Proposal by team Six Nearest Neighbors, selected for problem statement AM2 under Goldman Sachs for SIH'19

1. Jal
Organisation: Goldman Sachs
Problem Statement: Shared Roof top rainwater
harvesting
Team Name: Six Nearest Neighbors
Team Leader: Khyati Mahendru
College Code: 1-3512649004

2. Problem Statement and Motivation
 India has been facing serious droughts over the years. Also, due to increasing
population, the use of ground water has drastically increased leading to
constant depletion of water table.
 In nine out of past 15 years from 2000 to 2015, about
100 districts of the country have witnessed a drought
like-situation, triggered by failure of south-west
monsoon.
 In 2016 alone, 330 million people all over the country
were affected by severe droughts.
 When there is a lack of amenities as basic as water, other
technological innovations are futile for the growth of the country.
 There is great potential for rainwater harvesting in
various locations in India which should be utilised.
 Individual rainwater harvesting systems have high
installation and maintenance costs.

3. Problem Idea and Approach
 We treat this as a problem in Operations Research i.e. as a Linear Programming Problem (LPP).
 Objective of the LPP: Minimize the cost of construction and maintenance of the system.
 Constraints are obtained from the condition that estimated demand of each household for non-drinking
purposes must be met.
 Let n = Number of households, m = Number of stable underground locations
Di = Estimated demand for ith household,
Mj = Maximum possible capacity for tank at jth location (restriction might be due to some physical
factors),
Cij = Cost (construction and/or maintenance) from ith household to jth location
We define Xij = Amount of water received from jth tank to ith household,
and 𝑌𝑖𝑗 =
1 , 𝑋𝑖𝑗 > 0
0 , 𝑋𝑖𝑗 = 0
 The corresponding LPP can be generally written as:
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑍 =
𝑗=1
𝑚
𝑖=1
𝑛
𝐶𝑖𝑗 𝑌𝑖𝑗
𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜, 𝑗=1
𝑚
𝑋𝑖𝑗 ≥ 𝐷𝑖 𝑓𝑜𝑟 𝑖 = 1,2, 3, … , 𝑛
𝑖=1
𝑛
𝑋𝑖𝑗 ≤ 𝑀𝑗 𝑓𝑜𝑟 𝑠𝑜𝑚𝑒 𝑗 (if any)
 Other constraints (if any) can be added easily as well.
 The LPP can be easily solved using any open-source optimisation toolbox.

4. Technology Stack
 Python 3.6 with COIN-OR Optimization suite
 R with ggmap and ggplot libraries for map handling and visualisation
 GNU-Octave (Optimisation toolbox)
The choice will depend on the structure of data available.
Dependencies
 An estimate of construction cost per unit volume and maintenance
cost per unit volume for storage tanks is necessary.
 We have assumed that a household can receive water supply from
multiple storage tanks.

5. Showstopper
 Web-based interactive UI for maintenance and
grievance redressal.
 The portal maintains user database for all users in
the target area.
 Users can easily check their request status and
date of last maintenance.
Use Case
Database
Historical
rainfall and
household supply
data
Underground
map
Get
constraints
Estimate
costs
Get
objective
OPTIMISATION
TOOLBOX
Get optimal
solution