1. Viviane Gascon François Meunier UQTR INFORMS Healthcare 2011 1

2.  A public medical clinic offers activities to elderly at a daycare center  Users are transported to the daycare center by bus (2) or by taxi  Costs of taxis have been increasing in the last few years Questions :  Is it possible to reduce the costs related to the use of taxis ?  What would be the impact on the buses routes ? INFORMS Healthcare 2011 2

3.  Cost analysis  Determining new routes  Greedy algorithm  Ant colony heuristic  Interface INFORMS Healthcare 2011 3

4. Cost analysis: economy if reduction of total distance ◦ Bus 1: $1.283 /km ◦ Bus 2: $1.68 /km Taxis The costs vary with the #km traveled and the #users in a taxi on a given trip. Increase the #users traveled by bus if it costs less than by taxis Increase the #users traveled by bus if it costs less than by taxis Determine new routes Determine new routes INFORMS Healthcare 2011 4

5. Users  type of mobility: on foot, wheelchair, walker  living in a nursing home or not (they must come back to their nursing home for lunch)  with or without cognitive problems (users with cognitive problems must be in homogenous groups and stay the whole day)  visit frequency: once or twice a week  length of visit: half day or whole day  48 users on average per day INFORMS Healthcare 2011 5

6. Two buses  each bus covers a sector  bus capacity varies with users’ type of mobility (users with wheelchairs and walkers take more space reducing the bus capacity) INFORMS Healthcare 2011 6

7. Route constraints  total duration must not exceed 60 minutes (including traveling time and service time)  sector 1: three pick up and return routes per day  sector 2: two pick up and return routes from Monday to Wednesday, one on Thursday and three on Friday INFORMS Healthcare 2011 7

8.  Position users on a map: two sectors are considered, one for each bus  Define new clusters of users for each sector, for each day INFORMS Healthcare 2011 8

9.  Generate new routes ◦ keep same days of visit for users with cognitive problems (Tuesday and Friday) and add some users actually traveled by taxi ◦ Regroup users living in nursing home and users with cognitive problems on same days, if possible ◦ no transfer of users actually traveled by bus to taxis ◦ transfer users actually traveled by taxi to buses if it induces a cost reduction INFORMS Healthcare 2011 9

10.  Sector 1 ◦ 7% reduction of total traveling time ◦ 11% reduction of total distance ◦ 3 taxi users added to routes ◦ reduction of $93 per week on cost: considering 45 operating weeks this a reduction of $4,100 per year  Sector 2 ◦ 1.3% increase of total traveling time ◦ 8% increase of total distance ◦ 17 taxi users added to routes ◦ reduction of $85 per week on cost: considering 45 operating weeks this a reduction of $3,100 per year INFORMS Healthcare 2011 10

11. Consider m ants Start with an initial solution for each ant k ◦ contruct a route with all users ◦ ij = 1 for all edges ( i,j ) and all k Update pheromone trails Find new routes End if termination conditions satisfied INFORMS Healthcare 2011 11

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13. Parameters Probability of an ant k selecting an edge ( i,j ) INFORMS Healthcare 2011 13

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15. Values of parameters INFORMS Healthcare 2011 15

16. Offers the possibility to:  optimize routes when locations of users are known  visualize routes  generate detailed instructions to follow the route  keep routes in a data base for a later use  modify routes if new users are added or removed or if the type of mobility is modified  interact with GoogleMap INFORMS Healthcare 2011 16

17. INFORMS Healthcare 2011 17 Interface

18. INFORMS Healthcare 2011 18 Interface

19. INFORMS Healthcare 2011 19 Interface

20.  Asymmetric TSP problem with additional constraints  Use of heuristics to solve the problem: greedy algorithm and ant colony approach  Significant improvement of actual solutions with a simple greedy heuristic  User friendly tool to help administrators generate routes on an everyday basis INFORMS Healthcare 2011 20