AFRL: Multi-State Selective Maintenance Decisions (MM-0302)

1. AFRL: Multi-State Selective Maintenance Decisions (MM-0302) Principal Investigator: C. Richard Cassady, Ph.D., P.E. Co-Principal Investigators: Edward A. Pohl, Ph.D. Scott J. Mason, Ph.D., P.E. Research Assistants: Thomas Yeung

2. Project Motivation • All military organizations depend on the reliable performance of repairable systems for the successful completion of missions. • Due to limitations in maintenance resources, a maintenance manager must decide how to allocate available resources.

3. Project Motivation (cont) • Selective maintenance is defined as the process of identifying the subset of maintenance activities to perform from a set of desired maintenance actions. • Selective maintenance models formulated to date are based on the assumption of binary (functioning or failed) component, subsystem and system status.

4. Project Objective to develop a modeling-based methodology for managing selective maintenance decisions when multiple (more than two) system states are possible

5. Outline • scenario definition • decision-making • solution by total enumeration • heuristic solution • a dispatching rule • experimental design • experimental results

6. Scenario Definition • set of q independent and identical systems • each system comprised of m independent subsystems • motivating example (m = 41) • subsystems extracted from AFI121-103_ACCSUP1 (MESL) • F-16A/B/C/D MESL used because of our experience with the F-16 at Hill AFB

7. Scenario Definition (cont) • all systems idle and available for maintenance • state of system i • ai = (ai1, ai2, … , aim) • aij denotes the amount of time required to bring subsystem j of system i into a properly operating condition

8. Scenario Definition (cont) • Some maintenance actions require spare parts or other resources that are not readily available. • The ready time of subsystem j in system i, ij, is the time at which these resources are available and maintenance on the subsystem can begin. • i= (i1, i2, … , im)

9. Scenario Definition (cont) • n future missions planned (n q) • mission krequires some subset of the subsystems to be operational • sk = (sk1, sk2, … , skm)

10. Scenario Definition (cont) • motivating example (types of missions) • FSL – Full System List • ADC – Air Defense, Conventional • ASC – Air to Surface, Conventional • ASY – Air Superiority • ASN – Air to Surface, Nuclear • DSP – Defense Suppression • TNG – Training • TST – Testing

11. Decision-Making • Which system should be assigned to each mission?

12. Decision-Making (cont) Every mission gets a system. No system gets more than one mission.

13. Decision-Making (cont) • total time required for maintenance related to mission k • ready time for maintenance related to mission k

14. Decision-Making (cont) • Once the assignments are made, maintenance crews must perform the maintenance. •  = # of crews • We assume that a crew: • works on no more than one system at a time • works on a system only after it is “ready” • works on a system continuously until all maintenance is finished

15. Decision-Making (cont) • For each mission, when does maintenance begin and by which crew is maintenance performed?

16. Decision-Making (cont) Every mission gets a crew. We cannot start maintenance before we are ready.

17. Decision-Making (cont) A crew cannot work on two systems at the same time.

18. Decision-Making (cont) • completion time of maintenance for mission k

19. Decision-Making (cont) • wk = importance (weight) of mission k • larger weight implies more importance • objective is to minimize total weighted completion time of all maintenance

20. Decision-Making (cont) • The full optimization model is a binary programming problem with nonlinearities in both the objective function and several constraints.

21. Solution by Total Enumeration • procedure • enumerates all possible assignments • enumerates all possible schedules for each assignment • 102nγiterations required to enumerate all solutions • 3 missions, 3 systems, 2 crews = one trillion iterations

22. Solution by Total Enumeration (cont) • One trillions iterations requires weeks to complete. • Computation time is not practical for even small instances.

23. Heuristic Solution • The nonlinearities render the problem incapable of being solved by most commercial solvers. • The problem was broken apart into two linear problems: • Assignment problem • Scheduling problem

24. Heuristic Solution (cont) • For each system/mission combination, the following ratio is computed: • Assignments are made based on this ratio in descending order. • This computation takes a fraction of a second.

25. Heuristic Solution (cont) • Heuristic solution to the assignment problem is used as an input for the scheduling problem. • The optimal solution for the scheduling problem is obtained using a commercial solver.

26. A Dispatching Rule • We also considered a simplified version of the heuristic that does not require the commercial solver. • This dispatching rule is designed to be much simpler computationally than the heuristic approach.

27. A Dispatching Rule • For each system/mission combination, the following ratio is computed: • Missions are simply “dispatched” or scheduled based on this ratio in descending order.

28. Experimental Design • Realistic problem instances of the multi-state selective maintenance problem were generated. • Both the heuristic/optimization and dispatching rule approaches were tested for their performance in terms of: • Solution quality • Computation time

29. Experimental Design (cont) • The F-16 is our motivating example. • The numerical examples are evaluated at the squadron level (q = 24, n = 24). • All instances have six identical crews available for maintenance at any given time.

30. Experimental Design (cont) • Each mission is one of the eight different mission types outlined previously.

31. Experimental Design (cont)

32. Experimental Design (cont) • There is a 5% chance that a given subsystem needs some maintenance. • If a subsystem needs maintenance, the number of hours required to bring the subsystem to a fully functioning state is drawn from a distribution having a mean of 6 hours and a 5% chance of maintenance time exceeding 24 hours.

33. Experimental Design (cont)

34. Experimental Design (cont) • weight of a given mission ~ DU[1, 10]

35. Experimental Results • 233 replications of the experimental design were generated and solved using both the heuristic and dispatching rule approaches

36. Experimental Results (cont) • heuristic • heuristic for the assignment problem ran in a fraction of a second • solver took an average of 7.5 minutes to solve the scheduling problem • dispatching rule runs in less than a second

37. Experimental Results (cont) • The dispatching rule yields solutions that are on average only 0.33% inferior to the heuristic approach. • The dispatching rule outperformed the heuristic approach in 86 out of the 233 experiments.