Scheduling arc maintenance jobs in a network to maximize total flow over time

Boland, Natashia; Kalinowski, Thomas; Waterer, Hamish; Liu, Zheng

doi:10.1016/j.dam.2012.05.027

Cited by 29 publications

(48 citation statements)

References 6 publications

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“…In particular, the absence of c 3 |E|-approximation algorithms for some c > 0 for general graphs indicates that heuristics and IP-based methods [2,3,4] are a good way of approaching this problem. An interesting open question is whether the inapproximability results carry over to series-parallel graphs, as the network motivating [2,3,4] is series-parallel. Our results on the power of preemption as well as the efficient algorithm for preemptive instances show that allowing preemption is very desirable.…”

Section: Resultsmentioning

confidence: 99%

“…While network problems and scheduling problems individually are fairly well understood, the combination of both areas that results from scheduling network maintenance has only recently received some attention [2,4,17,1,11] and is theoretically hardly understood.…”

Section: Introductionmentioning

confidence: 99%

“…However, the specific problem of only maintaining connectivity over time between two designated nodes has not been studied to our knowledge. Boland et al [2,3,4] study the combination of non-preemptive arc maintenance in a transport network, motivated by annual maintenance planning for the Hunter Valley Coal Chain [5]. Their goal is to schedule maintenance such that the maximum s-t-flow over time in the network with zero transit times is maximized.…”

Section: Introductionmentioning

confidence: 99%

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Scheduling maintenance jobs in networks

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Chen

Disser

et al. 2019

Theoretical Computer Science

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We investigate the problem of scheduling the maintenance of edges in a network, motivated by the goal of minimizing outages in transportation or telecommunication networks. We focus on maintaining connectivity between two nodes over time; for the special case of path networks, this is related to the problem of minimizing the busy time of machines. We show that the problem can be solved in polynomial time in arbitrary networks if preemption is allowed. If preemption is restricted to integral time points, the problem is NP-hard and in the non-preemptive case we give strong non-approximability results. Furthermore, we give tight bounds on the power of preemption, that is, the maximum ratio of the values of non-preemptive and preemptive optimal solutions. Interestingly, the preemptive and the non-preemptive problem can be solved efficiently on paths, whereas we show that mixing both leads to a weakly NP-hard problem that allows for a simple 2-approximation.Algorithm 1 considers finitely many intervals, as all (sub-)interval bounds are defined by a time point r e , r e + p e , d e − p e or d e of some e ∈ E. As we can check the network for (s + , s − )-connectivity in polynomial time, and the algorithm does this for each (sub-)interval, Algorithm 1 runs in polynomial time.Theorem 6. Algorithm 1 is an (ℓ + 1)-approximation algorithm for non-preemptive MAXCONNECTIVITY on general graphs, with ℓ ≤ |E| being the number of different time points d e − p e , e ∈ E.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Scheduling maintenance jobs in networks

Abed

Chen

Disser

et al. 2019

Theoretical Computer Science

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“…The problem in general is NP‐hard . In this proof, the reduction gave rise to a network with a single transhipment node, which was not balanced, and in which the set of arcs with associated jobs did not contain a minimum cut.…”

Section: Network With Single Transhipment Nodementioning

confidence: 97%

“…Proposition If the network is series‐parallel and balanced, then it is optimal to schedule all jobs at the same time . Proof For a network

N = (V, A, s, t, u)

and a subset

J \subseteq A

let

F_{N, J}

denote the maximum flow value in the network

N = (V, A ∖ J, s, t, u |_{A ∖ J})

. The statement that it is optimal to schedule all jobs at the same time is equivalent to

F_{N, J \cup J^{'}} + F_{N, \emptyset} \geq F_{N, J} + F_{N, J^{'}}

for all

J, J^{'} \subseteq A

(see ). We prove the proposition by induction on the structure of the graph.…”

Section: General Networkmentioning

confidence: 99%

Scheduling unit time arc shutdowns to maximize network flow over time: Complexity results

et al. 2013

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We study the problem of scheduling maintenance on arcs of a capacitated network so as to maximize the total flow from a source node to a sink node over a set of time periods. Maintenance on an arc shuts down the arc for the duration of the period in which its maintenance is scheduled, making its capacity zero for that period. A set of arcs is designated to have maintenance during the planning period, which will require each to be shut down for exactly one time period. In general this problem is known to be NP-hard. Here we identify a number of characteristics that are relevant for the complexity of instance classes. In particular, we discuss instances with restrictions on the set of arcs that have maintenance to be scheduled; series parallel networks; capacities that are balanced, in the sense that the total capacity of arcs entering a (non-terminal) node equals the total capacity of arcs leaving the node; and identical capacities on all arcs.

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A bi‐objective optimization approach for the maintenance planning of networked systems

Zhang

2020

Quality & Reliability Eng

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Networked systems, such as telecommunications, transportation, and power transmission, are critical for the economic development and social well-being of a society and are required to keep the prescribed demand continuously satisfied. Therefore, when planning maintenance actions for such a system, the adverse influence on its reliability caused by the unavailability of the components in the process of being maintained needs to be taken into account. To deal with this problem, we propose a new bi-objective optimization approach to determine the Pareto optimal maintenance plans for a networked system, simultaneously maximizing its reliability within the concerned planning horizon and minimizing the total maintenance cost. Both perfect and imperfect maintenance actions are considered. The proposed approach can well balance the influence of maintenance actions on a networked system's reliability during their implementation and after being completed and, thus, can help ensure its reliability of continuously satisfying the prescribed demand. K E Y W O R D Sbi-objective optimization, continuous demand, maintenance optimization, networked system, unavailability

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Scheduling arc maintenance jobs in a network to maximize total flow over time

Cited by 29 publications

References 6 publications

Scheduling maintenance jobs in networks

Scheduling maintenance jobs in networks

Scheduling unit time arc shutdowns to maximize network flow over time: Complexity results

A bi‐objective optimization approach for the maintenance planning of networked systems

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