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ss strt trsts r - - PowerPoint PPT Presentation

May 20, 2023 587 likes •949 views

ss strt trsts r t r r Pr s rsr

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SLIDE 1

❆♥❛❧②s✐s ♦❢ ❛ ❈♦♥str✉❝t✐✈❡ ▼❛t❤❡✉r✐st✐❝s ❢♦r t❤❡ ❚r❛✈❡❧✐♥❣ ❯♠♣✐r❡ Pr♦❜❧❡♠

❘❡s❤♠❛ ❈✳ ❈❤❛♥❞r❛s❡❦❤❛r❛♥ ❚ú❧✐♦ ❆✳ ▼✳ ❚♦✛♦❧♦ ❚♦♥② ❲❛✉t❡rs

❈❖❉❡❙✱ ❑❯ ▲❡✉✈❡♥✱ ❇❡❧❣✐✉♠

▼❛t❤❙♣♦rt ■♥t❡r♥❛t✐♦♥❛❧ ✷✵✶✼ ❈♦♥❢❡r❡♥❝❡✱ ✷✻✲✷✽t❤ ❏✉♥❡✱ ✷✵✶✼

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SLIDE 2

❚❤❡ ❚r❛✈❡❧✐♥❣ ❯♠♣✐r❡ Pr♦❜❧❡♠

❚❤❡ ❚r❛✈❡❧✐♥❣ ❯♠♣✐r❡ Pr♦❜❧❡♠ ✭❚❯P✮ ✐s ❛ ❝♦♠❜✐♥❛t♦r✐❛❧ ♦♣t✐♠✐③❛t✐♦♥ ♣r♦❜❧❡♠ ❝♦♥❝❡r♥✐♥❣ t❤❡ ❛ss✐❣♥♠❡♥t ♦❢ ✉♠♣✐r❡s t♦ t❤❡ ❣❛♠❡s ♦❢ ❛ ✜①❡❞ ❞♦✉❜❧❡ r♦✉♥❞✲r♦❜✐♥ t♦✉r♥❛♠❡♥t✳ ❚❤❡ ❚❯P ✇❛s ✐♥tr♦❞✉❝❡❞ ❜② ❚r✐❝❦ ❛♥❞ ❨✐❧❞✐③ ✐♥ ✷✵✵✼✳

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SLIDE 3

❚❤❡ ❚r❛✈❡❧✐♥❣ ❯♠♣✐r❡ Pr♦❜❧❡♠

❚❤❡ ❚r❛✈❡❧✐♥❣ ❯♠♣✐r❡ Pr♦❜❧❡♠ ✭❚❯P✮ ✐s ❛ ❝♦♠❜✐♥❛t♦r✐❛❧ ♦♣t✐♠✐③❛t✐♦♥ ♣r♦❜❧❡♠ ❝♦♥❝❡r♥✐♥❣ t❤❡ ❛ss✐❣♥♠❡♥t ♦❢ ✉♠♣✐r❡s t♦ t❤❡ ❣❛♠❡s ♦❢ ❛ ✜①❡❞ ❞♦✉❜❧❡ r♦✉♥❞✲r♦❜✐♥ t♦✉r♥❛♠❡♥t✳ ❚❤❡ ❚❯P ✇❛s ✐♥tr♦❞✉❝❡❞ ❜② ❚r✐❝❦ ❛♥❞ ❨✐❧❞✐③ ✐♥ ✷✵✵✼✳

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SLIDE 4

❚❤❡ ❚r❛✈❡❧✐♥❣ ❯♠♣✐r❡ Pr♦❜❧❡♠

❚❤❡ ❚r❛✈❡❧✐♥❣ ❯♠♣✐r❡ Pr♦❜❧❡♠ ✭❚❯P✮ ✐s ❛ ❝♦♠❜✐♥❛t♦r✐❛❧ ♦♣t✐♠✐③❛t✐♦♥ ♣r♦❜❧❡♠ ❝♦♥❝❡r♥✐♥❣ t❤❡ ❛ss✐❣♥♠❡♥t ♦❢ ✉♠♣✐r❡s t♦ t❤❡ ❣❛♠❡s ♦❢ ❛ ✜①❡❞ ❞♦✉❜❧❡ r♦✉♥❞✲r♦❜✐♥ t♦✉r♥❛♠❡♥t✳ ❚❤❡ ❚❯P ✇❛s ✐♥tr♦❞✉❝❡❞ ❜② ❚r✐❝❦ ❛♥❞ ❨✐❧❞✐③ ✐♥ ✷✵✵✼✳

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SLIDE 5

❋❛✐r♥❡ss ❝♦♥str❛✐♥ts

✶✳ ❊✈❡r② ❣❛♠❡ ✐♥ t❤❡ t♦✉r♥❛♠❡♥t ✐s ♦✣❝✐❛t❡❞ ❜② ❡①❛❝t❧② ♦♥❡ ✉♠♣✐r❡

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SLIDE 6

❋❛✐r♥❡ss ❝♦♥str❛✐♥ts

✶✳ ❊✈❡r② ❣❛♠❡ ✐♥ t❤❡ t♦✉r♥❛♠❡♥t ✐s ♦✣❝✐❛t❡❞ ❜② ❡①❛❝t❧② ♦♥❡ ✉♠♣✐r❡ ✷✳ ❊❛❝❤ ✉♠♣✐r❡ ♦✣❝✐❛t❡s ❡①❛❝t❧② ♦♥❡ ❣❛♠❡ ♣❡r r♦✉♥❞

