A Bilevel Mixed Integer Linear Programming Model for Valves Location in Water Distribution Systems
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.
Isolation Valves Positioning
Bilevel Programming
Hydroinformatics
103-112
Regular Paper
Andrea
Peano
Andrea Peano
Maddalena
Nonato
Maddalena Nonato
Marco
Gavanelli
Marco Gavanelli
Stefano
Alvisi
Stefano Alvisi
Marco
Franchini
Marco Franchini
10.4230/OASIcs.SCOR.2012.103
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode