1
LINEAR OPTIMIZATION-exercises using land use systems
generated with LUCTOR
H. Hengsdijk
Introduction
This document with its exercises is a brief introduction how technical coefficients
generated with LUCTOR can be used in a linear programming model. This type of models is
frequently used in land use studies (Rabbinge & Latesteijn, 1992; WRR, 1992; Veeneklaas et
al., 1994). It goes beyond the scope of this document to fully explain the technical details and
background of linear programming. Merely suffice to say here that in the linear programming
exercises presented combinations of land use systems are selected that maximize the total
profit (net return) under various boundary conditions (restrictions). For educational purposes
simple optimization exercises have been developed in EXCEL8.0 with ready-made technical
coefficients for a number of crops and management options (cropping systems). A set of
scenarios with specific boundary conditions have been pre-programmed that can easily be
executed by the user.
The case study presented is for a (hypothetical) farm in the Neguev settlement in the
Atlantic Zone (location 83 33’E and 10 12”N). The altitude is between 10 and 50 m above sea
level in a region where climate can be classified as very humid, without dry months. The
settlement originated when squatters occupied land of the hacienda Neguev in 1979. The IDA
(Instituto de Desarollo Agropecuario) divided the Neguev into farms of 10, 15 and 17 ha
(Schipper, 1996). Three soils have been classified in the Neguev: fertile well drained (SFW),
infertile well drained (SIW) and fertile poorly drained soils (SFP). The latter soils are
unsuitable to grow crops due to waterlogging. The total area of the case study farm is 10 ha
and encompasses 5 ha of SIW and 5 ha of SFW soils.
Although pastures and forests are still the major land uses in the region the case study will
exclusively focus on crops. As part of a structural adjustment program, the Costarican
government lowered prices of basic food crops (including maize and beans) which have
pushed cropping towards palmheart and pineapple. Major concern in the region are low farm
incomes, while at the same time land is used in an unsustainable way. I.e. farmers deplete
their soils since insufficient fertilizers are used to maintain soil fertility. Moreover, biocides
27/06/2016 612930688
2
are frequently used, especially in pineapple cropping systems. Low credit availability limits
farmers to invest in more productive and sustainable production methods.
This case study will investigate the possibilities to improve the situation of farmers in the
Neguev while taking simultaneous account of income, sustainability and environmental
effects. LUCTOR was used to generate a number of land use systems. These land use systems
are offered to a (simple) Linear-programming model that optimizes farmers profit (net
revenue) given various restrictions related to sustainability, environmental and socioeconomic effects. The combination of the optimized objective (profit) and restrictions are
called ‘goals’. Using the LP-model with different goals, so-called ‘scenarios’ can be created.
The results of these scenarios quantify trade-offs that exist among various goals. Examples of
scenarios include a farmers profit scenario, a sustainability scenario or an environmental
scenario.
In brief, the LP model presented finds the ‘optimum’ number and types of land use
systems by maximizing ‘profits’, i.e. the sum of economic yield (i.e. sold products) minus the
sum of all input and labor costs (for field operations). Physical restrictions are set on soil use
(i.e. no more of each land unit can be used than the maximum available), on labor (no more
labor can be used than available at the farm), on the area that each crop may comprise (to
avoid soil born diseases, common in mono cropping systems), and - optionally - on
sustainability, environmental or socio-economic parameters. Prices of inputs and outputs are
those prevailing in the Atlantic Zone in mid 1996.
Installation
The exercises can be run on any type of computer with WINOWS95 and EXCEL. Copy
the file LP_MOD.XLS to any directory on your hard disk C:\. Open EXCEL by pressing the
EXCEL icon in your Microsoft toolbar or Initial start up. Press [Ctrl+o] to open the file
LP_MOD.XLS. After two introduction dialog boxes the user may view the technical
coefficients. The file consists of two worksheets with technical coefficients. The optimization
model is hidden. Worksheet MODEL1 contains technical coefficients of actual land use
systems only, while worksheet MODEL2 contains technical coefficients of both actual and
alternative land use systems.
Before starting the optimization exercises the user must press [Ctrl+x] to start a macro that
links the EXCEL solver file to the exercises. The location of this file may be different on pc’s
due to differences in installation of Microsoft office and/or WINDOWS95. When the
SOLVER.XLA file is not available on your hard disk C:\ a dialog box appears to inform you
27/06/2016 612930688
3
that you first should install SOLVER.XLA using your Microsoft Office software. Without
this file the exercises will not work. After you have installed SOLVER.XLA you have to
repeat the opening procedure of LP_MOD.XLS and press [Ctrl+x] once again to link the file
with the LP-exercises.
The exercises using technical coefficients of actual land use systems may be activated
pressing [Ctrl+y], while pressing [Ctrl+r] will activate the exercises using both actual and
alternative land use systems. It is advised to start with the exercises using actual land use
systems only. In this order the exercises will be discussed in the following.
