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

Ski Lift Pickup Point Ski Run IntersectionSki Lift Drop Off Point

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

Slope Classification ij ≤ Skier Ability

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

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

Attacks

Attack Mitigation

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

Ski Lift Pickup Point Ski Run IntersectionSki Lift Drop Off Point

Beginner Optimal Route

Intermediate Optimal Route

Advanced Optimal Route

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

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

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