4. D3 A6 P3 A3 A5 P2 D1 P1 A1 A2 D4 A4 D2

5. Ski Lift Pickup Point Ski Run IntersectionSki Lift Drop Off Point

6. Ski Lift Pickup Point Ski Run IntersectionSki Lift Drop Off Point Max ΣDistance ij * Y ij

7. Slope Classification ij ≤ Skier Ability

8. Y ij * (ΣSki Time ij + ΣLift Time ij ) ≤ Allowable Time Ski Time = Distance * (60 / Skier Speed)

9. Max ΣDistance ij * Y ij Y ij * (ΣSki Time ij + ΣLift Time ij ) ≤ Allowable Time Slope Classification ij ≤ Skier Ability Σ Y ij ≤ Capacity ij Flow In = Flow Out

10. Attacks

11. Attack Mitigation

12. Operator / Attacker Paths that determine the best MOE calculated Attacks can only occur on the original path Operator must determine the best locations to mitigate the attacks

13. Ski Lift Pickup Point Ski Run IntersectionSki Lift Drop Off Point

14. Beginner Optimal Route 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5

16. 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5 Intermediate Optimal Route

18. 1 2 23 3 3 4 4 4 4 5 5 5 5 5 Advanced Optimal Route

20. Analysis Summary Problem Scoped to Only Most-Used Paths Large Impact on MOE With Small Amount of Mitigating Equipment

21. Limitations Would Like Higher Granularity of Routes Mitigation of Attacks Are Done Manually Fixed Speed Values of Skier Limits Reality Add Recovery Time & Change Allowable Times

23. Primal Dual Dual Variables Max Σ( d(I,j) * Y(I,j) ) Min Σ( π(ji,j)*cap(I,j) + Tot_Time*θ(i)) ΣY(I,j) – ΣY(j,i) = 0 ρ(j) ρ(j) – ρ(i) + π(I,j) + Σθ(i)*t(I,j) ≥ d(I,j) Y(I,j) ≤ cap(I,j) for all (I,j) π(I,j) π(I,j) ≥ 0 Σ( Y(I,j) * t(I,j) ) ≤ Tot_Time θ(i) θ(i) ≥ 0 Y(I,j) ≥ 0 ρ is unrestricted