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2 nd 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 ».

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2 nd Lieutenant Antonios Fragkogios Aircraft Engineer, Ph.D. Candidate

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  1. 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 AntoniosFragkogios 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. 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 Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

  8. PROBLEM DESCRIPTION 3 main tasks performed by the technicians: • Pre (Pre-Flight Inspection) • Launch (Launch) • Post (Post-Flight Inspection) 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 taskj =0, if technician i is NOT assigned to taskj • 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. 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. 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. 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. MATHEMATICAL MODEL Data? NO DATA… Fragkogios - Saharidis, 3rd ICTTSAAMS, 05/05/2015

  25. 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): • 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 anddata 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. 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; solve; fix Difference2; objective only_LAUNCH; solve; fix Difference3; objective only_POST; solve; 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. Questions ? Thank you for your attention

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