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Fair Integral Network Flows

Author

Listed:
  • András Frank

    (MTA-ELTE Egerváry Research Group, Department of Operations Research, Eötvös University, Budapest H-1117, Hungary)

  • Kazuo Murota

    (The Institute of Statistical Mathematics, Tokyo 190-8562, Japan; Faculty of Economics and Business Administration, Tokyo Metropolitan University, Tokyo 192-0397, Japan)

Abstract

A strongly polynomial algorithm is developed for finding an integer-valued feasible st -flow of a given flow amount, which is decreasingly minimal on a specified subset F of edges in the sense that the largest flow value on F is as small as possible; within this, the second largest flow value on F is as small as possible; within this, the third largest flow value on F is as small as possible, and so on. A characterization of the set of these st -flows gives rise to an algorithm to compute a cheapest F -decreasingly minimal integer-valued feasible st -flow of given flow amount. Decreasing minimality is a possible formal way to capture the intuitive notion of fairness.

Suggested Citation

  • András Frank & Kazuo Murota, 2023. "Fair Integral Network Flows," Mathematics of Operations Research, INFORMS, vol. 48(3), pages 1393-1422, August.
    • Handle: RePEc:inm:ormoor:v:48:y:2023:i:3:p:1393-1422
    DOI: 10.1287/moor.2022.1303
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