MATH 411 - FALL 1996 - Mathematical Modeling
Instructor- Lou Gross
CLASS PROJECT - Sewer Line Planning: Choosing optimal routings based on
subscriber choice
The objective of this project is to investigate how alternative sewer
line plans might be implemented to best meet the requests of
subscribers. This is derived from a real situation which arose in the
Lyons Bend area of Knox County when the Knoxville Utilities Board (KUB)
submitted plans to the community for running sewer lines to various
subdivisions within the area. The plan was to allow individual
subscribers (e.g. households) to state whether or not they desired
sewer line service to their home. Each subscriber would have to pay a
substantial fee to be connected, but if a line were run by their house
and they chose not to be connected, they would still be charged a fee,
though smaller. Additionally, all homes that could be connected to a
line would be charged monthly bills depending upon water usage, even if
they did not use the sewer service (e.g. if they remained on their own
septic tank system). The goal of this project is to develop methods to
decide whether a sewer line should be run down a particular street or
not, depending upon the interest of subscribers on that street and the
associated costs to KUB and the subscriber for this.
A sample set of streets is illustrated on the attached graph, with the
boxes representing houses (only houses on one set of streets is
illustrated, but houses would be on all streets in reality. The
question to answer then is: To which points (labeled by capital letters
in the figure) should a sewer line be run to? The answer will depend
upon what the criteria are for determining where to run the lines. Some
possible criteria include:
1. Run lines so as to maximize the number of people who want service
who obtain it, while minimizing the number who do not want service who
will be forced to pay.
2. Run lines so as to minimize the total cost to subscribers who do not
want service while maximizing the number of subscribers who want
service who will obtain it.
3. Maximize the return to KUB for running the lines
There are obvious constraints in this problem as well. In particular,
you must run a line to point A before you can run to point B. Also
there are a variaety of costs which need to be considered, including
the cost per meter of running a sewer line, the cost of installation in
a household paid by KUB versus that paid by the owner, etc.
The project includes a number of Tasks, and class members will split
these amongst themselves. The instructor will act as project
coordinator, but each class member will be expected to participate in
the completion of at least one Task. Deadline for completion of the
project is the end of the semester.
Task 1. - Data acquisition and management. Obtain the appropriate data
on costs for running the lines and some sample actual spatial arrays of
houses. Either maintain these data in a form appropriate for the
simulations to be done under Task 4, or work with the participants
doing the other tasks to use the data. This task may involve obtaining
data from a GIS data base and putting it into a usable form . This will
involve contacts with KUB. (1 person)
Task 2. - Algorithm development. Develop an underlying model framework
for analyzing the problem. Decide what are appropriate algorithms to be
used to carry out analysis, and the switches necessary for appropriate
alternative assumptions about how the comparisons of different criteria
should be made. Decide appropriate output forms for the results. (2
people)
Task 3. - Program coding. Code the algorithms developed in Task 2, and
couple with the data files from Task 1. Utilize C, Fortran or Pascal on
an appropriate UNIX system, assuming the data can be utilized on this.
Document the program carefully, and have it driven mostly by prompts
from the screen. (2 people)
Task 4. - Production runs. Use the program developed in Task 3 to
investigate appropriate alternative assumptions about the distribution
of households who want service in a few sample spatial settings. Output
will presumably compare the different criteria and where lines are run
to as a function of the percentage of people wishing to subscribe. (2
people).
Task 5. - Report writing. Compose a report carefully stating the
assumptions used in this project, and giving the conclusions regarding
effects of a variety of alternative assumptions. Write this in a manner
suitable for eventual publication in a professional journal. (2 people)