Flow Expansion on Transportation Networks with Budget Constraints

Elalouf, Amir; Adany, Ron; Ceder, Avishai

doi:10.1016/j.sbspro.2012.09.831

Cited by 2 publications

(4 citation statements)

References 8 publications

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“…The super source is linked with the initial sources, and the initial sinks are linked with the super sink. The resulting s − t network is equivalent with the initial one [13]. So, without restricting the generality of the problem, we shall consider from now on that the network has one source and one sink, i.e., it is an s − t network.…”

Section: Network Flowmentioning

confidence: 99%

“…A minimum cost flow has to be calculated in G e . The algorithms for minimum cost flow are designed to work on integer values [13]. Since in G e the cost of the arcs from A e 1 ∪ A e 2 are integer values divided by 2 (see Equation ( 10), before applying the algorithm for minimum cost flow, all the costs of the arcs from A e are multiplied by 2, and, in the end, the cost of the obtained flow f e is divided by 2.…”

Section: Algorithm 1: Algorithm For Solving Mcnep (Amcnep)mentioning

confidence: 99%

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Flow Increment through Network Expansion

Deaconu¹,

Majercsik²

2021

Mathematics

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The network expansion problem is a very important practical optimization problem when there is a need to increment the flow through an existing network of transportation, electricity, water, gas, etc. In this problem, the flow augmentation can be achieved either by increasing the capacities on the existing arcs, or by adding new arcs to the network. Both operations are coming with an expansion cost. In this paper, the problem of finding the minimum network expansion cost so that the modified network can transport a given amount of flow from the source node to the sink node is studied. A strongly polynomial algorithm is deduced to solve the problem.

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Section: Network Flowmentioning

confidence: 99%

Section: Algorithm 1: Algorithm For Solving Mcnep (Amcnep)mentioning

confidence: 99%

Flow Increment through Network Expansion

Deaconu¹,

Majercsik²

2021

Mathematics

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“…Eventually, if the expanded capacity value on arc( , ) is equal to the capacity expansion is not possible and we can only reduce it. So, the costs are set as = +∞ and = − [6].…”

Section: The Capacity Expansion Algorithm (Cea)mentioning

confidence: 99%

“…One of them is flow expansion on transportation networks with budget constraints. This problem was studied by Elalouf et al [6]. The general budget-restricted max flow problem was first discussed by Eiselt and Frajer [7].…”

Section: Introductionmentioning

confidence: 99%

Capacity Expansion and Reliability Evaluation on the Networks Flows with Continuous Stochastic Functional Capacity

Hamzezadeh

Fathabadi

2014

Journal of Applied Mathematics

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In many systems such as computer network, fuel distribution, and transportation system, it is necessary to change the capacity of some arcs in order to increase maximum flow value from sourcesto sinkt, while the capacity change incurs minimum cost. In real-time networks, some factors cause loss of arc’s flow. For example, in some flow distribution systems, evaporation, erosion or sediment in pipes waste the flow. Here we define a real capacity, or the so-calledfunctional capacity,which is the operational capacity of an arc. In other words, the functional capacity of an arc equals the possible maximum flow that may pass through the arc. Increasing the functional arcs capacities incurs some cost. There is a certain resource available to cover the costs. First, we construct a mathematical model to minimize the total cost of expanding the functional capacities to the required levels. Then, we consider the loss of flow on each arc as a stochastic variable and compute the system reliability.

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Flow Expansion on Transportation Networks with Budget Constraints

Cited by 2 publications

References 8 publications

Flow Increment through Network Expansion

Flow Increment through Network Expansion

Capacity Expansion and Reliability Evaluation on the Networks Flows with Continuous Stochastic Functional Capacity

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