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N. Hooda and O. Damani / Procedia Engineering 186 (2017) 349 – 356
1
. Introduction
Piped water network cost optimization has been studied for more than 30 years now. Several constrained
optimization techniques from Linear Programming [4] to Genetic Algorithms [13] have been employed to solve
various variations of the cost optimization problem. In this work, we focus on the cost optimization of rural piped
water networks. These networks are typically gravity fed, since reliable electricity supply is not a given. Pumps are
deployed only at the water source and not in the rest of the distribution network. Acyclic (branched) networks are
common since the redundancy provided by cyclic (looped) networks is an unaffordable luxury.
One of the most important aspects in the design of these systems is the choice of pipe diameters from a discrete set
of commercially available pipe diameters. In general, each link (connection between two nodes) can consist of several
pipe segments of differing diameters. The larger the pipe diameters, the better the service (pressure), but the higher
is the capital cost. The branched piped water network cost optimization problem is the selection of pipe diameters that
minimize the system cost while providing the requisite service (pressure at demand points).
BRANCH [1] is an optimization tool by the World Bank that attempts to minimize pipe cost for branched pipe
networks with a single water source. Though it has limited capabilities in terms of number of pipes (at most 125), and
does not guarantee optimal solution, it is used ([11], [14], [15]) in the developing world as the only alternatives are
expensive commercial tools like WATERGEMS [2]. Even WATERGEMS does not guarantee optimal solution since
it uses a genetic algorithm.
In [3], an ILP formulation is proposed for the special case of one pipe diameter per link. This means that currently
one can either get an optimal solution for the special case of one piped segment per link [3] or get a non-optimal
solution for the general case of multiple pipe segments per link [1], [2]. In this work, our aim is to come up with a
formulation that solves the general formulation while still maintaining optimality.
For the general problem, in addition to the user provided pressure and flow related constraints, following additional
constraint is inferred from [5]: in the optimal solution, each link consists of at most two pipe segments of adjacent
diameters from the available diameter set. We take two approaches to the multiple pipes per link formulation. In the
first approach, we use the fact that the optimal solution will contain at most two pipe segments per link [5]. In the
other approach, we make no assumption on the number of pipe segments per link. Surprisingly, the latter formulation’s
runtime performance is much better than the former. But knowing the structure of the optimal solution and trying to
capture that as a constraint led to a much worse runtime performance! The second formulation solves the problem
optimally and efficiently. Its solution indeed only contains at most two pipe diameters for each link in the network.
The structure that we were trying to enforce for the first formulation has come out naturally in the second.
Using the general formulation we have implemented a water network design system called JalTantra. The system
also has GIS integration for ease of adding network details. The overall goal for JalTantra is wide reaching and will
attempt to solve several network design constraints like source selection, storage location/capacity, choice of pipe
diameters, water supply scheduling, cost allocation etc. The scope of the present study is restricted to determining the
pipe diameters in a single source acyclic (branched) network.
The rest of the paper is structured as follows. Section 2 describes the problem formulation. Section 3 is a brief
description of the environment used to build the JalTantra system. Section 4 describes the comparison results of the
different models on six different networks. Conclusions and future work directions are presented in Section 5.
Nomenclature
O(.)
NL
The total pipe cost which is a function of the pipe diameters chosen for each link
The number of links in the network
D
i
Pipe diameter for the link i
L
i
Length of link i
C
i
Cost per unit length of link i, a function of the pipe diameter D
i
NP
Number of commercially available pipe diameters
th
th
x
ij
boolean variable, 1 if the i link uses the j diameter, 0 otherwise
The minimum pressure that must be maintained at node n
The head supplied by the reference node R
Pn
H
R
Hino, Tsubasa
