Scheduling arc shut downs in a network to maximize flow over time with a bounded number of jobs per time period

Boland, Natashia; Kalinowski, Thomas; Kaur, Simranjit

doi:10.1007/s10878-015-9910-x

Cited by 9 publications

(9 citation statements)

References 18 publications

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“…On the other hand, when allowing preemptive schedules, we can process the job of edge e 2 in [0, 2] and the job of edge e 3 in [1, 2] and [3,4]. Then no maintenance job is scheduled in the time interval [2,3] and therefore we have connectivity for one unit of time.…”

Section: Power Of Preemptionmentioning

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%

“…Also, they show in [3] that in their non-preemptive setting, if the input is integer, there is always an optimal solution that starts all jobs at integer time points. In [2], they consider a variant of their problem, where the number of concurrently performable maintenances is bounded by a constant.…”

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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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: Power Of Preemptionmentioning

confidence: 99%

Section: Introductionmentioning

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 authors establish the complexity of the problem taking into account certain instance characteristics, such as special network structures and restrictions on the set of jobs. Boland et al (2016) extended the problem by adding a constraint to ensure that the number of jobs scheduled in any time period does not exceed a given number. Those problems are different from the network maintenance problem introduced in this paper as they assume that a set of maintenance jobs with their corresponding time windows are given a priori.…”

Section: Introductionmentioning

confidence: 99%

The network maintenance problem

Charkhgard¹,

Kalinowski²,

Waterer³

2017

Syme, G., Hatton MacDonald, D., Fulton, B. And Piantadosi, J. (Eds) MODSIM2017, 22nd International Congress on Modelling and Si

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In this research, we describe an optimization problem motivated by the need to maintain infrastructure networks over time. We consider infrastructure networks in which product is transported between distinct origin-destination pairs, and at the same time the infrastructure assets need to be maintained by resources moving in the network. In order to perform maintenance the assets have to be shut down from time to time thus reducing the system capacity for those time periods. The objective is to maximize the total transported product by aligning the maintenance activities appropriately. This problem combines flow maximization with maintenance scheduling capturing some important aspects of the motivating practical problem: (1) the interaction between utilization of network assets such as nodes and arcs and their maintenance demands, (2) the limited resources available to perform the maintenance, and (3) the time for moving the maintenance resources between different locations in the network. Depending on the application context, there are a number of natural ways to reflect these in a mathematical model, and this gives rise to a rich and challenging optimization problem which we call the network maintenance problem. We formally introduce the problem, and present a mixed integer programming formulation. Next, we consider the case of a single commodity and a single maintenance resource when the network is a single path. We describe a polynomial time algorithm which, under some simplifying assumptions, solve the single path case to optimality. The problem becomes more challenging when the simplifying assumptions are dropped.

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