A last remark: The regional settings of your pc should separate decimals with a dot. Some
of the exercises will show errors using comma separation of decimals. The English (United
States) setting uses dot separation.
Scenario 1: base scenario
First, a so-called base-scenario is run using technical coefficients of actual land use
systems only. This base scenario has no restrictions with regard to sustainability or
environmental effects, i.e. profit is maximized under restrictions of available soils and labor
availability. Soils available for each crop (crop rotation restrictions) have been set at 2 ha for
each crop type, i.e. a maximum of 2 ha of the farm area may be cropped with cassava, 2 ha
with beans, 2 ha with maize-grain and maize-fresh cobs, 2 ha with pineapple and 2 ha with
palmheart. In this scenario 64 actual cropping systems are studied as shown in the worksheet
MODEL1. For educational purposes only a selection of technical coefficients generated by
LUCTOR are shown and one coefficient has been added, gross income (column heading
GROSS) which is the value of the sold produce. The costs of production (column heading
CCOST) exclude costs for fertilizers and labor. However, in the optimization of profit (or net
revenue) fertilizer and labor costs are discounted for. Technical coefficients for actual
cropping systems have been generated for maize-grain, maize-fresh cobs, cassava, pineapple
for the local market and palmheart.
 Press [Ctrl+y] to open a dialog box with scenario options and select ‘base run’. Press
[OK] when the scenario is selected.
 The LP model will start to optimize the net return objective in an iterative way. The
optimization process stops when a solution is found that does not allow further
progression of the objective function. While running the LP-model the screen will flicker
now and then.
 When an optimal solution is found the LP-model returns with a bell sound and a message
box with solver results. It says that the solver found a solution and that all constraints and
27/06/2016 612930688
4
optimally conditions are satisfied. The option button with ‘Keep solver solution’ is turned
on. Press [Return] or click the OK button.
 The model continues with writing the objective values, selected land use systems and
constraint values to the output worksheet base_run. When finished the base_run
worksheet is the active sheet with results of the LP-model.
 View the contents of this worksheet.
The first item at the top of the base_run worksheet is the so-called ‘objective function’,
which is the variable that has been maximized. In our case study, this is the total profit of
cropping systems:
Total net revenue in col/year
Net revenue
SOLUTION
1619192
This net revenue is the highest profit that can be obtained with cropping systems at the
farm since - except for the restriction on maximum soil use, the crop rotation restriction and
the available labor that must be satisfied! - No restrictions on sustainability/environmental
effects or credit availability were imposed. The base run can thus be interpreted as pure
farmers’ profit scenario (short-term profit).
Then follows the list of selected land use systems that resulted in the highest profit realized
(see Annex I for the identification codes of land use system codes):
Land use systems in ha
SOLUTION
SFW.ME.F0HHL
2.00
SFW.ZC.F0HHL
1.00
SFW.AM.F0HLH
2.00
SIW.BG.F0HLL
2.00
Apparently, it is most profitable to concentrate on cassava, pineapple and palmheart
systems since these attain their maximum area. The fertile well-drained soils (SFW) are
preferred to the infertile well-drained soils (SIW): Of the total cropped area 5 ha are SFWsoils while only 2 ha of SIW-soils (with pineapple) are selected. The preference for SFW soils
can also be seen in the following section of the output, the part with restrictions. All the SFW
soils are used while 3 ha of SIW soils are left fallow.
27/06/2016 612930688
5
Soil use in ha
MAXIMUM
SOLUTION
SFW
5.00
5.00
SIW
5.00
2.00
This is not caused by a shortage of labor, which is shown by the labor restriction:
Labor use in days/yr
labor use
MAXIMUM
SOLUTION
300.00
228.90
The solution shows that less labor is required than the maximum available, which was set
at 300 days per year. The crop rotation restriction shows that three crops attain their
maximum allowable area (cassava, pineapple and palmheart). Since all SFW soils are used in
the solution the LP-model can not select any other land use systems because maize and beans,
which do not reach their limit, are unsuitable to grow at infertile well-drained soils (SIW).
Crop rotation in ha
MAXIMUM
SOLUTION
Cassava
2.0
2.0
Maize
2.0
1.0
Beans
2.0
0.0
Pineapple
2.0
2.0
Palmheart
2.0
2.0
On the other (costs and sustainability and environmental) indicators were no restrictions
set in this scenario. Note that the 7 ha of cropped area result in a N-deficit of about 157/7 = 22
kg N/ha. The total amount of biocide (herbicides, fungicides and insecticides) used is about
12/7 = 1,71 kg ai/ha.