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SLIDE 7

❋❛✐r♥❡ss ❝♦♥str❛✐♥ts

✶✳ ❊✈❡r② ❣❛♠❡ ✐♥ t❤❡ t♦✉r♥❛♠❡♥t ✐s ♦✣❝✐❛t❡❞ ❜② ❡①❛❝t❧② ♦♥❡ ✉♠♣✐r❡ ✷✳ ❊❛❝❤ ✉♠♣✐r❡ ♦✣❝✐❛t❡s ❡①❛❝t❧② ♦♥❡ ❣❛♠❡ ♣❡r r♦✉♥❞ ✸✳ ❊❛❝❤ ✉♠♣✐r❡ ♠✉st ✈✐s✐t t❤❡ ❤♦♠❡ ❧♦❝❛t✐♦♥ ♦❢ ❡❛❝❤ t❡❛♠ ❛t ❧❡❛st ♦♥❝❡

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SLIDE 8

❋❛✐r♥❡ss ❝♦♥str❛✐♥ts

✶✳ ❊✈❡r② ❣❛♠❡ ✐♥ t❤❡ t♦✉r♥❛♠❡♥t ✐s ♦✣❝✐❛t❡❞ ❜② ❡①❛❝t❧② ♦♥❡ ✉♠♣✐r❡ ✷✳ ❊❛❝❤ ✉♠♣✐r❡ ♦✣❝✐❛t❡s ❡①❛❝t❧② ♦♥❡ ❣❛♠❡ ♣❡r r♦✉♥❞ ✸✳ ❊❛❝❤ ✉♠♣✐r❡ ♠✉st ✈✐s✐t t❤❡ ❤♦♠❡ ❧♦❝❛t✐♦♥ ♦❢ ❡❛❝❤ t❡❛♠ ❛t ❧❡❛st ♦♥❝❡ ✹✳ ❆♥ ✉♠♣✐r❡ ❝❛♥♥♦t ✈✐s✐t t❤❡ s❛♠❡ ✈❡♥✉❡ ♠♦r❡ t❤❛♥ ♦♥❝❡ ✐♥ ❛♥② q✶ ❝♦♥s❡❝✉t✐✈❡ r♦✉♥❞s

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SLIDE 9

❋❛✐r♥❡ss ❝♦♥str❛✐♥ts

✶✳ ❊✈❡r② ❣❛♠❡ ✐♥ t❤❡ t♦✉r♥❛♠❡♥t ✐s ♦✣❝✐❛t❡❞ ❜② ❡①❛❝t❧② ♦♥❡ ✉♠♣✐r❡ ✷✳ ❊❛❝❤ ✉♠♣✐r❡ ♦✣❝✐❛t❡s ❡①❛❝t❧② ♦♥❡ ❣❛♠❡ ♣❡r r♦✉♥❞ ✸✳ ❊❛❝❤ ✉♠♣✐r❡ ♠✉st ✈✐s✐t t❤❡ ❤♦♠❡ ❧♦❝❛t✐♦♥ ♦❢ ❡❛❝❤ t❡❛♠ ❛t ❧❡❛st ♦♥❝❡ ✹✳ ❆♥ ✉♠♣✐r❡ ❝❛♥♥♦t ✈✐s✐t t❤❡ s❛♠❡ ✈❡♥✉❡ ♠♦r❡ t❤❛♥ ♦♥❝❡ ✐♥ ❛♥② q✶ ❝♦♥s❡❝✉t✐✈❡ r♦✉♥❞s ✺✳ ❆♥ ✉♠♣✐r❡ ❝❛♥♥♦t ♦✣❝✐❛t❡ t❤❡ ❣❛♠❡s ♦❢ t❤❡ s❛♠❡ t❡❛♠ ♠♦r❡ t❤❛♥ ♦♥❝❡ ✐♥ ❛♥② q✷ ❝♦♥s❡❝✉t✐✈❡ r♦✉♥❞s✳

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SLIDE 10

❈♦♥str✉❝t✐✈❡ ▼❛t❤❡✉r✐st✐❝s ▼❛t❤❡✉r✐st✐❝s

▼❛t❤❡✉r✐st✐❝s ❛r❡ ❤❡✉r✐st✐❝ ❛❧❣♦r✐t❤♠s ✇❤✐❝❤ ❛r❡ ❤②❜r✐❞s ♦❢ ♠❡t❛❤❡✉r✐st✐❝ ❛♥❞ ♠❛t❤❡♠❛t✐❝❛❧ ♣r♦❣r❛♠♠✐♥❣ ❛❧❣♦r✐t❤♠s✳

❈♦♥str✉❝t✐✈❡ ▼❛t❤❡✉r✐st✐❝s✿ ❚❤❡ ✐❞❡❛

  • ❉❡❝♦♠♣♦s❡ t❤❡ ♣r♦❜❧❡♠ ✐♥t♦ s✉❜♣r♦❜❧❡♠s
  • ❙♦❧✈❡ t❤❡ s✉❜♣r♦❜❧❡♠s ✉s✐♥❣ ❡①❛❝t ♠❡t❤♦❞s
  • ❈♦♠❜✐♥❡ t❤❡ s♦❧✉t✐♦♥s t♦ ❝♦♥str✉❝t ❛ s♦❧✉t✐♦♥ t♦ t❤❡ ❡♥t✐r❡

