2006
DOI: 10.1016/j.cor.2004.11.002
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Lagrangian duality applied to the vehicle routing problem with time windows

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Cited by 123 publications
(88 citation statements)
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“…For a direct control of dual variables (Kallehauge, Larsen, and Madsen, 2001) consider the dual RMP with additional box constraints centered around the current dual optimal solutionû, i.e.,û i − δ ≤ u i ≤û i + δ. The method is related to the work of Madsen (1975) in the sense that these bounds are adjusted automatically, depending on how well the dual restricted master problem approximates the Lagrangian dual problem.…”
Section: Trust Region Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…For a direct control of dual variables (Kallehauge, Larsen, and Madsen, 2001) consider the dual RMP with additional box constraints centered around the current dual optimal solutionû, i.e.,û i − δ ≤ u i ≤û i + δ. The method is related to the work of Madsen (1975) in the sense that these bounds are adjusted automatically, depending on how well the dual restricted master problem approximates the Lagrangian dual problem.…”
Section: Trust Region Methodsmentioning
confidence: 99%
“…Still, when the number of rows, and thus dual multipliers is very large, subgradient algorithms may be the only practical alternative. Hybrid methods are good compromises (Barahona and Jensen, 1998;Kallehauge, Larsen, and Madsen, 2001;Kohl and Madsen, 1997), e.g., starting the multiplier adjustment with a subgradient algorithm and finishing the computation using a linear program.…”
Section: Convexificationmentioning
confidence: 99%
“…These problems are baptized the Time Window Vehicle Routing Problem (TWVRP). [25] developed an exact algorithm for TWVRP and they tested the algorithm with problems Benchmark Solomon [26]. The work of [27] and [28] are part of the recent work related to TWVRP, they assumed that the deliveries to customers may be outside the time window (soft time windows) but they induced late penalties in the objective function.…”
Section: Vrppdtwmentioning
confidence: 99%
“…The goal here is minimize the total distance covered by the different vehicles. In turn, the Vehicle Routing Problem (VRP) generalizes m-TSP adding a customer-specific demand; geographically distributed depots and a vehicle-specific capacity (Kallehauge et al, 2006) (Fig. 1).…”
Section: The Vehicle Routing Problemmentioning
confidence: 99%