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Flows over time in time-varying networks: Optimality conditions and strong duality

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  • Koch, Ronald
  • Nasrabadi, Ebrahim

Abstract

There has been much research on network flows over time due to their important role in real world applications. This has led to many results, but the more challenging continuous time model still lacks some of the key concepts and techniques that are the cornerstones of static network flows. The aim of this paper is to advance the state of the art for dynamic network flows by developing the continuous time analogues of the theory for static network flows. Specifically, we make use of ideas from the static case to establish a reduced cost optimality condition, a negative cycle optimality condition, and a strong duality result for a very general class of network flows over time.

Suggested Citation

  • Koch, Ronald & Nasrabadi, Ebrahim, 2014. "Flows over time in time-varying networks: Optimality conditions and strong duality," European Journal of Operational Research, Elsevier, vol. 237(2), pages 580-589.
    • Handle: RePEc:eee:ejores:v:237:y:2014:i:2:p:580-589
    DOI: 10.1016/j.ejor.2014.01.051
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    References listed on IDEAS

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    1. Opasanon, Sathaporn & Miller-Hooks, Elise, 2006. "Multicriteria adaptive paths in stochastic, time-varying networks," European Journal of Operational Research, Elsevier, vol. 173(1), pages 72-91, August.
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    5. S. Hashemi & Ebrahim Nasrabadi, 2012. "On solving continuous-time dynamic network flows," Journal of Global Optimization, Springer, vol. 53(3), pages 497-524, July.
    6. Cai, X. & Sha, D. & Wong, C. K., 2001. "Time-varying minimum cost flow problems," European Journal of Operational Research, Elsevier, vol. 131(2), pages 352-374, June.
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    Cited by:

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    2. Muyldermans, L. & Van Wassenhove, L.N. & Guide, V.D.R., 2019. "Managing high-end ex-demonstration product returns," European Journal of Operational Research, Elsevier, vol. 277(1), pages 195-214.

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