♣r♦❜❧❡♠

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SLIDE 11

❈♦♥str✉❝t✐✈❡ ▼❛t❤❡✉r✐st✐❝ ♣r♦❝❡❞✉r❡

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SLIDE 12

❈♦♥str✉❝t✐✈❡ ▼❛t❤❡✉r✐st✐❝ ♣r♦❝❡❞✉r❡

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SLIDE 13

❈♦♥str✉❝t✐✈❡ ▼❛t❤❡✉r✐st✐❝ ♣r♦❝❡❞✉r❡

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SLIDE 14

❈♦♥str✉❝t✐✈❡ ▼❛t❤❡✉r✐st✐❝ ♣r♦❝❡❞✉r❡

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SLIDE 15

❋❧♦✇ ❢♦r♠✉❧❛t✐♦♥ ♦❢ t❤❡ ♣r♦❜❧❡♠

❞❡ ❞✐st❛♥❝❡ ♦❢ ❞✐r❡❝t❡❞ ❡❞❣❡ ❡ ❳❡✉ ✶ ✐❢ ❡❞❣❡ ❡ ✐s s❡❧❡❝t❡❞ ❢♦r ✉♠♣✐r❡ ✉ ✵ ♦t❤❡r✇✐s❡

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SLIDE 16

❋❧♦✇ ❢♦r♠✉❧❛t✐♦♥ ♦❢ t❤❡ ♣r♦❜❧❡♠

❞❡ : ❞✐st❛♥❝❡ ♦❢ ❞✐r❡❝t❡❞ ❡❞❣❡ ❡ ❳❡✉ =

  • ✶

✐❢ ❡❞❣❡ ❡ ✐s s❡❧❡❝t❡❞ ❢♦r ✉♠♣✐r❡ ✉ ✵ ♦t❤❡r✇✐s❡

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SLIDE 17

❋❧♦✇ ❢♦r♠✉❧❛t✐♦♥ ♦❢ t❤❡ ♣r♦❜❧❡♠

♠✐♥✐♠✐③❡✿

  • ❡∈❊
  • ✉∈❯

❞❡❳❡✉ ✭✶✮ s✉❜❥❡❝t t♦✿

  • ❡∈δ(❥)
  • ✉∈❯

❳❡✉ = ✶ ∀❥ ∈ ❱ \{s♦✉r❝❡✱ s✐♥❦} ✭✷✮

  • ❡∈δ(❥)

❳❡✉ −

  • ❡∈ω(❥)

❳❡✉ =      −✶ ✐❢ ❥ ✐s t❤❡ s♦✉r❝❡ +✶ ✐❢ ❥ ✐s t❤❡ s✐♥❦ ✵ ∀❥ ∈ ❱ \{s♦✉r❝❡✱ s✐♥❦} , ∀✉ ∈ ❯ ✭✸✮

  • ❡∈δ(❍✐ )

❳❡✉ ≥ ✶ ∀✐ ∈ ■, ∀✉ ∈ ❯ ✭✹✮

  • ❡∈δ(◗′

✐r )

❳❡✉ ≤ ✶ ∀✐ ∈ ■, ∀r ∈ ❘, ∀✉ ∈ ❯ ✭✺✮

  • ❡∈δ(◗′′

✐r )

❳❡✉ ≤ ✶ ∀✐ ∈ ■, ∀r ∈ ❘, ∀✉ ∈ ❯ ✭✻✮ ❳❡✉ ∈ {✵, ✶} ∀❡ ∈ ❊, ∀✉ ∈ ❯ ✭✼✮

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SLIDE 18

❈♦♥str✉❝t✐✈❡ ▼❛t❤❡✉r✐st✐❝ ♣r♦❝❡❞✉r❡

P✐t❢❛❧❧✿ ❈♦♥str❛✐♥t ✸ ❝❛♥ ❜❡ ❡✈❛❧✉❛t❡❞ ♦♥❧② ♦♥ ❛ ❢✉❧❧ s❝❤❡❞✉❧❡

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SLIDE 19

❈♦♥str✉❝t✐✈❡ ▼❛t❤❡✉r✐st✐❝ ♣r♦❝❡❞✉r❡

P✐t❢❛❧❧✿ ❈♦♥str❛✐♥t ✸ ❝❛♥ ❜❡ ❡✈❛❧✉❛t❡❞ ♦♥❧② ♦♥ ❛ ❢✉❧❧ s❝❤❡❞✉❧❡ ❖❜❥ =

  • ✉∈❯
  • ❡∈❊❜

(❳✉❡❞❡ −

  • ❜✵✇❳✉❡②✉❡)

✇❤❡r❡✱ ❊❜ : ❊❞❣❡s ✐♥ ❜❧♦❝❦ ❜ ✭✽✮ ❜✵ : st❛rt r♦✉♥❞ ♦❢ ❜❧♦❝❦ ❜ ✭✾✮ ②✉❡ =

  • ✶

❡❞❣❡ ❡ st❛rts ❛t ❛ ♥♦❞❡ ✇❤✐❝❤ ❤❛s ♥♦t ❜❡❡♥ ✈✐s✐t❡❞ ❜② ✉♠♣✐r❡ ✉ ✵ ♦t❤❡r✇✐s❡ ✭✶✵✮

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SLIDE 20

❉❡s✐❣♥ ♣❛r❛♠❡t❡rs

  • ❲❡✐❣❤t ✭✇✮

❖❜❥ =

  • ✉∈❯
  • ❡∈❊❜

(❳✉❡❞❡ −

  • ❜✵✇❳✉❡②✉❡)

