A Comparison of Traditional Worksheet and Linear
Programming Methods for Teaching Manure
Application Planning
M. A. Schmitt,*
R. A. Levins,
ABSTRACT
Manure
applicationplansprovideguidelinesfor manure
use
by livestock producers.Thisstudycompares
traditional manure
applicationplanningtechniques(worksheets),whichare calculated to meetagronomic
nutrientneedson a field-by-fieldbasis,
with plans developedusing computer-assisted
linear programmingoptimizationmethods.Manure
andcroppingdatacollected froma dairy farmin northwesternMinnesotawere used.
Traditionalworksheetandlinear programming
methodsof manureplanningwere compared
in termsof the amountof supplemental
fertilizer necessary
andthe amount
of excessnutrients
applied.Traditionalapplicationplansplacingpriority on corn
(ZeamaysL.) or wheat(TriticumaestivurnL.) fields resulted
in the greatestamount
of excessnutrientswhenrates werebased
on N. When
alfalfa (Medicago
sativa L.) tookpriority overcorn
or wheat,excess nutrientsweresignificantly reducedandsupplementalfertilizer costs werealso reduced.When
application
rates wereconstrainedby P withtraditionalor linear programmingmethods,there wasexcess manure.Anapplication plan
developedwith linear programming
withouta P restriction
resultedin the lowestlevels of excessnutrientsandthe least
amount
of supplemental
fertilizer. Linearprogramming
provided the most economicaland environmentallysound manure
applicationstrategy. Whilelinear programming
methods
require
computers,the advantagesof these methodshavebeen welcomedby people developing manuremanagement
plans.
IN
MINNESOTA, approximately
35.4
Tg of manure are
excreted each year by cattle, swine, and poultry
(Minn. Agric. Stat., 1992; MidwestPlan Service, 1985).
This manure contains approximately 203 000 Mg N,
56 810 MgP, and 130 310 MgK. Assuming full recovery of these nutrients, these quantities are equivalent to
roughly 40, 55, and 55%of the total N, P, and K consumed by crops in Minnesota annually, respectively.
Survey data from Minnesota and Wisconsin conclude,
however, that the majority of crop producers do not
reduce the amountof commercial fertilizers they use on
cropland where manure has been applied (Legg et al.,
1989; Nowakand Shepard, 1991). As a result, overapplication of nutrients by livestock producers onto
cropland poses an environmental threat to ground and
surface waters.
Formal nutrient managementplanning is increasing in
scope. In Minnesota, for example, the Soil Conservation
M.A. Schmitt, Dep. of Soil Science, R.A. Levins and D.W. Richardson, Dep. of Agricultural and Applied Economics, Univ. of Minnesota, St. Paul, MN55108. Contribution of the Minnesota Agric. Exp.
Stn. Scientific J. Series Paper no. 20 664. Received 17 June 1993.
*Corresponding author (mschmitt@soils.umn.edu).
Published in J. Nat. Resour. Life Sci. Educ. 23:23-26 (1994).
and D. W. Richardson
Service and the Minnesota Pollution Control Agencyare
increasing staff training in manuremanagementissues.
In addition, Cooperative Extension Services in several
states have produced publications addressing nutrient
credits from manureand resulting fertilizer recommendations for cropland (Schmitt, 1992; Wolkowski, 1983;
Klausner and Bouldin, 1983; Jacobs et al., 1992). Each
of these publications presents variations on traditional
worksheets intended to calculate a rate of manureapplication based on: (i) the analysis of the manure, (ii)
nutrient needs of the crop, and (iii) the selection of
indicator nutrient upon which to base the manureapplication rate. This process is done sequentially on a fieldby-field basis and is carried out until all of the manure
has been applied.
An alternative to these traditional methodsof determining application rates for manure is linear programming. Linear programminghas been used in industry for
decades to solve such problems as finding the least-cost
route for trucks and ships. In farm management,linear
programming is often used to develop profitable farm
financial plans, and livestock producers might recognize
linear programmingfrom its extensive use in least-cost
ration programs. Levins and Johnson (1989) provide
example of linear programming in farm managementdecision making.
A thorough introduction to the theory of linear
programmingis given by Beneke and Winterboer (1973).
The particular linear programmingmodelused in this article is described by Levins and Schmitt (1992). For purposes of this paper, it is not essential to understand in
detail how manure application plans are obtained with
linear programming. Instead, the emphasis will be on
comparing application plans from linear programming
with those obtained with traditional methodsin terms of
the amountof supplemental fertilizer necessary and the
amount of excess nutrients applied with the manure.
