medical school internships

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 hospitals o

N

f

otati

fering intership of ty

on :

s

t

t

S

T

T s S

S t T

H

pe




t T

P

d t T s S


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 hospital of

N

f

otati

ering intership of typ

on :

s

t

t

S

T

T s S

S t T

H

e




t T

P

d t T s S


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 hospital of

N

f

otati

ering internship of ty

on :

s

t

t

S

T

T s S

S t T

H

pe




t T

P

d t T s S


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



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 hospital of

N

f

otati


on :

s

t

t

S

T

T s S

S t T

H

pe




t T

P

d t T s S


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



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 hospital of

N

f

otati


on :

s

t

t

S

T

T s S

S t T

H

pe




t T

P

d t T s S


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

medical school internships

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