❇❧♦❝❦ s✐③❡ ✭ ✮ ❖✈❡r❧❛♣ ✭ ✮ r❡❧❛①❡❞ ❢✉t✉r❡ r♦✇s

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SLIDE 21

❉❡s✐❣♥ ♣❛r❛♠❡t❡rs

  • ❲❡✐❣❤t ✭✇✮
  • ❇❧♦❝❦ s✐③❡ ✭β✮

❖✈❡r❧❛♣ ✭ ✮ r❡❧❛①❡❞ ❢✉t✉r❡ r♦✇s

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SLIDE 22

❉❡s✐❣♥ ♣❛r❛♠❡t❡rs

  • ❲❡✐❣❤t ✭✇✮
  • ❇❧♦❝❦ s✐③❡ ✭β✮
  • ❖✈❡r❧❛♣ ✭θ✮

r❡❧❛①❡❞ ❢✉t✉r❡ r♦✇s

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SLIDE 23

❉❡s✐❣♥ ♣❛r❛♠❡t❡rs

  • ❲❡✐❣❤t ✭✇✮
  • ❇❧♦❝❦ s✐③❡ ✭β✮
  • ❖✈❡r❧❛♣ ✭θ✮
  • r❡❧❛①❡❞ ❢✉t✉r❡ r♦✇s
slide-24
SLIDE 24

❲❡✐❣❤t✭✇✮

30 40 50 60 70 80 90 Weight (w) 2 4 6 8 10 12 Violations

#(Teams) = 26, q1 = 5, q2 = 5

β = 3 β = 4 β = 5 β = 6

30 40 50 60 70 80 90 Weight (w) 1 2 3 4 5 6 7 8 9 Violations

#(Teams) = 28, q1 = 5, q2 = 5

β = 3 β = 4 β = 5 β = 6

30 40 50 60 70 80 90 Weight (w) 2 4 6 8 10 12 Violations

#(Teams) = 30, q1 = 5, q2 = 5

β = 3 β = 4 β = 5 β = 6

30 40 50 60 70 80 90 Weight (w) 2 4 6 8 10 12 14 Violations

#(Teams) = 32, q1 = 5, q2 = 5

β = 3 β = 4 β = 5 β = 6

slide-25
SLIDE 25

❇❧♦❝❦ s✐③❡ ✭β✮

30 40 50 60 70 80 90 Weight (w) 340000 345000 350000 355000 360000 365000 Distance

#(Teams) = 26, q1 = 5, q2 = 5

β = 3 β = 4 β = 5 β = 6

30 40 50 60 70 80 90 Weight (w) 385000 390000 395000 400000 405000 410000 Distance

#(Teams) = 28, q1 = 5, q2 = 5

β = 3 β = 4 β = 5 β = 6

30 40 50 60 70 80 90 Weight (w) 440000 445000 450000 455000 460000 465000 470000 475000 480000 485000 Distance

#(Teams) = 30, q1 = 5, q2 = 5

β = 3 β = 4 β = 5 β = 6

30 40 50 60 70 80 90 Weight (w) 490000 495000 500000 505000 510000 515000 520000 525000 530000 Distance

#(Teams) = 32, q1 = 5, q2 = 5

β = 3 β = 4 β = 5 β = 6

slide-26
SLIDE 26

❖✈❡r❧❛♣ ✭θ✮ ❛♥❞ ❉✐st❛♥❝❡

10 20 30 40 50 60 70 80 90 100 Weight (w) 335000 340000 345000 350000 355000 360000 Distance

#(Teams) = 26, q1 = 5, q2 = 5

θ = β − 1 θ = 0

20 30 40 50 60 70 80 90 100 Weight (w) 380000 385000 390000 395000 400000 405000 Distance

#(Teams) = 28, q1 = 5, q2 = 5

θ = β − 1 θ = 0

20 30 40 50 60 70 80 90 100 Weight (w) 435000 440000 445000 450000 455000 460000 Distance

#(Teams) = 30, q1 = 5, q2 = 5

θ = β − 1 θ = 0

20 30 40 50 60 70 80 90 100 Weight (w) 480000 485000 490000 495000 500000 505000 510000 515000 520000 Distance

