scatter search approach for routing home care nurses

Scatter Search Approachfor

Routing Home Care Nurses

by

B. Elbenani, University of Mohamed V, Rabat, Marocco

J.A. Ferland, University of Montreal, Canada

V. Gascon, University of Quebec at Three-Rivers, Canada

Faculty of Information Technology

University of Science

Vietnam National University of Ho Chi Minh City

March 2010

Outline Presentation

Problem

Formulation

Solution approach

Numerical results

Problem

nurses

Sector:patients

Patient: Visit time windows Duration (treatment)

Blood sample or not

Continuity of care

Nurse: regular

on call

Formulation

First set of constraints: VRPTW

Nurse Vehicule

Patient Customer

Usual formulation of VRPTW to specify a route for

each nurse over the network of the area where the

objective is to reduce the total travel cost

Formulation

Second set of constraints: Blood sample const raints

Blood sample limited time before the nurse

returned to the clinic

10h00 blood sample < 11h00

return before 11h00

blood sample < 10h00

return before 10h00

Complex constraints to be included only if the nurse

has to execute blood sample.

Formulation

salary of each nurse (labor cost)

traveling cost (from the VRPTW element)

additional cost if a patient is visited by

Components of the objectiv

a nurse

from anot

e functio

her secto

ad

n

r

:

ditional cost if a patient is not visited by

his regular nurse for the continuity of care

Current solution approach

Solution generated manually.

Solution generated for each sector individually

because the nurses and the patients belong to specific sector.

A nurse may visit patients from other sector if it is

required to complete her daily workload.

Our approach tries to comply with the sector constraint

Our solution approach

adaptive

Scatter search

memory includi

relying on an

ng pools of solu

method

tions

Scatter Search approach

Generate a set of feasible solutions for the problem.

These solutions may be improved using som

Init

e pr

ialisation

ocedure.

pA omo olng t inchese sol luding tutions, generate he best soluti a ons.

pool including

the most different from those in the first pool

Among the rest of the solutions, select a second

to explore more

extensively the feasible dom

ain.

some solutions from the pools according to some criteria.

Generate offspring solutions by (according to some operator)

different number of the selected sol

Select

reco

ution

mbining

Improve

s.

ea

Step 1

ch offspring solution according to some improving procedure.

some solutions from the pools according to some criteria.

Generate offspring solutions by (according to some operator)

different number of the selected sol

Select

reco

ution

mbining

Improve

s.

ea

Step 1

ch offspring solution according to some improving procedure.

For each offspring solution

if it is better than the worst solution in the first pool,

then it replaces the later in the first pool;

if not, and if it is more different from

Step

th

2

e

os

in the first pool

than one of the solution in the second pool, then it replaces

the later in the second pool;

otherwise, it is discarded.

If the pools have not been modified for a fixed number of iterations,

and the time limit is not reached, then repeat the to

generate a new set of feasible solutio

Step 3

initial

ns.

Otherwise,

isation

repeat if the time limit is not reStep 1 ached.





Step

th

2

e

os

in the first pool




Initialisation


Procedure to generate a feasible solution for the global problem

, determine a good solution by applying adapted

version of Tabu Search procedure

For each sec

s used to so

Phase

lve V

tor

1

RPTW


Procedure to generate a feasible solution for the global problem

, determine a good solution by applying adapted

version of Tabu Search procedure

For each sec

s used to so

Phase

lve V

tor

1

RPTW

Combine the solutions for the sectors to obtain a feasible

solution for the global p r

Phase 2

oblem.

this feasible solution for the global problem:

Eliminate some nurses having small workload by

reassingning their patients to other nurses

Apply

I

a

mp

T

rove

abu

P

S

hase 3

ear o

ch t

improve the solution of

the global problem

Initialisation

Use the former procedure to generate a set of feasible solutions

for the global problem.

Generate the pool of solutions including the best solutiofirst .

Generate the second pool of solutions inc

ns

luding the most different

from those in the firs

t pool

Step 1: recombining solutions

Procedure to generate a new offspring solution for the global problem

1. For each nurse, select a route in a solution of the pools:

Select randomly one of the two pools Select a solution in the selected pools The nurse's route in the selected solution is assigned to her roulette wheel, tournament, ...

2. Repair process to generate a new solution:

Combine the nurse routes

If a patient is visited by several nurses, eliminate him in

all these routes, except one

in the first route encountered

in the best solution

in the follow up nurse's route

Assign left out patient follow up nurse

nurse from his sector

nurse from other sector

new fictitious nurse

Procedure to generate a new offspring solution for the global problem1. For each nurse, select a route in a solution of the pools:

Select randomly one of the two pools Select a solution in the selected pools The nurse's route in the selected solution is assigned to her

2. Repair process to generate a new solution:

Combine the nurse routes If a patient is visited by several nurses, eliminate him in

all these routes, except one

Assign left out patient

3. Generate an offspring solution Redifine new sector including patients visited by

the nurses of the sector in the current solution

Solve the problem for each sector using an adapted

Tabu Search procedure

The initial solution for the global problem

is generated from those for the sectors.

Apply a Tabu Search to improve this solution of

the global problem

If the pools have not been modified for a fixed number of iterations,

and the time limit is not reached, then repeat the to

generate a new set of feasible solutio

Step 3

initial

ns.

Otherwise,

isation

repeat if the time limit is not reStep 1 ached.





Step

th

2

e

os

in the first pool




Numerical Results

Numerical results

Numerical results for parameters with different problems

Problem Mean cost Mean # nurses

Mean # patients without

follow-up

Mean time(sec.)

Day 1 Our sol. 9050.6 12.0 0.8 589.1

CLSC 9623.0 13.0 0.0 -

Day 2 Our sol. 9545.0 14.0 1.0 651.7

CLSC 10673.0 16.0 0.0 -

Day 3 Our sol. 9998.2 13.0 0.0 408.5

CLSC 11413.0 15.0 0.0 -

Problem # of patients

# of regular nurses

# of nurses from the recall list

% of visits with blood

sample

# patients with follow-

up

Day 1 84 9 4 34.5 34

Day 2 92 13 3 45.6 38

Day 3 82 9 6 23.1 34

Real Data

Reducing the number of nurses

Mean number of patient

without follow up

Contraintes de prises de sang

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(11)

(12)

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(17)

scatter search approach for routing home care nurses

Documents

regular nurses

university of quebec

university of montreal

university of mohamed

blood sample

recall list