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DOI: 10.4230/OASIcs.SCOR.2012.103
URN: urn:nbn:de:0030-drops-35519
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Peano, Andrea ; Nonato, Maddalena ; Gavanelli, Marco ; Alvisi, Stefano ; Franchini, Marco

A Bilevel Mixed Integer Linear Programming Model for Valves Location in Water Distribution Systems

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The positioning of valves on the pipes of a Water Distribution System (WDS) is a core decision in the design of the isolation system of a WDS. When closed, valves permit to isolate a small portion of the network, so called a sector, which can be de-watered for maintenance purposes at the cost of a supply disruption. However, valves have a cost so their number is limited, and their position must be chosen carefully in order to minimize the worst-case supply disruption which may occur during pipe maintenance. Supply disruption is usually measured as the undelivered user demand. When a sector is isolated by closing its boundary valves, other portions of the network may become disconnected from the reservoirs as a secondary effect, and experience supply disruption as well. This induced isolation must be taken into account when computing the undelivered demand induced by a sector isolation. While sector topology can be described in terms of graph partitioning, accounting for induced undelivered demand requires network flow modeling. The aim of the problem is to locate a given number of valves at the extremes of the network pipes so that the maximum supply disruption is minimized. We present a Bilevel Mixed Integer Linear Programming (MILP) model for this problem and show how to reduce it to a single level MILP by exploiting duality. Computational results on a real case study are presented, showing the effectiveness of the approach.

BibTeX - Entry

  author =	{Andrea Peano and Maddalena Nonato and Marco Gavanelli and Stefano Alvisi and Marco Franchini},
  title =	{{A Bilevel Mixed Integer Linear Programming Model for Valves Location in Water Distribution Systems}},
  booktitle =	{3rd Student Conference on Operational Research},
  pages =	{103--112},
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-39-2},
  ISSN =	{2190-6807},
  year =	{2012},
  volume =	{22},
  editor =	{Stefan Ravizza and Penny Holborn},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-35519},
  doi =		{10.4230/OASIcs.SCOR.2012.103},
  annote =	{Keywords: Isolation Valves Positioning, Bilevel Programming, Hydroinformatics}

Keywords: Isolation Valves Positioning, Bilevel Programming, Hydroinformatics
Collection: 3rd Student Conference on Operational Research
Issue Date: 2012
Date of publication: 26.06.2012

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