Finding Maximum Minimum Cost Flows to Evaluate Gas Network Capacities

Hoppmann, Kai; Schwarz, R.

doi:10.1007/978-3-319-89920-6_46

Cited by 3 publications

(4 citation statements)

References 2 publications

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“…And second, can the APX-hardness result be extended to MaxMCF as defined in Section 2, i.e., with the connectedness-condition? Additionally, we are currently developing algorithmic approaches to efficiently solve MaxMCF and MaxTP instances originating in practice, for example, instances from the real-world application in natural gas transport as described by Hoppmann and Schwarz [9].…”

Section: Discussionmentioning

confidence: 99%

“…First of all, the variant of MaxMCF where the capacity restrictions on the arcs are dropped has previously been considered by Hennig and Schwarz [8] and Hoppmann and Schwarz [9]. This so-called Maximum Transportation Problem (MaxTP) and its complexity are further discussed in Section 6.…”

Section: Related Workmentioning

confidence: 99%

“…Before discussing the complexity of MaxMCF, we first state a mathematical programming formulation for it, which is adapted from Hoppmann and Schwarz [9]. In particular, we show that MaxMCF can be modelled as a linear bilevel optimization program with interdicting objective functions.…”

Section: A Bilevel Model For Maxmcfmentioning

confidence: 99%

“…However, in many real-world applications the supplies and demands are not necessarily fixed and can only be narrowed down to a certain range. An example for this is given by Hoppmann and Schwarz [9], who model an optimization problem arising in the context of natural gas transport as MCF. Here the supplies and demands can take on values within predefined intervals, which are given for each source and each sink individually.…”

Section: Introductionmentioning

confidence: 99%

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On the Complexity of Computing Maximum and Minimum Min‐Cost‐Flows

Hoppmann-Baum

2021

Networks

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Consider a flow network, i.e., a directed graph where each arc has a nonnegative capacity value and an associated length, together with nonempty supply intervals for the sources and nonempty demand intervals for the sinks. The Maximum Min-Cost-Flow Problem (MaxMCF) is to find fixed supply and demand values within these intervals such that the optimal objective value of the induced Min-Cost-Flow Problem (MCF) is maximized. In this paper, we show that MaxMCF as well as its uncapacitated variant, the Maximum Transportation Problem (MaxTP), are NP-hard. Further, we prove that MaxMCF is APX-hard if a connectedness-condition regarding the sources and the sinks of the flow network is dropped. Finally, we show how the Minimum Min-Cost-Flow Problem (MinMCF) can be solved in polynomial time.

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Section: Discussionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: A Bilevel Model For Maxmcfmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the Complexity of Computing Maximum and Minimum Min‐Cost‐Flows

Hoppmann-Baum

2021

Networks

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Optimal Operation of Transient Gas Transport Networks

et al. 2021

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In this paper, we describe an algorithmic framework for the optimal operation of transient gas transport networks consisting of a hierarchical MILP formulation together with a sequential linear programming inspired post-processing routine. Its implementation is part of the KOMPASS decision support system, which is currently used in an industrial setting. Real-world gas transport networks are controlled by operating complex pipeline intersection areas, which comprise multiple compressor units, regulators, and valves. In the following, we introduce the concept of network stations to model them. Thereby, we represent the technical capabilities of a station by hand-tailored artificial arcs and add them to network. Furthermore, we choose from a predefined set of flow directions for each network station and time step, which determines where the gas enters and leaves the station. Additionally, we have to select a supported simple state, which consists of two subsets of artificial arcs: Arcs that must and arcs that cannot be used. The goal is to determine a stable control of the network satisfying all supplies and demands. The pipeline intersections, that are represented by the network stations, were initially built centuries ago. Subsequently, due to updates, changes, and extensions, they evolved into highly complex and involved topologies. To extract their basic properties and to model them using computer-readable and optimizable descriptions took several years of effort. To support the dispatchers in controlling the network, we need to compute a continuously updated list of recommended measures. Our motivation for the model presented here is to make fast decisions on important transient global control parameters, i.e., how to route the flow and where to compress the gas. Detailed continuous and discrete technical control measures realizing them, which take all hardware details into account, are determined in a subsequent step. In this paper, we present computational results from the KOMPASS project using detailed real-world data.

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Identifying the critical factors of transmission efficiency loss in China’s natural gas network

Wang

Zhang

et al. 2023

Front. Energy Res.

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China’s market-oriented reform supports the sustainable development of energy mix and the low-carbon target, and natural gas has bridged the transition from traditional fossil energy to clean and renewable energies. The third-party access policy, launched recently by China’s natural gas market, drives the decouple between gas trade and transport. The decouple might lead to the transmission resources of physical network not optimally used, which is caused by the contractual arrangement between entry and exit capacities in commercial network. Aiming at this issue, we established a mathematical programming with equilibrium constraints (MPEC) to integrate the allocations of commercial capacity and physical flows, based on a minimum cost maximum flow problem (MCMF) abstracted from China’s existing gas network. The MPEC model was then used to strategically evaluate the transmission efficiency, and identify the critical factors of its loss. Our results show that there is transmission efficiency loss of China’s gas network from the shortage of geospatial gas supply and the invisible segmentation of gas network due to interdicted cost of pipeline, bottleneck of pipeline capacity and economic radius of gas supply chains to transport gas. Therefore, the critical factor of the loss to be identified will be helpful for strategically reducing the cost of decoupling gas trade and transport.

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Finding Maximum Minimum Cost Flows to Evaluate Gas Network Capacities

Cited by 3 publications

References 2 publications

On the Complexity of Computing Maximum and Minimum Min‐Cost‐Flows

On the Complexity of Computing Maximum and Minimum Min‐Cost‐Flows

Optimal Operation of Transient Gas Transport Networks

Identifying the critical factors of transmission efficiency loss in China’s natural gas network

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