Network construction problems with due dates

Averbakh, Igor; Pereira, Jordi

doi:10.1016/j.ejor.2015.02.014

Cited by 21 publications

(47 citation statements)

References 13 publications

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“…Let us briefly review related research on planning restoration activities in networks. In single‐server network restoration problems were studied with the objectives of minimizing the sum of the weighted recovery times , and minimizing the maximum lateness or the number of tardy nodes given due dates for recovery times of nodes . The main contribution of is lower bounding techniques and branch‐and‐bound algorithms for these problems on general networks.…”

Section: Introductionmentioning

confidence: 99%

“…In single‐server network restoration problems were studied with the objectives of minimizing the sum of the weighted recovery times , and minimizing the maximum lateness or the number of tardy nodes given due dates for recovery times of nodes . The main contribution of is lower bounding techniques and branch‐and‐bound algorithms for these problems on general networks. Although the makespan objective can be viewed as a special case of the maximum lateness objective, the results of cannot be used for the problem studied in the present paper because the focus in is only on the single‐server problems.…”

Section: Introductionmentioning

confidence: 99%

“…The main contribution of is lower bounding techniques and branch‐and‐bound algorithms for these problems on general networks. Although the makespan objective can be viewed as a special case of the maximum lateness objective, the results of cannot be used for the problem studied in the present paper because the focus in is only on the single‐server problems. In , polynomial time dynamic programming algorithms were presented for network restoration problems with a broad range of objectives on path networks.…”

Section: Introductionmentioning

confidence: 99%

“…They prove that the considered problems are NP‐hard, and present heuristics based on dispatching rules. One difference between the INDS settings considered in , and the network construction / restoration settings used in and the present article, is that in the INDS models of there is no assumption that the servers can travel only in the already restored parts of the network, which affects significantly the structure of feasible solutions, especially in multi‐server / multi‐depot cases. Another major difference is that in the INDS environment of different servers cannot cooperate on restoration of an arc, that is, only one server can work on restoration of a specific arc, whereas in and the present article, it is assumed that several servers can work simultaneously on restoration of an arc and their restoration speeds combine additively.…”

Section: Introductionmentioning

confidence: 99%

“…We also prove that the problem is NP‐hard even if there are only two servers. The formal statement of the problem is given in network design terms (selection of the edges to restore) which is different from previously studied network restoration problems where a scheduling / sequencing component was inevitable in the formulation. In Section 3, we develop some preliminary results, by considering the feasibility version of the problem (given a number

α > 0

, is it possible to recover all the nodes by time

α

) and proving a decomposition property for that problem if the network has a bridge.…”

Section: Introductionmentioning

confidence: 99%

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Minimizing the makespan in multiserver network restoration problems

Averbakh

2017

Networks

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Suppose that a destroyed network needs to be restored by a number of servers (construction crews) that are initially located at some nodes of the network (depots). Each server can restore one unit of length of the network per unit of time. When several servers are simultaneously working at the same point, their restoration speeds combine additively. The servers can travel within the already restored part of the network with infinite speed, which means that travel times are negligible with respect to construction times. It is required to minimize the time when each node becomes connected to at least one of the depots. We show that the problem is strongly NP‐hard on general networks, and present fast polynomial algorithms for trees and cactus networks which are connected networks where each node and each edge belong to at most one cycle. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(1), 60–68 2017

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

α > 0

, is it possible to recover all the nodes by time

α

) and proving a decomposition property for that problem if the network has a bridge.…”

Section: Introductionmentioning

confidence: 99%

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Minimizing the makespan in multiserver network restoration problems

Averbakh

2017

Networks

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In search of network resilience: An optimization‐based view

et al. 2020

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Fifty years of research in Networks coincides with 50 years of advances in resilience theory and applications. The purpose of this review is to identify how these two technical communities influenced each other in the past and can bolster each other in the future. Advances in resilience theory show that there are at least four ways networks demonstrate resilience: robustness, rebound, extensibility, and adaptability. Research published in Networks and by the broader network optimization community has focused primarily on technical methods for robustness and rebound. We review this literature to organize seminal problems and papers on the ability of networks to manage increasing stressors and return to normal activities after a stressful event. In contrast, the Networks community has made less progress addressing issues for network extensibility and adaptability. Extensibility refers to the ability to stretch current operations to surprising situations and adaptability refers to the ability to sustain operations into the future. We discuss ways to harness existing network optimization methods to study these forms of resilience and outline their limitations. We conclude by providing a research agenda that ensures the Networks community remains central to future advances in resilience while being pragmatic about the limitations of network optimization for achieving this task.

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Quantitative Models for Infrastructure Restoration After Extreme Events: Network Optimization Meets Scheduling

Sharkey

Pinkley

2019

Mathematics of Planet Earth

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Network construction problems with due dates

Cited by 21 publications

References 13 publications

Minimizing the makespan in multiserver network restoration problems

Minimizing the makespan in multiserver network restoration problems

In search of network resilience: An optimization‐based view

Quantitative Models for Infrastructure Restoration After Extreme Events: Network Optimization Meets Scheduling

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