1. Non-Linear Programming Application
Modeling Water Use Decisions for Households in Jordan
Dr. David E. Rosenberg
CEE 6410 – Water Resources Systems Analysis
Hello. My name is Davis Rosenberg and I will briefly talk this afternoon about modeling integrated water-user decisions in intermittent supply systems.

2. Learning Objectives
Describe conditions for residential water users in Jordan
Select linear, integer, and non-linear variables to use in modeling
Identify these features in existing optimization model code
Summarize key results and implications for management
The goal of this work is integrate different source, availability, reliability, quality and conservation considerations to estimate water use. The talk is organized as follows… … One of results are some key insights to target and market conservations actions to customers. The talk will proceed as follows:
Background: Bathroom of low-income household in Jordan with bathtub, floor drain, squat toilet, squeegee, faucet, and bucket for flushing

3. Key Problems Insufficient/unreliable public supplies
Red Sea
SAUDI ARABIA
EGYPT
IRAN
PAL.
Insufficient/unreliable public supplies
Complex (tiered) rate structures
Municipal water often considered unsafe to drink
Expensive alternative sources
Limited water conservation data
Significant differences among users
Intermittent supplies mean…. In Jordan, public piped water is generally available for between 12 and 72 hrs per week.
Right: Tanker truck refills storage tank
Above: 1 m3 rooftop water tanks

4. Modeling Approach Identify options Characterize options
Describe interdependencies
Identify availability events
Top: Treatment barrels for grey-water reuse (CSBE)
Optimize
Repeat for a wide range of data values
Our integrated modeling approach works as follows. First, we identify a wide range of supply enhancement and conservation actions. These include long-term infrastructure investments like… And short-term coping strategies such as. Second,
Right: Drinking water shop sells 20-liter jugs
Above: Low-flow faucet, bidet, and toilet

5. Water supplies and storage
Roof drain and downspout
Cistern
Water meter
Municipal network
Rain falling on roof
Water vended and delivered by tanker truck
Water vended in bottles
Water vended and delivered in jugs
Well, nearby public standpipe, or stolen
Water borrowed from neighbors
Ground tank
Roof tank
To all household fixtures

6. Water consumption and use
To all household fixtures
Waste to septic tank or sewer
Wash car
Bathroom
Kitchen
Other rooms
Treated drinking water
Laundry machine
Grey-water potentially separated for re-use
Wash veranda
Floor washing
Kitchen faucet
Sink
Toilet
Irrigate landscaping
Roof tank
Leaks
Shower
Squat toilet

7. Ex 1. How to model the residential water rate structure for Amman, Jordan?

8. Ex 2. What decision variables are needed to model these additional household options?
First, we identified 39 potential actions. I won’t take the time to describe them here, but the list includes all actions mentioned and shown on the introductory slides.

9. Non-linear program with recourse
Objective: Minimize expected annual costs [Eq 1]
1st stage actions: Infrastructure investments (Lhi)
Stochastic events: Public water availability (e)
2nd stage actions: Public and alternative supply uses; behavior modifications (Shje)
Subject to:
Meet water requirements in each event [Eq 2a]
Upper limits on actions [Eq 3 and 4a-d]
Mass balance [Eq 5]
Storage capacity [Eq 6a-b]
Block pricing on network use [Eq 7a-e]
1st Stage
Event
2nd Stage
= Decision
= State where stochastic
information acquired

10. Ex 3. What decision variables represent use of the public network and how are they included?
Household model code
First, we identified 39 potential actions. I won’t take the time to describe them here, but the list includes all actions mentioned and shown on the introductory slides.

11. Using the model for a large number of residential users in Amman, Jordan
We will now demonstrate the approach for residential water users in Amman, Jordan.

12. Monte Carlo Simulation
Several model parameters differ by household
Costs of options (c1hi and c2hje)
Probabilities of water availability events (phe),
Water gained or saved by implementing options
Repeat the optimization a large number of times (with different parameter values)
Empirical data
8 prior studies (10-383,000 families)
Interviews (40 salesmen + 16 families)
Billed water use (18 families)
Engineering judgment
Second we characterize action costs and effectiveness for each potential actions. We draw from prior empirical studies plus our own informal and semi-structured interviews and surveys. We use this empirical basis to develop probability distributions for 56 water use and conservation related parameters. We then randomly sample from the parameters, and combine sample values in specific ways according to effectiveness and use functions to estimate the optimization model inputs.
Above: Drip irrigation store

13. Calibrate to the distribution of piped water use
500 Monte-Carlo simulated households
Adjust occupancy parameter (vacant residences)
Running the optimization model for 500 Monte-Carlo simulated households and adjusting the occupancy parameters gives a calibrated distribution of network water use that closely matches the billed use reported for We can then make various parametric modifications to the calibrated model inputs to explore the effects on network water use and other outputs.

14. Demand response simulating three historic rate structures
There are a variety of ways to calculate a representative price for a particular rate structure as well as for demand shift after promoting adoption of conservation actions.
Note: η = ± [α = 1%; 10,564 HH; Salman et. al (2008)]

15. Distributions of water savings for conservation actions in Amman
(error bars represent 10th and 90th percentiles)
This figure compares the percent of customers that should find it cost effective to install a conservation action with the water saved by the installation.

16. Willingness-to-pay to avoid network rationing
In a final parametric run, we estimate household willingness to pay to avoid rationing as the difference betwee household costs in the base case with limited network water availability and a second run where water was fully available.

17. Ex 4. How to represent these rate structures in the model?

18. Demand response under alternative rate structures and price schedules
In a final parametric run, we estimate household willingness to pay to avoid rationing as the difference betwee household costs in the base case with limited network water availability and a second run where water was fully available.

19. Limitations Risk neutral decision criteria Independent events
Minimize costs not maximize utility
I’ll now turn to the limitations. First, weighting short-term action costs by event probabilities implies a risk-neutral decision criteria. Further, financial discounting must relate short- and long-term costs. T
Left: Manhole and screen to collect and treat grey-water (CSBE)
Right: Rose garden of one family surveyed

20. Major Findings
Modeling integrates source, availability, quality, storage, costs, conservation, and user behaviors.
Empirically estimate water use in Amman, Jordan.
Simultaneous output of:
Conservation technology adoption
Water use response
Household willingness-to-pay
Target conservation to select customers.
Above: Store selling rooftop water tanks

21. Further Information
David E. Rosenberg, Samer Talozi, and Jay Lund (2008) "Intermittent Water Supplies: Challenges and Opportunities for Residential Water Users in Jordan." Water International. 33 (4), pp doi: /
David E. Rosenberg, Tareq Tawarneh, Rania Abdul-Khaleq, Jay Lund (2007). "Modeling Integrated Water-User Decisions in Intermittent Supply Systems." Water Resources Research W07425, doi:10:1029/2006WR
And with that, I am happy to refer you to these forthcoming publications for the full modeling details and take your questions.