The linear programmingmodel we used is incorporated into the computer program Manure Application Planner (Levins and Schmitt, 1992). The program’s objective
is to minimizethe cost of commercialfertilizer applied
to fields available for spreading manure. The plan developed by linear programming must satisfy two broad
sets of constraints. First, a set of technical constraints
assures that manureapplication cannot exceed available
supply and that the nutrient requirements for each field
must be met. Second, a set of environmental constraints
was constructed. For a manure application plan to meet
current agency guidelines, the N requirements for fields
with nonlegume crops cannot exceed specified limits.
Phosphorusrequirements for all crops can be greater than
the requirement on a case-by-case basis where soil erosion and proximity of surface water are not problems.
J. Nat. Resour. Life Sci. Educ., Vol. 23, no. 1, 1994 ¯ 23
As environmental stewardship mandates that manure
management plans he implemented by all livestock
producers, determining manureapplication plans that effectively address both the economic and environmental
concerns of the farmer is of paramount importance.
Agricultural professionals
working with livestock
producers--current and soon-to-be (college students)need to be familiar with calculation techniques that are
available. The objective of this study is to comparetraditional manureapplication planning techniques, which are
calculated to meet agronomic nutrient needs on a fieldby-field basis, with manure application plans developed
using linear programming methods.
MATERIALS
AND METHODS
Manure and cropping data collected from an active
dairy farm in northwestern Minnesota were used to compare manureapplication plans calculated by the traditional and linear programmingmethods. This case farm was
a Holstein (Bos taurus) dairy operation with 121.5 ha of
tillable cropland. The crops were wheat (62.8 ha), corn
(16.2 ha), and alfalfa (42.5 ha). There were 40 milking
cows with 30 other livestock comprising the replacement
stock. Manure from the lactating cows was handled as
a liquid in an earthern storage structure. There were 767.3
m3 produced/yr, and the analysis of this manure per
0.378 m3 was 15-10.1-15.8
(kg of N-P-K). Manure
from the dry cows and other animals totaled 288 Mg/yr
and was stored as a solid pack, the analysis of which was
6-3.1-10.8 kg N-P-K/t. Storage facilities were such that
manurewas spread in the fall and spring. All of the manure was surface-broadcast; therefore, incorporation within a couple days was possible for that land planted to
wheat and corn.
Fertilizer recommendationsfor the three fields were
based on soil tests, crop rotation, yield goals, and soil
characteristics. The alfalfa, corn, and wheat recommendations were 0+24.9+125.3, 50+29.3+64.7, and 67
÷ 14.9+28.2 kg/ha N, P, and K, respectively (Rehmet
al., 1993a,b, c). A soil N test to measureresidual nitrateN was used because the location of the farm was in the
more arid region of Minnesota. The farm had no significant slopes in its landscape and was not near surface water
bodies, so no P restrictions were mandatedby Minnesoo
ta’s Pollution Control Agency. Any needed supplemental fertilizer was surface-applied and incorporated into
the soil. Fertilizer nutrients were valued at $0.29, $1.01,
and $0.29 per kg of N, P, and K, respectively.
Traditional manure application plans were calculated
based on the nutrient requirement of the field and the
nutrient content of the manure. Nitrogen availability indices were 0.40 for when the manure was applied to the
wheat and corn and 0.20 when applied to the alfalfa, the
difference due to incorporation (Schmitt, 1992). It was
assumedthat a field could be partitioned into smaller portions. This allowed manureto be applied at the appropriate rate until the manure supply was gone.
With traditional methods, the choice of which source
of manure(liquid or solid) to use first, the order in which
the fields were treated with manure, and the nutrient upon
which applications were based was left to the judgment
24 ¯ J. Nat. Resour. Life Sci. Educ., Vol. 23, no. 1, 1994
Table 1. Seven manure application managementstrategies determined by selection of manure source, crop, and nutrient constraint priorities.
Sequential solution order~
Strategy
designation
A
B
C
D
E
F
G
H
Manure
1st
2nd
L
S
L
S
S
L
L
S
L
S
L
S
Simultaneous
Simultaneous
Crop
1st
2nd
3rd
C
C
C
W
A
A
W
W
W
C
C
C
Simultaneous
Simultaneous
A
A
A
A
W
W
Nutrient
constraint
N
P
N
N
N~
P
N
P
Abbreviations
usedare:L = liquid,
S = solid,
C = corn,W = wheat,
andA = alfalfa.