#(Teams) = 32, q1 = 5, q2 = 5

θ = β − 1 θ = 0

slide-27
SLIDE 27

❖✈❡r❧❛♣ ✭θ✮ ❛♥❞ ❱✐♦❧❛t✐♦♥s ✭❦✮

✇ β❂ ✸ β❂ ✹ β❂ ✺ β❂ ✻ ❖❜❥ ❦ t✐♠❡✭s✮ ❉✐st✳ ❦ t✐♠❡✭s✮ ❉✐st✳ ❦ t✐♠❡✭s✮ ❉✐st✳ ❦ t✐♠❡✭s✮ ✶✵ ✹✹✹✵✽✼ ✷✷ ✷✷✳✻✼ ✹✸✺✾✼✽ ✶✺ ✶✻✸✳✷✻ ✹✸✵✼✼✸ ✶✾ ✼✸✼✾✳✾✻ ✹✸✺✺✸✺ ✶✾ ✸✷✹✺✸✳✼✸ ✷✵ ✹✹✺✵✺✵ ✶✷ ✷✷✳✹✺ ✹✸✽✸✹✶ ✽ ✶✽✺✳✸✺ ✹✸✻✼✻✵ ✼ ✹✸✻✵✳✺✽ ✹✸✻✽✻✾ ✶✵ ✷✵✸✻✼✳✵✻ ✸✵ ✹✺✷✶✶✺ ✽ ✷✸✳✸✶ ✹✹✹✻✵✷ ✶ ✶✻✾✳✺✽ ✹✸✾✷✷✶ ✷ ✻✷✻✼✳✼✵ ✹✸✺✼✷✸ ✷ ✷✶✷✶✶✳✺✵ ✹✵ ✹✺✸✷✸✵ ✶ ✷✻✳✻✾ ✹✺✵✵✽✵ ✷ ✶✾✸✳✽✾ ✹✹✸✻✸✷ ✵ ✺✾✶✷✳✺✻ ✹✹✶✶✹✵ ✶ ✶✾✼✸✻✳✾✻ ✺✵ ✹✺✸✽✶✶ ✵ ✶✾✳✻✻ ✹✹✼✻✽✹ ✶ ✷✶✷✳✽✷ ✹✹✻✵✵✹ ✵ ✸✷✺✷✳✷✺ ✹✹✹✻✸✺ ✵ ✶✻✸✺✹✳✼✹ ✻✵ ✹✺✺✵✷✽ ✶ ✷✶✳✶✾ ✹✺✸✽✸✻ ✵ ✷✷✷✳✼✼ ✹✹✼✶✻✵ ✵ ✸✺✷✽✳✹✵ ✹✹✻✾✽✵ ✵ ✷✷✶✼✹✳✶✵ ✼✵ ✹✺✼✺✶✹ ✶ ✷✷✳✵✽ ✹✺✶✽✵✻ ✵ ✶✽✾✳✼✸ ✹✹✽✸✽✽ ✵ ✸✸✽✼✳✾✼ ✹✹✼✺✵✺ ✵ ✶✾✷✼✹✳✼✼ ✽✵ ✹✻✸✵✾✻ ✵ ✶✾✳✽✸ ✹✺✹✷✺✽ ✵ ✶✾✸✳✻✽ ✹✺✶✹✼✶ ✵ ✷✽✵✷✳✷✼ ✹✹✼✵✺✾ ✵ ✶✸✽✼✺✳✵✺ ✾✵ ✹✻✽✾✽✺ ✵ ✷✵✳✶✹ ✹✻✵✹✷✾ ✵ ✶✽✽✳✵✾ ✹✹✻✷✶✹ ✵ ✸✷✻✾✳✼✸ ✹✺✻✸✻✵ ✵ ✷✶✺✹✻✳✼✷ ✶✵✵ ✹✻✽✺✻✶ ✵ ✷✵✳✾✹ ✹✻✺✵✸✹ ✵ ✷✹✸✳✵✵ ✹✺✺✺✾✾ ✵ ✷✾✾✷✳✸✹ ✹✺✺✷✵✷ ✵ ✷✵✷✼✵✳✸✼

10 20 30 40 50 60 70 80 90 100 Weight (w) 5 10 15 20 25 Violations (k)

#(Teams) = 30, q1 = 5, q2 = 5, θ = 1

β = 3 β = 4 β = 5 β = 6

slide-28
SLIDE 28

❚❛❜❧❡✿ ❘❡s✉❧ts ❢♦r ❧❛r❣❡ ✐♥st❛♥❝❡s

★✭❚❡❛♠s✮ q✶ q✷ ❉✐st✳ ❦ β ✇ β − θ ❚✐♠❡ ✭s✮ ❇❡st ❙♦❧✉t✐♦♥ ✪ ●❛♣ ✷✻ ✶✸ ✻ ✷✻ ✺ ✺ ✸✹✺✸✹✵ ✵ ✻ ✺✵ ✷ ✷✽✻✸✳✶✼✷ ✷✽ ✶✹ ✼ ✷✽ ✺ ✺ ✸✾✵✾✸✸ ✵ ✻ ✺✵ ✷ ✾✷✻✻✳✶✽✾ ✸✵ ✶✺ ✼ ✸✵ ✺ ✺ ✹✹✶✾✸✶ ✵ ✻ ✺✵ ✷ ✼✾✹✻✳✶✵✺ ✹✺✵✾✶✾ ✲✶✳✾✾✸ ✸✷ ✶✻ ✽ ✸✷ ✺ ✺ ✹✾✾✸✵✺ ✵ ✺ ✻✵ ✷ ✼✽✶✾✳✹✸✼

