SOUTHERN JOURNAL OF AGRICULTURAL ECONOMICS
DECEMBER, 1985
OPTIMAL IRRIGATION PIVOT LOCATION ON IRREGULARLY
SHAPED HELDS
L. Upton Hatch, William E. Hardy, Jr., Eugene W. Rochester, and Gregory C. Johnson
Abstract
Although annual rainfall in the Southeast
is adequate, its distribution is a potential
constraint to agricultural production. Farm-
ers require production information concern-
ing efficient use of irrigation technology
adapted to regional growing conditions. Se-
lection of optimal position, size, and number
of pivots in center pivot irrigation systems
poses special problems on small, irregularly
shaped fields. In the southeastern United
States, field size and shape are often varied
and irregular. A mixed integer programming
model was constructed to assist in irrigation
investment decisions. The model is illus-
trated using irrigated peanut production in
southeast Alabama. Results indicate the im-
portance of economic engineering consid-
erations.
Key words: mixed integer programming,
supplemental irrigation, eco-
nomic engineering.
Selection of the optimal position, size,
and number of pivots in a center pivot irri-
gation system poses special problems on
small, Irregularlyshaped fields. In the south-
eastern United States, field size and shape are
often varied and irregular. Irrigation tech-
nology is rapidly being adopted; however,
most research on center pivot irrigation sys-
tems has focused on large regularly shaped
fields. Farmers in the Southeast require pro-
duction information concerning the efficient
use of irrigation technology adapted to re-
gional growing conditions. This paper ap-
plies a new methodology for selection of the
optimal number, size, and position of irri-
gation pivots that may be used with any field
size or shape.
Most irrigation research has focused on arid
regions because of the obvious importance
of water in these areas (Ruttan; Burt and
Stauber). However, irrigation economics is
receiving increased attention in the South-
east, particularly in Alabama, Florida, Geor-
gia, and Mississippi (Curtis; Boggess et al.;
McClelland et al.; SaIassi et al.). This in-
creased research effort has resulted from the
realization that the need for irrigation is de-
pendent upon the distribution of rainfall over
the growing season. Annual rainfall in the
region is adequate; however, its distribution
is a potential constraint to agricultural pro-
duction (Getz and Owsley). Thus, annual
rainfall data can provide a misleading impres-
sion of the usefulness of irrigation technol-
ogy-
several techniques have been developed
to optimize irrigation resource allocation.
Trava et al. used a linear programming model
to determine the date and quantity of water
to apply to agricultural crops. Integer pro-
gramming was incorporated to specify the
decision to irrigate. Udeh and Busch incor-
porated Bayesian decision theory into an op-
timal irrigation management strategy model
to address stochastic, probabilistic, and risk
elements. In addition, optimal irrigation water
use from probability distributions of evapo-
transpiration and benefit-cost analyses of ir-
rigation systems has been estimated (Khan-
jani and Busch, 1982). Khanjani and Busch
(1983) also developed a method to deter-
mine optimal size and location of farm irri-
gation reservoirs.
A technique has been developed that de-
scribes a field as a series of grid points and
attempts to analyze field coverage by center
pivot irrigation systems (Rochester). An in-
teger programming analysis was utilized to
determine the optimal locations and number
of center pivots that would maximize cov-
erage of the field (Anderson et al.). Solutions
were obtained which examined the effect of
two different irrigation strategies: one per-
L. Upton Hatch and William E. Hardy, Jr. are Assistant Professor and Professor, respectively, Department of
Agricultural Economics, Auburn University. Eugene W. Rochester and Gregory C. Johnson are Associate Professor
and Research Associate, respectively, Department of Agricultural Engineering, Auburn University.
Alabama Agricultural Experiment Station Journal Article No. 1-85920.
163