Source sink flows with capacity installation in batches

Chopra, Sunil; Gilboa, Itzhak; Sastry, S.

doi:10.1016/s0166-218x(98)00024-9

Cited by 35 publications

(36 citation statements)

References 5 publications

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“…In deterministic network design, cutset inequalities have been proven to be of particular importance [8,23,27,46,59]. This is true from the theoretical point of view as they define facets but also from the computational point of view as they are known and proven to improve on the performance of branch-andcut based approaches to solve network design problems.…”

Section: Valid Inequalitiesmentioning

confidence: 99%

“…From r i,j < 1 follows i < j and the break point b i,j is fractional and hence (27) is non-trivial for R Γ (S). Let F be the face of P Γ (S) defined by (27). There is a point (x,π) with a <x < a + 1 in the linear relaxation of X Γ cut off by (27).…”

Section: Corollary 318 Given a Node Set S ⊂ V Such That The Two Shomentioning

confidence: 99%

“…Let F be the face of P Γ (S) defined by (27). There is a point (x,π) with a <x < a + 1 in the linear relaxation of X Γ cut off by (27). Using a single edge e we may of course lift this point to a valid point (x,ȳ,π,p) of the linear relaxation of P Γ (S).…”

Section: Corollary 318 Given a Node Set S ⊂ V Such That The Two Shomentioning

confidence: 99%

“…Using the callback functionality of CPLEX, we added a separator for the inequalities (15), (26), (27), and (28). The separator is called at the root node of the branch-and-cut tree.…”

Section: Valid Inequalitiesmentioning

confidence: 99%

“…To study the effectiveness of the valid inequalities we implemented an exact separation algorithm which enumerates all network cuts explicitly and generates all violated inequalities of type (15), (26), (27), and (28). Clearly, this approach is suited for small networks only as the number of network cuts that must be enumerated increases exponentially.…”

Section: Exact Separation (Enumeration)mentioning

confidence: 99%

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Robust network design: Formulations, valid inequalities, and computations

2013

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Traffic in communication networks fluctuates heavily over time. Thus, to avoid capacity bottlenecks, operators highly overestimate the traffic volume during network planning. In this paper we consider telecommunication network design under traffic uncertainty, adapting the robust optimization approach of [21]. We present three different mathematical formulations for this problem, provide valid inequalities, study the computational implications, and evaluate the realized robustness.To enhance the performance of the mixed-integer programming solver we derive robust cutset inequalities generalizing their deterministic counterparts. Instead of a single cutset inequality for every network cut, we derive multiple valid inequalities by exploiting the extra variables available in the robust formulations. We show that these inequalities define facets under certain conditions and that they completely describe a projection of the robust cutset polyhedron if the cutset consists of a single edge.For realistic networks and live traffic measurements we compare the formulations and report on the speed up by the valid inequalities. We study the "price of robustness" and evaluate the approach by analyzing the real network load. The results show that the robust optimization approach has the potential to support network planners better than present methods.

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Section: Valid Inequalitiesmentioning

confidence: 99%

Section: Corollary 318 Given a Node Set S ⊂ V Such That The Two Shomentioning

confidence: 99%

Section: Corollary 318 Given a Node Set S ⊂ V Such That The Two Shomentioning

confidence: 99%

“…Using the callback functionality of CPLEX, we added a separator for the inequalities (15), (26), (27), and (28). The separator is called at the root node of the branch-and-cut tree.…”

Section: Valid Inequalitiesmentioning

confidence: 99%

Section: Exact Separation (Enumeration)mentioning

confidence: 99%

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Robust network design: Formulations, valid inequalities, and computations

2013

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A characterization of the two-commodity network design problem

Sastry

2000

Networks

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On the uncapacitated K‐commodity network design problem with zero flow‐costs

Sastry

Leung

et al. 2004

Naval Research Logistics

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Extending Sastry's result on the uncapacitated two-commodity network design problem, we completely characterize the optimal solution of the uncapacitated K-commodity network design problem with zero flow costs for the case when K ϭ 3. By solving a set of shortest-path problems on related graphs, we show that the optimal solutions can be found in O(n 3 ) time when K ϭ 3, where n is the number of nodes in the network. The algorithm depends on identifying a list of "basic patterns"; the number of basic patterns grows exponentially with K. We also show that the uncapacitated K-commodity network design problem can be solved in O(n 3 ) time for general K if K is fixed; otherwise, the time for solving the problem is exponential.

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Source sink flows with capacity installation in batches

Cited by 35 publications

References 5 publications

Robust network design: Formulations, valid inequalities, and computations

Robust network design: Formulations, valid inequalities, and computations

A characterization of the two-commodity network design problem

On the uncapacitated K‐commodity network design problem with zero flow‐costs

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