❇❡♥❝❤♠❛r❦ ✇❡❜s✐t❡✿ ❤tt♣✿✴✴❣❡♥t✳❝s✳❦✉❧❡✉✈❡♥✳❜❡✴t✉♣

slide-29
SLIDE 29

❚❛❜❧❡✿ ❘❡s✉❧ts ❢♦r ♠❡❞✐✉♠ ✐♥st❛♥❝❡s

★✭❚❡❛♠s✮ q✶ q✷ ❉✐st✳ β ✇ β − θ ❚✐♠❡ ✭s✮ ❇❡st ❙♦❧✉t✐♦♥ ✪ ●❛♣ ✶✷ ✼ ✷ ✽✻✽✽✾ ✽ ✶✵ ✶ ✹✳✸✾✾ ✽✻✽✽✾ ✵ ✶✷ ✺ ✸ ✾✸✻✼✾ ✻ ✷✵ ✶ ✷✳✷✼✻ ✾✸✻✼✾ ✵ ✶✷ ✹ ✸ ✾✵✷✺✹ ✽ ✽✵ ✶ ✶✶✳✶✾✻ ✽✾✽✷✻ ✵✳✹✼✻ ✶✹ ✽ ✸ ✶✽✸✻✸✶ ✾ ✾✵ ✶ ✸✶✵✳✹✵✷ ✶✼✷✶✼✼ ✻✳✻✺✷ ✶✹ ✽ ✷ ✶✹✾✵✶✼ ✼ ✺✵ ✶ ✼✳✸✶✶ ✶✹✼✽✷✹ ✵✳✽✵✼ ✶✹ ✼ ✸ ✶✻✹✹✹✵ ✶✵ ✶✵ ✷ ✾✹✳✸✺✾ ✶✻✹✹✹✵ ✵ ✶✹ ✼ ✷ ✶✹✻✾✽✵ ✽ ✷✵ ✶ ✶✽✳✺✺ ✶✹✻✻✺✻ ✵✳✷✷✶ ✶✹ ✻ ✸ ✶✺✾✺✵✼ ✶✵ ✶✵✵ ✶ ✸✶✷✳✶✽✹ ✶✺✽✽✼✺ ✵✳✸✾✽ ✶✹ ✻ ✷ ✶✹✺✹✶✹ ✶✵ ✻✵ ✺ ✶✼✳✽✼✽ ✶✹✺✶✷✹ ✵✳✷ ✶✹ ✺ ✸ ✶✺✻✼✽✵ ✽ ✾✵ ✹ ✶✸✳✾✷✺ ✶✺✹✾✻✷ ✶✳✶✼✸ ✶✹ ✺ ✷ ✶✹✸✺✹✽ ✽ ✷✵ ✸ ✻✳✾✽✸ ✶✹✸✸✺✼ ✵✳✶✸✸ ✶✹❆ ✽ ✸ ✶✼✵✵✷✻ ✾ ✹✵ ✻ ✸✹✳✷✽✷ ✶✻✻✶✽✹ ✷✳✸✶✷ ✶✹❆ ✽ ✷ ✶✹✹✶✻✺ ✾ ✽✵ ✶ ✷✼✳✹✼✸ ✶✹✸✵✹✸ ✵✳✼✽✹ ✶✹❆ ✼ ✸ ✶✻✵✽✸✵ ✶✵ ✶✵✵ ✺ ✶✸✼✳✼✻✷ ✶✺✽✼✻✵ ✶✳✸✵✹ ✶✹❆ ✼ ✷ ✶✹✶✻✼✸ ✽ ✶✵ ✶ ✶✾✳✺✹✽ ✶✹✵✺✻✷ ✵✳✼✾ ✶✹❆ ✻ ✸ ✶✺✹✹✵✷ ✽ ✾✵ ✹ ✶✸✳✵✹✺ ✶✺✷✾✽✶ ✵✳✾✷✾ ✶✹❆ ✻ ✷ ✶✸✾✼✼✺ ✻ ✸✵ ✸ ✷✳✽✷✹ ✶✸✽✾✷✼ ✵✳✻✶ ✶✹❆ ✺ ✸ ✶✹✾✼✺✶ ✽ ✻✵ ✶ ✺✾✳✷✺✻ ✶✹✾✸✸✶ ✵✳✷✽✶ ✶✹❆ ✺ ✷ ✶✸✼✽✺✸ ✼ ✻✵ ✷ ✺✳✻✾✾ ✶✸✼✽✺✸ ✵ ✶✹❇ ✽ ✸ ✶✻✽✶✵✼ ✻ ✶✵ ✶ ✻✳✶✹✺ ✶✻✺✵✷✻ ✶✳✽✻✼ ✶✹❇ ✽ ✷ ✶✹✶✻✷✽ ✶✵ ✶✵ ✶ ✼✷✳✹✼✶ ✶✹✶✸✶✷ ✵✳✷✷✹ ✶✹❇ ✼ ✸ ✶✺✼✽✽✹ ✾ ✶✵ ✶ ✶✺✷✳✸✵✽ ✶✺✼✽✽✹ ✵ ✶✹❇ ✼ ✷ ✶✸✾✷✵✽ ✺ ✷✵ ✶ ✷✳✷✽✹ ✶✸✽✾✾✽ ✵✳✶✺✶ ✶✹❇ ✻ ✸ ✶✺✹✷✼✺ ✼ ✻✵ ✶ ✷✽✳✻✹✾ ✶✺✷✼✹✵ ✶✳✵✵✺ ✶✹❇ ✻ ✷ ✶✸✽✷✾✼ ✽ ✸✵ ✷ ✶✽✳✻✶✶ ✶✸✽✷✹✶ ✵✳✵✹✶ ✶✹❇ ✺ ✸ ✶✺✶✵✶✺ ✽ ✾✵ ✸ ✸✵✳✶✸✽ ✶✹✾✹✺✺ ✶✳✵✹✹ ✶✹❇ ✺ ✷ ✶✸✻✷✹✺ ✽ ✼✵ ✸ ✶✽✳✵✵✸ ✶✸✻✵✻✾ ✵✳✶✷✾

