P
y u t T p P h H
l L y u
t T p P h H
L
0
0 or 1 , , ,
sthp
sthp
y
y s S t T p P h H
Apply Tabu search technique based on exchange procedures
already available to solve
Solution
this ATP
proced
pr
ure
oblem