Figure 1. Illustration of Grid System Used to Sim-
ulate Field Coverage for Pivot Irrigation Systems
of Various Sizes and Different Locations.
Equation (1) is the objective function rep-
resenting the difference in revenues (the value
of peanut production plus income from land
rental) and costs (for producing both irri-
gated and поп-irrigated peanuts). Equation
(2) assures that only one size pivot may be
located at a given point. The relationship
expressed in equation (3) accounts for the
peanut production and selling alternatives
and requires that all production be sold.
Equation (4) controls total land use, while
equations (5) and (6) limit the quantity that
can be sold at quota and contract prices.
Figure 1 illustrates a nine-by-nine grid field
with irrigation coverage that could be ex-
pected from placing either of three size cen-
ter pivot systems at two of several potential
locations. For example, if the medium sized
center pivot system were placed at point 6,4,
the following grid areas would be covered:
4,4; 5,3; 5,4; 5,5; 6,2; 6,3; 6,4; 6,5; 6,6;
7,3; 7,4; 7,5; and 8,4. Obviously, portions
of other grids would be covered and some
area associated with the specified grid areas
would not be covered. The error associated
with simulating the exact area covered is not
large as long as the grid size is kept relatively
small.
As is illustrated in Figure 1, overlapping
coverage could result from the selection of
certain sizes and locations of pivots. In actual
field applications, irrigation units could be
restricted to partial circles so that overwa-
tering would not occur. Overlapping is con-
sidered in the programming model.
Partial budgets giving the ownership, op-
erating, and additional production costs for
the specified sizes of irrigation systems were
developed (Boutwell and Curtis). These cost
estimates were combined with production
budgets obtained from the Alabama Coop-
erative Extension Service, experimental crop
response data (Rochester et al.), and peanut
prices (quota, non-quota, and world) to ob-
tain profit. Thus, the model is able to select
the optimal grid points at which to locate a
center pivot and the optimal size of that
pivot. Also, the profit associated with that
irrigation system is estimated. The model per-
mits determination of the number of acres
that should be grown without irrigation and
the number of acres that should be rented
out for a given field.2
Cost data from partial budgets for small,
intermediate, and large pivot systems are
summarized in Table 1. A typical water sup-
ply system was specified using Soil Conser-
vation Service and Extension Service data
(Boutwell and Curtis). Economies of size are
evident in ownership and operating costs.
The effect of pivot size is particularly dra-
matic on ownership costs. Pivot size limi-
tations are imposed by field size and shape.
Operating cost per acre differ by only 1.3
Table 1. Costs and Breakeven Prices for Selected
Center Pivot Sizes for Irrigation Systems on Peanuts
in Southeast Alabama, 1984
|
Irrigation system sizea | |
|
Item |
Small Intermediate Large |
Ownership cost
|
(dollars∕acre) ............ |
86.96 |
72.51 |
65.94 |
|
Operating costb |
30.33 |
30.08 |
29.93 |
|
Additional production |
14.04 |
14.04 |
14.04 |
|
Total annual cost |
131.33 |
116.63 |
109.91 |
Breakeven price'
(dollars∕pound) ........ .253 .225 .211
* Acreage reflects radius and grid size selected for the
model.
b Operating costs are estimated for 8 acre-inches of
irrigation water. This was the mean level of annual
application in the crop response experiment, 1976-1981
(Rochester et al.).
‘ Based on average response of 520 lb. of peanuts per
acre on class 1 soils.
2 The “rented out” option was included to reflect potential allocation of the land resource to other uses.
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