Redesigning Benders Decomposition for Large-Scale Facility Location
Citations
506 citations
Cites background from "Redesigning Benders Decomposition f..."
...To the best of our knowledge, only Fischetti et al. (2010) have developed a unified framework for both types of cuts....
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...Fischetti et al. (2004) observed that the subproblem may reduce to a knapsack problem, which has a closed-form solution....
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287 citations
117 citations
Cites background or methods or result from "Redesigning Benders Decomposition f..."
...Following our previous proposal for uncapacitated facility location [20], we did not implement a bundle method but a simple in-out variant very much in the spirit of [9, 18, 35]....
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...that slave decomposition into smaller subproblems is inhibited by the presence of the capacity constraints (4): if we temporarily relax them, we get an uncapacitated problem for which Benders cuts can be derived very efficiently by using simple ad-hoc algorithms [20]....
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...As to the choice of parameters α and λ, for congested CFL we adopted the values originally proposed in [20], namely α = 0....
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...Based on similar observations, we have recently demonstrated that a revival of Benders decomposition for uncapacitated facility location is a promising move in the direction of developing sparse MIP models to cope with large-scale input data [20]....
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...We refer the reader to [20] for details of a similar approach applied to uncapacitated facility location with separable quadratic costs....
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80 citations
Cites background from "Redesigning Benders Decomposition f..."
...Some of these problems generalize fundamental FLPs such as the uncapacitated facility location problem (UFLP) [30, 43, 75] and the capacitated FLP [42]....
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References
3,694 citations
"Redesigning Benders Decomposition f..." refers background in this paper
...It is well known from knapsack theory [39] that the following Dantzig algorithm produces an optimal primal solution x∗ and optimal dual variables ui ≥ 0 associated with constraints (21) for a given y∗ ∈ [0, 1] with ∑ i∈I y ∗ i ≥ 2....
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2,133 citations
"Redesigning Benders Decomposition f..." refers background in this paper
...) Using Lagrangian duality and KKT conditions, and assuming constraint qualifications hold, [16] (see also Balas [2]) proved that a subgradient can be obtained as...
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...Barring subscript j to ease notation, because of convexity, function Φ(y) can be underestimated by a supporting hyperplane in y∗, so we can write the following linear inequality, known as Generalized Benders (GB) cut [16] w (≥ Φ(y)) ≥ Φ(y∗) + ∑...
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1,939 citations
"Redesigning Benders Decomposition f..." refers methods in this paper
...For testing the impact of Benders decomposition to the separable quadratic case, we consider two families of benchmark instances: (1) UFLLIB instances mentioned above plus the instances from the ORLIB [5] (with original allocation costs equal to 0 being replaced by 10−5), and (2) randomly generated instances used in previous computational studies by Bonami et al....
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...For testing the impact of Benders decomposition to the separable quadratic case, we consider two families of benchmark instances: (1) UFLLIB instances mentioned above plus the instances from the ORLIB [5] (with original allocation costs equal to 0 being replaced by 10−5), and (2) randomly generated instances used in previous computational studies by Bonami et al. [8], Günlük et al. [21] and Günlük and Linderoth [22]....
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1,770 citations
"Redesigning Benders Decomposition f..." refers background in this paper
...Recent survey articles focus on applications of facility location in design of distribution systems [28], or supply chain management [41], and a more general survey on UFL is given in Verter [47]....
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1,737 citations