slide-30
SLIDE 30

❚❛❜❧❡✿ ❘❡s✉❧ts ❢♦r ♠❡❞✐✉♠ ✐♥st❛♥❝❡s

★✭❚❡❛♠s✮ q✶ q✷ ❉✐st✳ β ✇ β − θ ❚✐♠❡ ✭s✮ ❇❡st ❙♦❧✉t✐♦♥ ✪ ●❛♣ ✶✹❈ ✽ ✸ ✶✼✽✸✶✵ ✼ ✼✵ ✶ ✷✻✳✵✹ ✶✻✶✷✻✷ ✶✵✳✺✼✷ ✶✹❈ ✽ ✷ ✶✹✶✾✾✽ ✽ ✶✵ ✶ ✶✹✳✺✸✷ ✶✹✶✵✶✺ ✵✳✻✾✼ ✶✹❈ ✼ ✸ ✶✺✾✽✶✷ ✽ ✷✵ ✶ ✽✺✳✷✵✼ ✶✺✹✾✶✸ ✸✳✶✻✷ ✶✹❈ ✼ ✷ ✶✸✽✾✷✽ ✺ ✼✵ ✶ ✶✳✻✸✽ ✶✸✽✽✸✷ ✵✳✵✻✾ ✶✹❈ ✻ ✸ ✶✺✸✺✹✶ ✻ ✽✵ ✶ ✾✳✹✵✼ ✶✺✵✽✺✽ ✶✳✼✼✽ ✶✹❈ ✻ ✷ ✶✸✻✾✶✸ ✺ ✸✵ ✶ ✷✳✶✸✸ ✶✸✻✸✾✹ ✵✳✸✽✶ ✶✹❈ ✺ ✸ ✶✹✾✹✺✾ ✼ ✻✵ ✸ ✾✳✷ ✶✹✽✸✹✾ ✵✳✼✹✽ ✶✹❈ ✺ ✷ ✶✸✺✸✵✷ ✺ ✸✵ ✶ ✷✳✸✽✼ ✶✸✹✾✶✻ ✵✳✷✽✻ ✶✻ ✽ ✸ ♥♦ s♦❧ ✶✽✾✹✶✺ ✶✻ ✽ ✷ ✶✻✽✻✵✹ ✽ ✾✵ ✸ ✶✶✼✳✶✸✾ ✶✻✶✾✾✾ ✹✳✵✼✼ ✶✻ ✼ ✹ ♥♦ s♦❧ ✶✾✼✵✷✽ ✶✻ ✼ ✸ ✶✻✽✺✽✺ ✼ ✹✵ ✷ ✺✻✳✹✹✷ ✶✻✺✼✻✺ ✶✳✼✵✶ ✶✻ ✼ ✷ ✶✺✷✺✻✸ ✼ ✹✵ ✶ ✶✷✵✳✵✼✻ ✶✺✵✹✸✸ ✶✳✹✶✻ ✶✻❆ ✽ ✸ ♥♦ s♦❧ ✷✶✹✺✶✷ ✶✻❆ ✽ ✷ ✶✼✾✻✾✷ ✼ ✻✵ ✷ ✶✾✳✸✷✺ ✶✼✶✽✽✷ ✹✳✺✹✹ ✶✻❆ ✼ ✹ ♥♦ s♦❧ ✷✶✸✹✶✻ ✶✻❆ ✼ ✸ ✶✽✵✻✹✶ ✽ ✺✵ ✷ ✸✶✶✳✻✹✼ ✶✼✽✺✶✶ ✶✳✶✾✸ ✶✻❆ ✼ ✷ ✶✻✻✷✷✹ ✼ ✶✵ ✶ ✼✶✳✷✾✹ ✶✻✸✼✵✾ ✶✳✺✸✻ ✶✻❇ ✽ ✸ ♥♦ s♦❧ ✷✶✼✼✻✹ ✶✻❇ ✽ ✷ ♥♦ s♦❧ ✶✽✵✼✷✽ ✶✻❇ ✼ ✹ ♥♦ s♦❧ ✷✷✸✽✻✽ ✶✻❇ ✼ ✸ ✶✽✹✻✸✻ ✽ ✺✵ ✶ ✻✵✵✸✳✹✻ ✶✽✵✷✵✹ ✷✳✹✺✾ ✶✻❇ ✼ ✷ ✶✻✾✺✻✺ ✽ ✺✵ ✸ ✶✹✸✳✻✻✾ ✶✻✼✶✾✵ ✶✳✹✷✶

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SLIDE 31

❚❛❜❧❡✿ ❘❡s✉❧ts ❢♦r ♠❡❞✐✉♠ ✐♥st❛♥❝❡s

★✭❚❡❛♠s✮ q✶ q✷ ❉✐st✳ β ✇ β − θ ❚✐♠❡ ✭s✮ ❇❡st ❙♦❧✉t✐♦♥ ✪ ●❛♣ ✶✻❈ ✽ ✸ ♥♦ s♦❧✳ ✷✶✹✾✾✸ ✶✻❈ ✽ ✷ ✶✽✻✹✸✼ ✻ ✽✵ ✸ ✹✳✸✶✽ ✶✼✾✾✸✾ ✸✳✻✶✶ ✶✻❈ ✼ ✹ ♥♦ s♦❧ ✷✵✾✵✽✽ ✶✻❈ ✼ ✸ ✶✽✺✼✻✾ ✽ ✾✵ ✸ ✶✵✻✼✳✻✾✸ ✶✽✵✹✽✸ ✷✳✾✷✾ ✶✻❈ ✼ ✷ ✶✻✾✹✻✻ ✼ ✺✵ ✶ ✶✹✺✳✻✽✸ ✶✻✻✹✼✾ ✶✳✼✾✹ ✶✽ ✾ ✹ ♥♦ s♦❧✳ ✷✻✼✸✶✶ ✶✽ ✾ ✸ ♥♦ s♦❧✳ ✷✻✷✾✽✼ ✶✽ ✽ ✹ ♥♦ s♦❧✳ ✷✺✹✶✺✺ ✶✽ ✽ ✸ ✷✵✹✻✺✽ ✻ ✺✵ ✸ ✷✶✳✶✾✶ ✷✹✽✸✵✷ ✲✶✼✳✺✼✼ ✶✽ ✼ ✹ ✷✶✻✵✺✶ ✻ ✻✵ ✷ ✼✹✳✽✹✸ ✷✶✼✺✵✷ ✲✵✳✻✻✼ ✷✵ ✶✵ ✺ ♥♦ s♦❧✳ ✷✷ ✶✶ ✺ ♥♦ s♦❧✳

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SLIDE 32

❚❛❜❧❡✿ ❙♦♠❡ ❜❡st r❡s✉❧ts

★✭❚❡❛♠s✮ q✶ q✷ ❉✐st✳ β ✇ β − θ ❇❡st ❙♦❧✉t✐♦♥ ✪ ●❛♣ ✶✽ ✽ ✸ ✷✵✷✻✻✷ ✽ ✶✵ ✷ ✷✹✽✸✵✷ ✲✶✽✳✸✽✵ ✶✽ ✼ ✹ ✷✶✺✶✷✾ ✼ ✷✵ ✹ ✷✶✼✺✵✷ ✲✶✳✵✾✶ ✷✻ ✺ ✺ ✸✹✺✸✹✵ ✻ ✺✵ ✷ ✷✽ ✺ ✺ ✸✽✻✺✷✽ ✺ ✺✵ ✶ ✸✵ ✺ ✺ ✹✹✶✾✸✶ ✻ ✺✵ ✷ ✹✺✵✾✶✾ ✲✶✳✾✾✸ ✸✷ ✺ ✺ ✹✾✺✸✸✽ ✺ ✺✵ ✸

