1. Tabu Search for Solving Personnel Scheduling Problem
Amol C. Adamuthe
Rajankumar S. Bichkar
Presenter: Aaron Leonard
CS 6385
Nov 9, 2016

2. Personnel scheduling problem
Special case of Constraint Satisfaction Problem
Assign tasks to employees
Without violating constraints
And getting the “best” assignment

3. Personnel scheduling problem
Known number of tasks in advance
Time effort required
Half day, full day, week, …
Person effort required
One person, two person, …
Priority
Dependency on other tasks

4. Personnel scheduling problem
Known set of employee personnel
Skillset
What can/can't they do?
How well can they do it?
Especially compared to their coworkers
Work schedule

5. Hard scheduling constraints
Must be satisfied, or the schedule is worthless
Task effort
Each task should have required number of personnel
Work schedule regulations
Each person should not work more than possible to schedule them
Or when they can’t be scheduled
Skillset
Task should be assigned to person with ability to do it

6. Soft scheduling constraints
OK not to satisfy, but solution is considered worse than if they had been
Task should be assigned to person with best skillset for the task
Or if not the best, then the 2nd best
Or if not the 2nd best, then the 3rd best...

7. Our personnel scheduling problem
Schedule a lab for one week of tasks
Tasks
7 tasks
Each takes whole week
Each requires 1 or 2 people
Employees
14 employees
Each employee available any given day
May work maximum of 16, 24, or 40 hours depending on employee
We know the skillsets of each
History of hours they work on each task.
More hours => bettter skill

8. Our personnel scheduling problem
Skillsets:

9. Our personnel scheduling problem
Tasks
5 tasks require 1 person
2 tasks require 2 persons

10. Tabu search Applied to any optimization problem
Neighborhood search algorithm
Start from an initial position
Search for best neighbor position
Continue until convergence, or run out of time
Keep list of “tabu” neighborhood moves, to prevent returning to previous solutions
Allow search to proceed in non optimal direction, when it can help avoid local optima
Helps “push” the solution out of local optima

11. Applying tabu search Search space Any schedule
We'll see how to restrict searching to partially feasible schedules

12. Applying tabu search Neighborhood structure
Given a schedule, how to find neighbors?
Swapping: Take two task assignments, and swap them
If person 1 has task A, person 2 has task B in first schedule
Person 1 has task B, person 2 has task A in second schedule
Neighborhood is all new schedules that we can form by 1 or 2 swaps.

13. Applying tabu search Initial position
Conventionally, pick a random schedule
Instead, we start from partially feasible schedule
Pick a schedule where work effort constraints are satisfied
Just randomly assign people to each task until that’s done
Neighborhood search won’t let this constraint become violated

14. Applying tabu search Tabu list What is tabu? Swapping
Tabu tenure length
List of size 15, FIFO behavior

15. Applying tabu search Objective function
Weighted sum of constraint violations
H is a hard constraint violated by the solution
Whether the person is assigned too much work
Whether the person is assigned a task they aren't qualified for
S is a soft constraint violated by the solution
Whether the person is assigned a task they aren't the best at
The weight for hard constraint violations should be much larger than soft constraint
Concrete numbers aren't specified in the paper

16. Applying tabu search Aspiration criteria
Should we sometimes allow tabu moves?
Allow a tabu move, if objective function value is higher than the current known maximum
Since the new solution hasn’t been seen and is better
Probabilistic neighborhood evaluation
Only evaluate a random subset of the neighborhood, to save time

17. Results Tabu will find some optimal schedule Is it globally optimal?
Search tree is gigantic, 9^70 distinct nodes
We cannot exhaustively search
Is it good?
Compare to solutions found using other algorithms
Yes

18. Evaluating schedule Enumerating skillset score
Employee has experience with 5 tasks
32 hrs, 36 hrs, 48 hrs, 64 hrs, 68 hrs
Value for task is the rank of time spent on that task
If employee is assigned that task in the schedule
In order, they receive values 1, 2, 3, 4, 5
If a schedule assigns that task, add the value to schedule’s score
Compute and sum for all employees

19. Evaluating schedule Weighted skillset score
Take variation of hours into account
Should be more precise
Employee has experience with 5 tasks
32 hrs, 36 hrs, 48 hrs, 64 hrs, 68 hrs
Value for task is the fraction of time spent on that task, compared to total hours worked in skillset
In order, they receive values 0.129, 0.145, 0.194, , 0.274
If a schedule assigns that task, add the value to schedule’s score
Compute and sum for all employees

20. Schedule quality

21. Convergence time

22. Generalizing Does it generalize?
We only tried a single problem instance so far
What happens if we try with different employee skillsets?
5 “simple” skillsets
Tabu gives better results in less time
5 “complex” skillsets
Tabu is only better in two instances

23. Generalizing 6 “simple” skillsets
Tabu gives better results in less time

24. Generalizing 4 “complex” skillsets
Tabu is only better in two instances

25. Conclusion
Defined the personnel scheduling problem as an optimization problem
Solved it using tabu search
Compared the solution to prior results, and found it to be
Better
Less time to converge
Compared prior results for new solution instances
Tabu still better at simple instances
Tabu only better in 2 of 4 of complex instances