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

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Ski Lift Pickup Point Ski Run IntersectionSki Lift Drop Off Point

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

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Slope Classification ij Skier Ability

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Y ij * (Ski Time ij + Lift Time ij ) Allowable Time Ski Time = Distance * (60 / Skier Speed)

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Max Distance ij * Y ij Y ij * (Ski Time ij + Lift Time ij ) Allowable Time Slope Classification ij Skier Ability Y ij Capacity ij Flow In = Flow Out

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Attacks

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Attack Mitigation

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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

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Ski Lift Pickup Point Ski Run IntersectionSki Lift Drop Off Point

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

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

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

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

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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

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Primal Dual Dual Variables Max ( d(I,j) * Y(I,j) ) Min ( (ji,j)*cap(I,j) + Tot_Time*(i)) Y(I,j) Y(j,i) = 0 (j) (j) (i) + (I,j) + (i)*t(I,j) d(I,j) Y(I,j) cap(I,j) for all (I,j) (I,j) (I,j) 0 ( Y(I,j) * t(I,j) ) Tot_Time (i) (i) 0 Y(I,j) 0 is unrestricted