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Infinite Programming pp 136–153Cite as

Network Programming in Continuous Time with Node Storage

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 259))

Abstract

Given a network having costs and upper bound constraints on the flows in its arcs, the minimum-cost network flow problem is that of finding flows which satisfy a flow-conservation constraint at each node and minimize the total cost of flow. If the arc capacities and costs are allowed to vary as functions of time, and storage is permitted (with some incurred cost) at the nodes of the network, then the problem becomes an infinite-dimensional linear program with a network structure. We describe some preliminary work on the development of an algorithm to solve such problems. This algorithm is a continuous version of the network simplex algorithm.

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References

  1. Dantzig G.B,, “Linear Programming and Extensions”, Princeton University Press, 1963.

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  2. Hajek B. and Ogier R.G., “Optimal Dynamic Routing in Communications Networks with Continuous Traffic”, Networks, 14 pp. 457–487, 1984.

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Author information

Authors and Affiliations

  1. Engineering Department, Cambridge University, Cambridge, England

    A. B. Philpott

Authors
  1. A. B. Philpott
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Editor information

Editors and Affiliations

  1. Management Studies Group Engineering Department, Cambridge University, Mill Lane, Cambridge, CB2 1RX, UK

    Edward J. Anderson  & Andrew B. Philpott  & 

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© 1985 Springer-Verlag Berlin Heidelberg

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Philpott, A.B. (1985). Network Programming in Continuous Time with Node Storage. In: Anderson, E.J., Philpott, A.B. (eds) Infinite Programming. Lecture Notes in Economics and Mathematical Systems, vol 259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46564-2_11

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  • DOI: https://doi.org/10.1007/978-3-642-46564-2_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15996-4

  • Online ISBN: 978-3-642-46564-2

  • eBook Packages: Springer Book Archive

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