Phosphorus
isusedas constraining
nutrient
whenrates
foralfalfa
fields
arebeing
calculated.
of the person using the method. To show how different
solution strategies affected the plan developed, the traditional method was used in six different ways in which
starting manure source, crop ordering, and indicator
nutrient were varied (Table 1). The linear programming
method was to calculate two plans--one with N and one
with P as the indicator nutrient. For each solution, the
total nutrients applied in excess of crop requirements and
the cost of supplemental fertilizer were calculated. Because linear programmingconsiders all fields (crops) and
manure sources simultaneously, the order of the fields
or manure sources was irrelevant.
RESULTS AND DISCUSSION
The manure application plans developed for the case
farm using different strategies are shownin Table 2. The
first six plans were developed using variations on the
traditional method, and the last two were developed with
linear programming. Liquid manure application rates
ranged from 1.9 to 41.3 m3/ha, depending on the strategy used to calculate the rates. Solid manurerates ranged
from 0.8 to 24.0 Mg/ha. Although traditional application plans calculated manureapplication rates using only
one source of manure for a given hectare, the solution
using linear programming(strategies G and H) could determine application rates for both sources of manurefor
a given field. Supplemental commercial fertilizer was
often recommendedusing traditional rate calculation
methodson fields after the supply of manurewas exhausted. Also, strategies that used P as the constraining nutrient generally required commercialN to be applied to the
corn and wheatfields. All strategies required applications
of supplemental K to the alfalfa crop.
The excess nutrients and cost of supplemental fertilizer are shownin Table 3. None of the strategies allowed
for excess N to be applied to any of the fields.. WhenP
was the constraining nutrient (three of the eight strategies), no excess N was applied. Although N was recommended for alfalfa, the N was not considered excess.
Based on the potential N amounts applied in a P-constraining calculation, research data have not found this
N to be a high environmental risk due to the rapid disappearance of inorganic N (Schmitt et al., 1992). When
Table 2. Application rates of liquid manure,solid manure, and commercialfertilizer
for case farm’s crops as a function of selected strategy.
Application
rates
Strategy
A
B
C
D
E
F
G
H
Crop
Wheat
Alfalfa
Corn
Wheat
Alfalfa
Corn
Wheat
Alfalfa
Corn
Wheat
Alfalfa
Corn
Wheat
Alfalfa
Corn
Wheat
Alfalfa
Corn
Wheat
Alfalfa
Corn
Wheat
Alfalfa
Corn
Liquidmanure
Hectares
m3/ha
41.3
Solidmanure
Hectares
N + P+ K
Mg/ha
6.5
........
16.2
62.8
25.1
16.2
18.6
30.9
5.5
9.4
11.0
41.3
....
41.3
24.0
12.2
67 + 14.9 + 28.2
0 24.9 125.3
........
.....
18.6
.......
....
7.6
....
....
58+ 0 + 5
0 + 0 + 64.7
32+0+ 19.9
67 + 14.9 + 28.2
0 + 24.9 + 125.3
17.4
17.9
12.5
16.2
23.1
........
....
9.4
30.9
5.5
9.4
11.0
6.8
1.9
15.9
7.5
3.8
7.5
42.5
12.2
33.6
42.5
16.2
62.8
42.5
16.2
62.8
42.5
16.2
Hectares
kg/ha
24.0
....
17.9
4.5
....
....
....
6.7
....
0.8
4.6
2.9
8.9
4.1
29.2
42.5
62.8
42.5
16.2
44.1
42.5
67 ÷ 14.9 ÷ 28.2
0 + 24.9 + 125.3
50 ÷ 29.3 + 64.7
67 + 14.9 + 28.2
0 + 0 + 87.2
62.8
42.5~"
16.2
44.1
42.5
-o
21.1
42.5
16.2
53.9
42.5
57+ 0 + 5
0 + 0 + 87.2
32+ 0 + 19.9
56+ 0 + 0
0 + 0 + 36.5
25 + 0 +0
57+ 0 + 0
0 + 0 + 54.8
30 + 0 + 0
62.85
42.5
16.2
62.8
42.5
16.2
62.8
42.5
16.2
Rates of Kwere 35.7 kg for 25.1 ha and 13.3 kg for 17.4 ha.
Rates of N were 24 kg for 33.6 ha and 22 kg for 29.2 ha and the 1.7 kg of K was for only 336 ha.
summedfor the entire case farm, excess nutrients ranged
from 514 to 3059 kg for P and from 761 to 5452 kg for
K. The cost of supplemental fertilizer varied from $1571
to $4494for the case farm. The fertilizer expense for the
case farm if no manure were available would be $6303.
