The traditional metropolitan water -supply planning problem is
characterized by two main steps:
(a) project future water requirements based on present rates of
economic growth,, and
(b) schedule water development projects to be introduced into the
system on time to meet these predicted requirements.
The City of Tucson plans its water supply essentially in this manner. The
prime objective of this phase of our research was to formally review the
above problem and to formulate it in terms of concepts of management
science. Implied commitments to accept Colorado River water and gradual
changes in quality of Tucson's groundwater force serious consideration of
the economic tradeoffs between alternative sources and uses of water.
These alternatives lead to a need for a restatement of water - supply planning
objectives in more precise forms than have heretofore been put forth. The
doctoral dissertation by G. Clausen addresses itself to the above restatement
with actual data on the Tucson basin.
The various water -supply planning objective functions including the
traditional one are all expressions which maximize the difference between
gains and losses involved with water development. They can be expressed
mathematically and differentiated on the basis of how these gains and
losses are defined. In the traditional sense, gains derived from meeting
projected requirements are assumed to be infinite, and losses are taken to
be actual project costs and not social costs associated with undesirable
economic growth. Therefore, maximization of net gains is accomplished by
minimizing project costs, and gains do not even have to be expressed.
Consideration of alternatives, however, requires that gains be expressed
quantitatively as benefits to individuals, communities, or regions, i.e.,
primary, secondary, or tertiary benefits. The same logic holds for the
expression of total costs.
An objective function, used to express the water- supply problem in the
Tucson Basin, considers gains as cash revenue to a hypothetical central
water - control agency which sells water to the users within the basin.
Losses are considered as marginal costs to the agency for producing, treating,
and distributing water. The concept of economic demand is used to estimate
the amount of water that municipal, industrial, and agricultural users will
purchase at different prices. Linear demand functions are postulated. The
possible sources of supply considered are groundwater from within the basin,
groundwater from the neighboring Avra Valley Basin, reclaimed waste water,
and Central Arizona Project water from the Colorado River. Constraints are
formulated to allow for limits on water availability, for social limits on
water prices, and for minimal requirements of each user over a specified
time period; these permit a determination of optimal allocations of water
under different conditions to answer "what if' questions, given the
assumptions of the model. The resulting static model is termed a pricing
model and is optimized by first decomposing the objective function into
component parts with each part representing terms involving only one source of water. In instances involving inequality constraints, quadratic
programming is used. In other instances where equality constraints or
unconstrained conditions exist, Lagrange multipliers and calculus methods
are used. These latter conditions arise when it is determined at which
point certain constraints become inactive. In the completely general case,
this type of decomposition is not possible, but it appears that in many
specific uses objective functions of this nature can be profitably
decomposed and optima determined much more conveniently than otherwise
possible. The model clearly identifies the opportunity costs associated
with the required use of Colorado River water in lieu of the cheaper
Tucson groundwater.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/620123 |
| Date | 06 1900 |
| Creators | Clausen, George S. |
| Contributors | Department of Hydrology & Water Resources, The University of Arizona |
| Publisher | Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ) |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | text, Technical Report |
| Source | Provided by the Department of Hydrology and Water Resources. |
| Rights | Copyright © Arizona Board of Regents |
| Relation | Technical Reports on Hydrology and Water Resources, No. 1 |
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