1. 2nd Lieutenant Antonios Fragkogios Aircraft Engineer, Ph.D. Candidate
UNIVERSITY OF THESSALY
POLYTECHNIC SCHOOL
DEPARTMENT OF MECHANICAL ENGINEERING
Division of Production Management & Industrial Administration
«A Pure Integer Mathematical Formulation for the Technical Support of the Daily Flight Schedule by the Flight Line in an Air Force Squadron»
2nd Lieutenant Antonios Fragkogios
Aircraft Engineer, Ph.D. Candidate
Dr. Georgios K.D. Saharidis
Assistant Professor

2. AIM
The fair assignment of the workload of the Flight Line of an Air Force Squadron among its technicians through an assignment model using Integer Programming
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

3. PRESENTATION STRUCTURE
FLIGHT LINE
PROBLEM DESCRIPTION
MATHEMATICAL MODEL
VISUAL BASIC CODE
EXAMPLE
CONCLUSION
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

4. BASE MAINTENANCE SQUADRON
FLIGHT LINE
COMBAT WING
WAR SQUADRONS
BASE MAINTENANCE SQUADRON
OTHER SQUADRONS
FLIGHT LINE
MAINTENANCE HANGAR
WEAPONS
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

5. FLIGHT LINE Flight Line Officer Technical Inspectors Technicians
MAIN TASK:
Inspection and servicing of Squadron’s Aircrafts performing flight
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

6. PRESENTATION STRUCTURE
FLIGHT LINE
PROBLEM DESCRIPTION
MATHEMATICAL MODEL
VISUAL BASIC CODE
EXAMPLE
CONCLUSION
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

7. PROBLEM DESCRIPTION Daily Flight Schedule
READINESS
1st WAVE
2nd WAVE
A/C S/N
Ready Time 01
7:00 04
7:30 08
11:50 02 05
8:30 09 06 07
12:05
 09
8:45 10 11
12:30 12
BACK-UP
 03
Daily Flight Schedule
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

8. No of Technicians needed
PROBLEM DESCRIPTION
3 main tasks performed by the technicians:
Pre (Pre-Flight Inspection)
Launch (Launch)
Post (Post-Flight Inspection)
Task
Duration (mins)
No of Technicians needed
Pre 60 1
Launch 45
Flight
Post 75
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

9. PROBLEM DESCRIPTION Task Timetable Ready Time Start of Pre
Take-off Time
Landing Time
Finish of Post
60 mins
45 mins
60 mins
75 mins
45 mins
60 mins
75 mins
Flight
Flight
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

10. PRESENTATION STRUCTURE
FLIGHT LINE
PROBLEM DESCRIPTION
MATHEMATICAL MODEL
VISUAL BASIC CODE
EXAMPLE
CONCLUSION
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

11. MATHEMATICAL MODEL Assignment Problem:
Assign a number of agents to a number of tasks
Sets & Subscripts:
TECHNICIANS Subscript: i
Tasks PRE Subscript: j
Tasks LAUNCH Subscript: j
Tasks POST Subscript: j
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

12. MATHEMATICAL MODEL Binary Decision Variables:
xPre [i,j]
xLaunch [i,j]
xPost [i,j]
=1, if technician i is assigned to task j
=0, if technician i is NOT assigned to task j
General Integer Decision Variables:
upper1: Max number of tasks assigned to one Technician
lower1: Min number of tasks assigned to one Technician
upper(2-4): Max number of (PPE-Diwximo-MPE) assigned to one Technician
lower(2-4): Min number of (PPE-Diwximo-MPE) assigned to one Technician
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

13. Multi-criteria problem
MATHEMATICAL MODEL
Multi-criteria problem
Goal: The fair assignment of tasks among the technicians
Each type of task requires different labor and has a different duration
Minimize the difference between the max and the min No of tasks of each type and in total that are assigned to each technician
4 Objective Functions:
Difference1=upper1-lower1
Difference2=upper2-lower2
Difference3=upper3-lower3
Difference4=upper4-lower4
minimize
The sum of all tasks
Only PRE
Only LAUNCH
Only POST
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

14. 1. Every task has to be assigned to exactly one technician.
MATHEMATICAL MODEL
Constraints:
1. Every task has to be assigned to exactly one technician.
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