The strategy selected had significant effects on application rates, excess nutrients, and the cost of supplemental fertilizer.
Using traditional application planning
methods,applying the solid or liquid manurefirst did not
result in substantially different plans (Strategies A and
C). These two strategies had comparable excess P and
K nutrients and relatively high supplemental fertilizer
COSt.
The prioritization order given the three crops on this
farm did have a noticeable effect when comparing the
three strategies (A, D, and E). Similar results were
achieved when either wheat or corn were the first two
crops to receive manure (Table 3). However,whenalfalfa was given first priority for manure, the amounts of
excess P and K were decreased by an average of 42 and
29%0,respectively. Averagesupplemental fertilizer costs
decreased by 26%. Contrary to the perception that alfalfa should be the crop with the lowest priority for manure applications, the economic fertilizer replacement
value of the P and K nutrients can be substantial, as this
scenario illustrates.
Basing manure application rates either on N or P had
a noteworthy effect on the overall plans using traditional worksheetstrategies. Withstrategies that used P as the
primary nutrient constraint (B and F), the case farm had
excess manure(156 Mg) that could not be spread on the
available land. With this P constraint, excess nutrient
amounts were considerably less than with comparable
Table 3. The effect of selected strategy on excess nutrients and
supplemental fertilizer for case farm.
Excess nutrients
Strategy
N~
P
K
Supplemental
fertilizer:~
A
B
C
D
E
F
G
H
0
0
0
0
0
0
0
0
kg
2254
0
3059
2385
1353
0
514
0
5061
0
3512
5452
3746
761
0
0
$
4494
2188
4494
4541
3360
2395
1571
1859
Nitrogen applied to alfalfa is not considered excess.
This is the total cost of the case farm’s fertilizer accounting for the
nutrient credit of the applied manure.
strategies using an N constraint, and the commercialfertilizer costs were also less (Table 3). Whenthe linear
programmingstrategy that was constraining for P was
used (Strategy H), there were no excess nutrients applied,
a relatively small increase in supplementalfertilizer costs,
and an excess of 197.3 m3 of manure.
The application plan that was N-based and used the
linear programmingmethod (Strategy G) had the smallest
supplemental fertilizer bill (Table 3). However,the low
manureapplication rates suggested (Table 2) pose a concern to most producers, because applying these rates can
be challenging with current equipment options. Although
this logistical concernis pertinent to the strategies involving linear programming
or whenapplication rates are constrained by P in this case study, traditional manure
worksheet plans can also result in low application rates
depending on manure nutrient content and the nutrient
needs of a field.
J. Nat. Resour. Life Sci. Educ., Vol. 23, no. 1, 1994 ¯ 25
SUMMARY
Traditional application plans can result in a wide range
of excess nutrients and supplemental fertilizer costs depending on the priority of the crops to be fertilized and
the nutrient that is the basis for the application rate. For
the case farm studied, priority given to corn or wheat
fields resulted in the greatest amount of excess nutrients
when rates were based on N. Prioritizing manure application rates for alfalfa before corn and wheat or limiting applications for all crops based on P resulted in
relatively lower levels of excess nutrients. However,
whenever P was used as the constraining nutrient, all of
the manure could not be applied on the producer's fields.
Application plans that used linear programming to determine application rates resulted in the lowest cost for
supplemental fertilizer. Linear programming calculation
provided the most economical manure application strategy, but the practicality of applying some of the low manure rates may limit widespread adoption of this type of
manure management plan calculation.
The teaching of manure application planning and rate
calculation using linear programming has been well accepted in Minnesota. We have conducted educational programs for state agency and county extension personnel
and have first used traditional worksheet methods to create awareness about the amounts of excess nutrient and
supplemental fertilizer costs before introducing the linear
programming option. Although using linear programming will always require computers, participants were
generally comfortable with the software after the demonstrations and workshop sessions. The advantages of the
linear programming strategies compared with traditional worksheet methods were clearly recognized.
ACKNOWLEDGMENT
The case farm used in this article was adapted from
a case study project prepared by Rhonda Amundson,
Minnesota Extension Service, and Wendy Lewis, form-
26
• J. Nat. Resour. Life Scl. Educ., Vol. 23, no. 1, 1994
erly a graduate research assistant with the Department
of Agricultural and Applied Economics, University of
Minnesota.