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SLIDE 33

❋✉t✉r❡ ✇♦r❦

  • ❙t✉❞② ✐♥t❡r❛❝t✐♦♥ ♦❢ ❞❡s✐❣♥ ♣❛r❛♠❡t❡rs
  • ❊①♣❡r✐♠❡♥ts ♦♥ r❡❧❛①❡❞ ❢✉t✉r❡
  • ❖r❞❡r ♦❢ ❡①❡❝✉t✐♦♥ ♦❢ s✉❜♣r♦❜❧❡♠s
  • ❈♦♠♣❛r✐s♦♥ ♦❢ ✈❛r✐♦✉s ❢♦r♠✉❧❛t✐♦♥s ❢♦r t❤❡ ❚❯P
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SLIDE 34

❘❡❢❡r❡♥❝❡s

❚♦✛♦❧♦✱ ❚✳ ❆✳ ▼✳✱ ❲❛✉t❡rs✱ ❚✳✱ ❱❛♥ ▼❛❧❞❡r❡♥✱ ❙✳✱ ✫ ❱❛♥❞❡♥ ❇❡r❣❤❡✱ ●✳ ✭✷✵✶✻✮✳ ❇r❛♥❝❤✲❛♥❞✲❜♦✉♥❞ ✇✐t❤ ❞❡❝♦♠♣♦s✐t✐♦♥✲❜❛s❡❞ ❧♦✇❡r ❜♦✉♥❞s ❢♦r t❤❡ ❚r❛✈❡❧✐♥❣ ❯♠♣✐r❡ Pr♦❜❧❡♠✳ ❊✉r♦♣❡❛♥ ❏♦✉r♥❛❧ ♦❢ ❖♣❡r❛t✐♦♥❛❧ ❘❡s❡❛r❝❤✱ ✷✺✵✭✸✮✱ ✼✸✼✕✼✹✹✳ ❚r✐❝❦✱ ▼✳ ❆✳✱ ✫ ❨✐❧❞✐③✱ ❍✳ ✭✷✵✵✼✮✳ ❇❡♥❞❡r✬s ❝✉ts ❣✉✐❞❡❞ ❧❛r❣❡ ♥❡✐❣❤❜♦r❤♦♦❞ s❡❛r❝❤ ❢♦r t❤❡ tr❛✈❡❧✐♥❣ ✉♠♣✐r❡ ♣r♦❜❧❡♠✳ ■♥ P✳ ❱✳ ❍❡♥t❡♥r②❝❦ ✫ ▲✳ ❲♦❧s❡② ✭❊❞s✳✮✱ ■♥t❡❣r❛t✐♦♥ ♦❢ ❆■ ❛♥❞ ❖❘ t❡❝❤♥✐q✉❡s ✐♥ ❝♦♥str❛✐♥t ♣r♦❣r❛♠♠✐♥❣ ❢♦r ❝♦♠❜✐♥❛t♦r✐❛❧ ♦♣t✐♠✐③❛t✐♦♥ ♣r♦❜❧❡♠s✳ ▲❡❝t✉r❡ ♥♦t❡s ✐♥ ❝♦♠♣✉t❡r s❝✐❡♥❝❡ ✭❱♦❧✳ ✹✺✶✵✱ ♣♣✳ ✸✸✷✕✸✹✺✮✳ ❇❡r❧✐♥ ❍❡✐❞❡❧❜❡r❣✿ ❙♣r✐♥❣❡r ❞❡ ❖❧✐✈❡✐r❛✱ ▲✳✱ ❞❡ ❙♦✉③❛✱ ❈✳ ❈✳✱ ✫ ❨✉♥❡s✱ ❚✳ ✭✷✵✶✹✮✳ ■♠♣r♦✈❡❞ ❜♦✉♥❞s ❢♦r t❤❡ tr❛✈❡❧✐♥❣ ✉♠♣✐r❡ ♣r♦❜❧❡♠✿ ❆ str♦♥❣❡r ❢♦r♠✉❧❛t✐♦♥ ❛♥❞ ❛ r❡❧❛①✲❛♥❞✲✜① ❤❡✉r✐st✐❝✳ ❊✉r♦♣❡❛♥ ❏♦✉r♥❛❧ ♦❢ ❖♣❡r❛t✐♦♥❛❧ ❘❡s❡❛r❝❤✱ ✷✸✻✭✷✮✱ ✺✾✷✕✻✵✵✳ ❲❛✉t❡rs✱ ❚✳✱ ❱❛♥ ▼❛❧❞❡r❡♥✱ ❙✳✱ ✫ ❱❛♥❞❡♥ ❇❡r❣❤❡✱ ●✳ ✭✷✵✶✹✮✳ ❉❡❝♦♠♣♦s✐t✐♦♥ ❛♥❞ ❧♦❝❛❧ s❡❛r❝❤ ❜❛s❡❞ ♠❡t❤♦❞s ❢♦r t❤❡ tr❛✈❡❧✐♥❣ ✉♠♣✐r❡ ♣r♦❜❧❡♠✳ ❊✉r♦♣❡❛♥ ❏♦✉r♥❛❧ ♦❢ ❖♣❡r❛t✐♦♥❛❧ ❘❡s❡❛r❝❤✱ ✷✸✽✭✸✮✱ ✽✽✻✕✽✾✽✳

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SLIDE 35

❚❍❆◆❑ ❨❖❯✦