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3.4 Vehicle Routing

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3.4 Vehicle Routing

Gegeben:

• Vollst¨andiger gerichteter Graph D

• Ausgezeichneter Knoten d

2

V

(

D

)

(Depot)

• Bogenl¨angen c

2

QA(G)

• Bestellvolumina b

2

QV+(D) an den Knoten

• Kapazit¨aten k

2

Qt+ der t Fahrzeuge Gesucht:

Kreise C1, . . . ,Ct

✓

A

(

D

)

mit Knotenmengen V

(

Ci

)

so dass Âit=1 c

(

Ci

)

m¨oglichst klein ist unter den Nebenbedin- gungen:

• d

2

V

(

Ci

)

f ¨ur alle i

2 [

t

]

• Jeder Knoten v

2

V

(

D

)

\ {d} ist in genau einem V

(

Ci

)

enthalten.

• F ¨ur jedes i

2 [

t

]

ist die Summe der Bestellvolumina bv aller Knoten v

2

V

(

Ci

)

h¨ochstens die Kapazit¨at ki.

[51]

– 49 –

(2)

3.5 Spannb¨aume

Gegeben:

• Graph G

• Kantengewichte w

2

QE(G) Gesucht:

Ein Spannbaum T

✓

E

(

G

)

von G mit m¨oglichst geringem Gewicht w

(

T

) =

Âe2E(G) we. [52]

– 50 –

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