Minimum flow problem on network flows with time-varying bounds

Fathabadi, H. Salehi; Khodayifar, Salman; Raayatpanah, Mohammad Ali

doi:10.1016/j.apm.2011.11.067

Cited by 12 publications

(3 citation statements)

References 6 publications

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“…Examples and further applications can be found in the literature such as [1,3,4,15,16,19]. This class of network flows was first introduced by Ford and Fulkerson [3].…”

Section: Introductionmentioning

confidence: 98%

A simple algorithm for reliability evaluation in dynamic networks with stochastic transit times

Fathabadi

Khezri

Khodayifar

2015

Journal of Industrial and Production Engineering

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In a network flow, transit time of an arc is the time span that a unit of flow takes to travel through this arc. In most real-world systems, such as road traffic, communication networks, pipeline systems, transit time of an arc is not constant and may take a value, randomly, from among several possible values. In such systems, reliability is the main concern. Given a demand d, time threshold T, and budget B, we define the reliability as the probability that d units of flow can be sent from the source to the sink under time horizon T and budget B. In this paper, we propose a simple algorithm to evaluate the reliability of networks in which the transition times are stochastic variable.

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“…Examples and further applications can be found in the literature such as [1,3,4,15,16,19]. This class of network flows was first introduced by Ford and Fulkerson [3].…”

Section: Introductionmentioning

confidence: 98%

A simple algorithm for reliability evaluation in dynamic networks with stochastic transit times

Fathabadi

Khezri

Khodayifar

2015

Journal of Industrial and Production Engineering

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“…A particular case in time-varying NFP was first introduced by Ford and Fulkerson in [9]. This case was named dynamic NFP and was developed later (see [2,8,10,12,16]). In [9], Ford and Fulkerson introduced the concept of dynamic flows in networks with the maximal dynamic NFP.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, she assumed that the supply and demand functions and capacities of edges also depend on time [8]. Dynamic generative network flow with a timevarying bound was considered by Salehi Fathabadi and Hosseini in [16], in which the flow was dynamically generated at a source node, and dynamically consumed at a sink node and where the arc-flow bounds are time dependent. The general form of time-varying NFP have been discussed in [4,5,13,14,15,17].…”

Section: Introductionmentioning

confidence: 99%

Robust time-varying shortest path with arbitrary waiting time at vertices

Shirdel¹,

Rezapour²

2017

Croat. Oper. Res. Rev.

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Abstract. In this paper, we propose an algorithm for solving the robust time-varying shortest path problem in which the waiting time at any vertex is not restricted. The problem is to find the shortest path connecting source node s and sink node i in a timevarying network flow such that the time of the path is at most T , where T is a given integer, the transit costs are uncertain and waiting time is arbitrarily allowed at any of the vertices.

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