15. MATHEMATICAL MODEL Constraints:
2. What is the maximum and the minimum number of tasks (ALL) assigned to a technician?
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

16. MATHEMATICAL MODEL Constraints:
3. What is the maximum and the minimum number of tasks (PRE-FLIGHT) assigned to a technician?
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

17. MATHEMATICAL MODEL Constraints:
4. What is the maximum and the minimum number of tasks (LAUNCH) assigned to a technician?
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

18. MATHEMATICAL MODEL Constraints:
5. What is the maximum and the minimum number of tasks (POST-FLIGHT) assigned to a technician?
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

19. MATHEMATICAL MODEL Constraints:
6. What is the difference between the maximum and the minimum number of tasks (ALL, PRE, LAUNCH, POST) assigned to a technician?
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

20. MATHEMATICAL MODEL Constraints:
7. Every technician is assigned to 2 Pre-flight inspections at most
8. Every technician is assigned to 1 Launch at least
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

21. MATHEMATICAL MODEL Constraints:
9. Time overlap between the tasks-Every technician cannot be assigned to 2 or more tasks that overlap each other.
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

22. 10. The technician who prepares an A/C will perform its Launch
MATHEMATICAL MODEL
Constraints:
10. The technician who prepares an A/C will perform its Launch
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

23. MATHEMATICAL MODEL Constraints:
11. The first Pre’s and the last Post’s of each day are performed by the technicians “ON DUTY”
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

24. NO DATA… MATHEMATICAL MODEL Data?
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

25. Differ every day depending on the daily flight schedule
MATHEMATICAL MODEL
Constraints:
Every technician is assigned to 2 Pre at most
Every technician is assigned to 1 Launch at least
Only the tasks between 07:15 and 14:45 will be assigned
Time overlap between the tasks
The technician who prepares an A/C will perform its Launch
The first Pre’s and the last Post’s of each day are performed by the technicians “ON DUTY”
Differ every day depending on the daily flight schedule
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

26. MATHEMATICAL MODEL AMPL (Free Edition): .txt file: model
300 integer variables
CPLEX solver
.txt file: model
.txt file: data
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

27. PRESENTATION STRUCTURE
FLIGHT LINE
PROBLEM DESCRIPTION
MATHEMATICAL MODEL
VISUAL BASIC CODE
EXAMPLE
CONCLUSION
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

28. VISUAL BASIC CODE Daily problem Constraints differ every day
Automation of the procedure of building the mathematical model
model and data files
Constraints and Data
Visual Basic Code
Excel File
AMPL
Results file
Results
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

29. PRESENTATION STRUCTURE
FLIGHT LINE
PROBLEM DESCRIPTION
MATHEMATICAL MODEL
VISUAL BASIC CODE
EXAMPLE
CONCLUSION
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

30. EXAMPLE Interaction sheet
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

31. EXAMPLE Task Timetable
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

32. EXAMPLE Final Task Timetable
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

33. EXAMPLE Αρχεία model και data
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

34. Solving the multi-criteria problem using AMPL
EXAMPLE
Solving the multi-criteria problem using AMPL
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

35. EXAMPLE Solving the multi-criteria problem using AMPL
model fl_model.txt
data fl_data.txt
option solver cplex;
objective ALL;
solve;
fix Difference1;
objective only_PRE;
fix Difference2;
objective only_LAUNCH;
fix Difference3;
objective only_POST;
fix Difference4;
The problem is solved 4 times and every time the value of the minimized objective function is kept fixed.
Save the results in file results.txt
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

36. EXAMPLE
Results
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

37. PRESENTATION STRUCTURE
FLIGHT LINE
PROBLEM DESCRIPTION
MATHEMATICAL MODEL
VISUAL BASIC CODE
EXAMPLE
CONCLUSION
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

38. CONCLUSION
The assignment of Flight Line’s tasks among its technicians in the fairest way is a difficult problem solved every day by the Flight Line Officer
The fairest feasible solution of the problem, which arises from every day’s flight schedule, can be found by using Integer Programming and modeling the task timetable
Automatic way through Visual Basic in order to build every day’s model and print the results
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

39. CONCLUSION
Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

40. Thank you for your attention
Questions ?
Thank you for your attention