Train Crew Rostering Application

1
Train Crew Rostering Application

• Mantas Gudynas
• School of Computing,
• University of Leeds
• 2008

2
The Problem

• The company has
• A scheduled trains timetables
• 3 grades of catering crew
• Service Managers (SM)
• Chefs (CF)
• Customer Service Assistants (CSA)
• A number of turn each day for each grade
• A list of business rules
• The company needs
• Efficient roster (timetable) for catering crew
  obeying the constraints

3
The Rules

• Hard
• Each employee must have at least 94 rest days per
  year.
• There must be at least 12 hour gap between two
  consecutive turns.
• There must be at least 28 hours gap between two
  turns if there is a rest day between them.
• The duration of the line of work must not exceed
  48 hours.
• Every day some of turns have to be covered by
  spare turns.
• Soft
• The weekly duration of the line of work should be
  as close to 41 hours as possible.

4
Spare Turns

• Each day some of turns have to be covered by
  spare turns.
• The turns is covered by a spare turn if the spare
  one starts no more than 2 hours before the turn.
• The task of the algorithm is to find the starting
  times and durations of spare turns.
• Additional spare turns may be added at the last
  step of the algorithm to improve the efficiency
  of the whole roster.

5
Structure of the roster

• Some rest days can be turned into spare turns to
  improve the efficiency.
• Black lines separates sublinks.
• Lines in sublinks rotate on weekly basis.
• Another task for the algorithm divide lines
  into sublinks!

6
Evaluation function

• In this particular problem it is easier to say
  how bad the
• solution is therefore the penalty function is
  used.

For each line we calculate the difference
between the weekly duration and 41 hours (in
minutes), add them up and add the number of
invalid shifts (i.e. late ones followed by the
early ones) multiplied by constant (which in this
case 1000)
7
Overview of the Algorithm

• Create required number of spare turns. This is
  carried out by module based on greedy set
  covering algorithm.
• Create a list (population) of tables
  (individuals) randomly distributing turns in each
  of them.
• Repeat arbitrary number of times
• Create an empty list (new population)
• Select a number of individuals from population
  and add them to the new list.
• Select a number of individuals, change their
  structure (mutate) and add them to the new list.
• Select a number of pairs of individuals and for
  each pair produce the new one having properties
  of both parents (crossover).
• Create a sublink structure.

8
More on Algorithm

• The selection of the individual from the
  population is implemented as Roulette Wheel
  Selection algorithm
• We look for the individual with the largest
  penalty LP and set T LP 1
• Create an empty list S
• For each individual in population
• N T penalty
• Add individual to S N times
• Randomly select individual from S
• Individuals with smaller penalty have better
  chance to be selected.