Viviane Gascon François Meunier UQTR INFORMS Healthcare 2011 1.

Viviane GasconViviane GasconFrançois MeunierFrançois Meunier

UQTRUQTR

INFORMS Healthcare 2011INFORMS Healthcare 2011 1

A public medical clinic offers activities to elderly at a A public medical clinic offers activities to elderly at a daycare centerdaycare center

Users are transported to the daycare center by bus (2) Users are transported to the daycare center by bus (2) or by taxior by taxi

Costs of taxis have been increasing in the last few yearsCosts of taxis have been increasing in the last few years

QuestionsQuestions : : Is it possible to reduce the costs related to the use of Is it possible to reduce the costs related to the use of

taxis ?taxis ? What would be the impact on the buses routes ?What would be the impact on the buses routes ?

INFORMS Healthcare 2011INFORMS Healthcare 20112

Cost analysisCost analysis Determining new routesDetermining new routes Greedy algorithmGreedy algorithm Ant colony heuristicAnt colony heuristic InterfaceInterface


Cost analysis: economy if reduction of total distanceCost analysis: economy if reduction of total distance◦ Bus 1Bus 1: $1.283 /km: $1.283 /km◦ Bus 2Bus 2: $1.68 /km: $1.68 /km

TaxisTaxisThe costs vary with the #km traveled and the #users in a taxi on The costs vary with the #km traveled and the #users in a taxi on

a given trip.a given trip.

Increase the #users traveled by bus if it costs less than Increase the #users traveled by bus if it costs less than by by taxistaxis Determine new routesDetermine new routes


UsersUsers

type of mobility: on foot, wheelchair, walkertype of mobility: on foot, wheelchair, walker living in a nursing home or notliving in a nursing home or not

(they must come back to their nursing home for lunch)(they must come back to their nursing home for lunch) with or without cognitive problemswith or without cognitive problems

(users with cognitive problems must be in homogenous groups and stay (users with cognitive problems must be in homogenous groups and stay the whole day)the whole day)

visit frequency: once or twice a weekvisit frequency: once or twice a week length of visit: half day or whole daylength of visit: half day or whole day 48 users on average per day48 users on average per day


Two busesTwo buses

each bus covers a sectoreach bus covers a sector bus capacity varies with users’ type of mobilitybus capacity varies with users’ type of mobility

(users with wheelchairs and walkers take more space reducing the bus (users with wheelchairs and walkers take more space reducing the bus capacity)capacity)


Route constraintsRoute constraints

total duration must not exceed 60 minutestotal duration must not exceed 60 minutes(including traveling time and service time)(including traveling time and service time)

sector 1: three pick up and return routes per daysector 1: three pick up and return routes per day sector 2: two pick up and return routes from Monday to sector 2: two pick up and return routes from Monday to

Wednesday, one on Thursday and three on FridayWednesday, one on Thursday and three on Friday


Position users on a map: two sectors are considered, Position users on a map: two sectors are considered, one for each busone for each bus

Define new clusters of users for each sector, for each Define new clusters of users for each sector, for each dayday


Generate new routes Generate new routes ◦ keep same days of visit for users with cognitive problems keep same days of visit for users with cognitive problems

(Tuesday and Friday) and add some users actually traveled by (Tuesday and Friday) and add some users actually traveled by taxitaxi

◦ Regroup users living in nursing home and users with cognitive Regroup users living in nursing home and users with cognitive problems on same days, if possibleproblems on same days, if possible

◦ no transfer of users actually traveled by bus to taxisno transfer of users actually traveled by bus to taxis◦ transfer users actually traveled by taxi to buses if it induces a transfer users actually traveled by taxi to buses if it induces a

cost reductioncost reduction


Sector 1Sector 1◦ 7% reduction of total traveling time 7% reduction of total traveling time ◦ 11% reduction of total distance11% reduction of total distance◦ 3 taxi users added to routes3 taxi users added to routes◦ reduction of $93 per week on cost: considering 45 operating weeks reduction of $93 per week on cost: considering 45 operating weeks

this a reduction of $this a reduction of $4,100 per year4,100 per year

Sector 2Sector 2◦ 1.3% increase of total traveling time 1.3% increase of total traveling time ◦ 8% increase of total distance8% increase of total distance◦ 17 taxi users added to routes17 taxi users added to routes◦ reduction of $85 per week on cost: considering 45 operating weeks reduction of $85 per week on cost: considering 45 operating weeks

this a reduction of $this a reduction of $3,100 per year3,100 per year


Consider m antsConsider m antsStart with an initial solution for each ant Start with an initial solution for each ant kk◦ contruct a route with all userscontruct a route with all users◦ ijij = 1 for all edges ( = 1 for all edges (i,ji,j) and all ) and all kk

Update pheromone trailsUpdate pheromone trailsFind new routesFind new routesEnd if termination conditions satisfiedEnd if termination conditions satisfied


ParametersParameters

Probability of an ant Probability of an ant kk selecting an edge ( selecting an edge (i,ji,j) )


( , )ij i j amount of pheromone on 1

ij ijij

d i jd

where is the distance between and

ki kΝ feasible neighborhood of ant

ki

ij ijkij

il ill N


1

0 1

( 1) (1 ) ( ) ( ) ,

where is the trail evaporation rate and is the number of ants

at iteration m

kij ij ij

k

m

t t t t

1( , )

( )

0

k kij

i j kL t

if arc is used by ant

otherwise

( ) ( , )

( )

amount of pheromone ant deposits on arc

length of the th ant's tour

kij

k

t k i j

L t k

Values of parametersValues of parameters


1

1

0,1

1 for all edgesinitial

Offers the possibility to:Offers the possibility to: optimize routes when locations of users are knownoptimize routes when locations of users are known visualize routesvisualize routes generate detailed instructions to follow the routegenerate detailed instructions to follow the route keep routes in a data base for a later usekeep routes in a data base for a later use modify routes if new users are added or removed or if modify routes if new users are added or removed or if

the type of mobility is modifiedthe type of mobility is modified interact with GoogleMapinteract with GoogleMap



InterfaceInterface

INFORMS Healthcare 201118

InterfaceInterface


InterfaceInterface

Asymmetric TSP problem with additional constraintsAsymmetric TSP problem with additional constraints Use of heuristics to solve the problem: greedy Use of heuristics to solve the problem: greedy

algorithm and ant colony approachalgorithm and ant colony approach Significant improvement of actual solutions with a Significant improvement of actual solutions with a

simple greedy heuristicsimple greedy heuristic User friendly tool to help administrators generate User friendly tool to help administrators generate

routes on an everyday basisroutes on an everyday basis


Viviane Gascon François Meunier UQTR INFORMS Healthcare 2011 1.

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