指導老師:林燦煌 博士 學生 : 劉芳怡 Vehicle routing with time windows: Two...
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指導老師:林燦煌 博士 學生 : 劉芳怡 Vehicle routing with time windows: Two optimization algorithms Marshall L. Fisher ,Kurt O. Jornsten,Oli B. G. Madsen Operation Research,Vol.45,No3,May-June 1997,pp.48 8-492
指導老師:林燦煌 博士 學生 : 劉芳怡 Vehicle routing with time windows: Two optimization algorithms Marshall L. Fisher,Kurt O. Jornsten,Oli B. G. Madsen Operation Research,Vol.45,No3,May-June
: Vehicle routing with time windows: Two optimization
algorithms Marshall L. Fisher,Kurt O. Jornsten,Oli B. G. Madsen
Operation Research,Vol.45,No3,May-June 1997,pp.488-492
(15) ik 1 : min- (16) subject to (13) and (14) Solution
Methods- Lagrangian relaxation(3/7)
Slide 21
2 : min (17) subject to (2)-(12) (shortest path problem with
time windows and capacity constraints,SPTWCC) SPTWCC cycles
two-cycle elimination(Kolen et al.1987) Solution Methods-
Lagrangian relaxation(4/7)
Slide 22
(15) : (18) Where Solution Methods- Lagrangian
relaxation(5/7)
Slide 23
x y (Gap=(Optimal solution-Lower bound)/Lower bound in %) case
VRPTW lower bound (18) (subgradient optimization) branch-and-bound
method (Variable Splitting Approach) lower bounds Solution Methods-
Lagrangian relaxation(6/7)
Slide 24
branching process: (1) y ik 1 0 (2) Solution Methods-
Lagrangian relaxation(7/7)
Slide 25
Solution Method - K-tree Approach(1/3) Tree: Basis: one node is
a tree K-tree: Basis: K children is a K-tree