Driver Assignment system for Metro S.A.

Transcription

1 Driver Assignment system for Metro S.A. Victor Mateluna Ximena Schultz Department of Planning, Programming and Control Metro de Santiago Chile 1

2 INTRODUCTION For Metro de Santiago, the process of scheduling trains and drivers is one of the main tasks in running every day operations This process is completed in three separate stages Train Scheduling HASTUS Driving Duties Assignment of drivers CACTUS 2

3 INTRODUCTION: Train Scheduling Train Scheduling Trip Number of trips that our trains must take in order to serve our customers 3

4 INTRODUCTION: Driving Duties Driving Duty Trip Driving Duties Grouping these trips together in order to create driving duties A driving duty is a certain amount of trips that one person is able to drive in one shift 4

5 INTRODUCTION: Assignment of drivers Assignment of drivers Assign the driving duties to the drivers along with other types of responsibilities For a period of one to two weeks at a time The system assigns about 900 drivers to approximately 3,200 duties a week 5

6 Assignment of drivers: Types of Drivers Four Types of Drivers: Regular Full Time Drivers Flexible Full Time Drivers Regular Part Time Drivers Weekend Part Time Drivers 6

7 Assignment of drivers: Types of Drivers Four Types of Drivers: Regular Full Time Drivers 44 or 45 hours a week Minimum/Maximum of driving hours a day Training Assign to a Line and a Terminal Assign to a shift Special type of rotation: 5 days on 2 days off 6 days on 2 days off In what week of their rotation they are Special sequence 7

8 Assignment of drivers: Types of Drivers Four Types of Drivers: Flexible Full Time Drivers 44 or 45 hours a week Minimum/Maximum of driving hours a day Training Flexible in terms of line, terminal and shift At least 9 hours off between shifts Special type of rotation: 5 days on 2 days off 6 days on 2 days off 5 days on 2 days off (not together) In what week of their rotation they are Mo Tu We Th Fr R Sa R R Su R R R R R R R 8

9 Assignment of drivers: Types of Drivers Four Types of Drivers: Regular Part Time Drivers 30 or 45 hours a week Minimum/Maximum of driving hours a day Training Availability Flexible in terms of line, terminal and shift At least 9 hours off between shifts At most 6 days 2 Sundays off a month 9

10 Assignment of drivers: Types of Drivers Four Types of Drivers: Saturdays, Sundays and Holidays Minimum/Maximum of driving hours a day Training Flexible in terms of line, terminal and shift At least 9 hours off between shifts Weekend Part Time Drivers 10

11 PROCESS: Assignment of drivers We divide this process into two steps: Assigning duties to Full Time drivers (regular and flexible) Assigning the remaining duties to Part Time drivers (regular and weekend s) 11

12 PROCESS: Assignment of drivers The method used to assign duties is very similar for both steps It consists of an iterative process in which a duty is assigned to a driver This process is run for a period of one or two weeks at a time Four stages: Evaluation Duty ranking Drivers ranking Assignment 12

13 PROCESS: Evaluation Every duty is connected to each driver that is able to work that duty Main Constraints involved: Availability Training Minimum/Maximum driving hours Maximum working hours Line, terminal and shift Days off Duty Nº11131 Driver 1 Driver 44 Driver 98 13

14 PROCESS: Duty Ranking Duties are ranked in terms of connections they posses Every time a driver is assigned to a duty, this rank measure changes for all of the remaining duties 14

15 PROCESS: Drivers Ranking A rank measure is calculated for each driver, which involves: The Amount of worked hours vs. contracted hours during the analysed period The Amount of duties he can perform Drivers are sorted by this rank measure Every time a driver is assigned to a duty, this rank changes for that driver, due to the fact that he is now working more hours than before 15

16 PROCESS: Assignment It consists of deciding which driver will perform which duty Consider every duty on the analyzed period Assign the most critical duty to the driver with the better rank measure that is connected to it Duty ranking and driver ranking are recalculated due to this assignment It then checks the next most critical duty and assigns it to the better ranked driver that is connected to it It will continue like this until it checks every duty If no feasible solution is found it will go back to the previous duty and will choose a different solution 16

17 PROCESS: Assignment Once a feasible solution is found a total rank measure for the entire solution is calculated as the standard deviation of the worked hours vs. the contracted hours for every driver 2 WHi WH i represents the worked hours of the driver i 1 WHi i CHi σ = D i CHi D D is the total amount of drivers CH i represents the contracted hours of the driver i The objective function is to minimize this rank measure. Not all the possible solutions are checked but only those connections with similar ranking are checked It takes 2 hours to solve the problem for a one week period 17

18 Conclusions The percentage of error in the objective function Reduction of time: 95% Compared to HASTUS, the reduction of time is: 70% Testing different cost structures for the different drivers is currently under development CACTUS was developed in house, so we are able to make adjustments in case we need them Less than 5% It is easy to adapt to other companies that have similar problems to solve 18

19 Driver Assignment system for Metro S.A. Victor Mateluna Ximena Schultz Department of Planning, Programming and Control Metro de Santiago Chile 19