Resource Constrained Training

1. Resource Constrained Training CDR Edward Dewinter LT Zachary Schwartz MAJ Russell Gan

2. Motivation Goal is to optimize training schedule with constrained resources that minimizes total time to complete training for two Platoons

3. Background • EOD Training Unit Two, Fort Story, VA • Train EOD Platoons prior to deployment • Ideal plan is to train two Platoons at the same time

4. Ultimately we want to find out.. • How many attacks on the resources can we tolerate? • Which resources are targeted the most? • What can we do about it?

5. Tasks and Resource Requirements

6. Initially.. Shortest Path Formulation • Nodes – Tasks completed, indexed on time AB, tA + tB tB A, tA tA tC S AC, tA + tC tB B, tB LOOKS GOOD SO FAR….

7. But.. AB, tA + tB+2 AB, tA + tB AB, tA + tB+1 AB, tA + tB+3 1 1 1 tB Probably not the best approach..

8. Integer Program Formulation

9. Results • 60 days to complete. • Assuming no precedence, resource and contiguity constraints – 50 days to complete.

10. Let’s attack the model.. • What constitutes an attack: • Terrorist actions • Natural calamities • Murphy

11. Penalties

12. Interdiction Model … PROBLEM!

13. Side note • Cannot use “dual trick” • Benders does not work well with pure ILPs • Upper & lower bounds may not converge

14. Why doesn’t Benders work well for ILPs?

15. Why doesn’t Benders work well for ILPs?

16. Side note • Cannot use “dual trick” • Benders does not work well with pure ILPs • Upper & lower bounds may not converge • But, if a valid Benders cut is generated at every iteration, then the algorithm converges to optimality.

17. New Plan • Solve relaxed interdiction problem using Benders • Hard code interdiction results into ILP subproblem Limitations • Attacker placed at a disadvantage • Optimal attack in the relaxed version is suboptimal to the original problem • In relaxed version, attacker considers options which do not actually exist to the operator in the original problem

18. Relaxed Interdiction Model

19. Interdiction Results (Relaxed)

20. FA1 FA2 Attacking early would pose less of a problem to the operator. Could easily schedule tasks that do not require that resource to “fill the gap”. Chem 1 Chem 2 NUC1 NUC2 FTX POST FTX MCM1 MCM2 SURF 1 SURF 2 This is where the bottle neck starts.

21. Interdiction Results (Integer) * 0 tolerance was used throughout for both B&B and Benders

22. Randomly Generated Attacks • Done for 1 attack scenario: • 100 random attacks generated • Worst case – 65 days • Benders on ILP still provides more realistic outputs • Attacking all resources on the same day would be suboptimal to attacker.

23. Operator Resilience Curve 38% 23% 17% 10%

24. Which resources are targeted the most?

25. What can we do about it? • Relieve bottleneck • Adjust FTX lesson plan • Create redundancy • More EOD Trainers • More demo ranges • Leverage on simulation instead of L/F ranges • Improve security of resources • Housing Rhino’s close to base security

26. We want to find out.. • How many attacks can we tolerate? • Which resources are targeted the most? • What can we do about it?

27. Future Research • Expand the model to include all EOD training pipelines. • Applying model to other types of training programs subject to similar constraints. • Develop algorithm to solve max-min ILP problems exactly.

28. Questions?