Total farm costs in col/yr
MAXIMUM
SOLUTION
Infinite
744857
N-balance in kg N
Infinite
-157
P-balance in kg P
Infinite
27
K-balance in kg K
Infinite
-330
biocide use in kg a.i
Infinite
12
Costs without fertilizer and labor
Sustainability indicators
27/06/2016 612930688
6
The base run scenarios shows the optimal combinations of cropping systems given the
boundary conditions imposed for an individual farm. When all farmers in a region would use
the same cropping pattern over-production of certain products could lead to price drops while
for other products (e.g. beans in this example) a shortage will result in a price increase. It is
obvious that this kind of price effects will determine the optimal combination of selected
cropping systems. Note also, that the selected production systems are highly unsustainable as
expressed by the large amounts of soil nutrient depletion, which means that yields cannot be
maintained on the long run. In the following exercise we will analyze the effect of fertilizers
to counter balance the loss of nutrients.
 Fill-in some summary information in Table 1 (at the end of this document) for
comparison with other scenarios (pre-filled-in as example).
Scenario 2: Reduced N-depletion scenario
In this scenario, the same model with its technical coefficients as in the base scenario is
run, the only difference consists of a restriction on the N-balance. The base scenario showed
that current-cropping practices without a restriction on the allowable soil nutrient depletion
would result in a considerable exhaustion of soil nutrients. Ultimately this will result in
declining yields and farm profits. The reduced N-depletion scenario expresses a hypothetical
(political) wish to for a more sustainable agriculture by reducing soil depletion. In this
scenario it is assumed that nutrient depletion is reduced by 50% compared to the base run. I.e.
the maximum allowable N-depletion is set at –79 kg N for the entire farm.
 Press [Ctrl+y] to open a dialog box with scenario options and select ‘Reduced N depletion
scenario ’. Press [OK] when the scenario is selected.
 The LP model will start to optimize the net return objective. The optimization process
stops when a solution is found that does not allow further progression of the objective
function. While running the LP-model the screen will flicker now and then.
 When an optimal solution is found the LP-model returns with a bell sound and a message
box with solver results. It says that the solver found a solution and that all constraints and
optimally conditions are satisfied. The option button with ‘Keep solver solution’ is turned
on. Press [Return] or click the OK button.
 The model continues with writing the objective values, selected land use systems and
constraint values to the output worksheet N_restriction_run. When finished the
N_restriction_run worksheet is the active sheet with results of the scenario.
27/06/2016 612930688
7
 View the contents of this worksheet and fill in Table 1 (at the end of the document). Note
the differences with the base run (scenario 1), as well as the trade-offs between indicator
values.
Due to the N-restriction imposed the area of the most nutrient depleting crop (cassava) is
decreased compared to the base run. Maize that does not contribute much to the farm profit is
no longer selected. Compared to the base run a part of the cassava is produced at infertile well
drained (SIW-land units) with lower yields and less negative N-balances compared to cassava
systems at SFW land units. Palmheart systems have a positive N-balance due to the currently
high N-gifts. Since N-losses are smaller at SFW land units than SIW land units, palmheart is
shifted to SFW land units on which N-balances are more positive than on SIW land units. The
net revenue decreases with 14% compared to the base run, indicating the ‘price’ of a more
sustainable system (however, still not 100% sustainable!). It is emphasized that in this
scenario only actual production systems are analyzed. The effect of introduction of alternative
land use systems, which are aimed at equilibrium nutrient balances, will be analyzed in
scenario 4, 5 and 6.
Scenario 3: Reduced biocide scenario
The same model as in the base scenario is run, with a restriction on the use of biocides as
quantified by BIOA in the technical coefficients. The scenario expresses a hypothetical
(political) wish to decrease the use of biocides by 50% from the base situation. Therefore, a
restriction on BIOA is set as 50% of 12 kg ai = 6 kg a.i for the total farm area.
 Press [Ctrl+y] to open a dialog box with scenario options and select ‘Reduced biocide
scenario ’. Press [OK] when the scenario is selected.
 When the optimization procedure is finished save the results by clicking OK button or
pressing [Return].
 The model results are written to the worksheet biocide_run. When finished this worksheet
is the active sheet with results of the scenario.
 View the contents of this worksheet and fill in Table 1 (at the end of the document). Note
the differences with the base run (scenario1), as well as the trade-offs between indicator
values.
Reduction of the use of biocides is realized by selecting low herbicide systems. Note that
the low pesticide option is not chosen. Apparently, the yield reduction due to low pesticide
use is too large to be profitable. To satisfy the biocide restriction the pineapple area is
27/06/2016 612930688
8
reduced. Pineapple is the most demanding crop concerning biocides. This allows shifting a
part of the palmheart towards more productive land units (SFW). The total area is reduced to
5.4 ha while the net revenue is reduced with 16% compared to the base run. Note that the
costs of production are much lower. Why?
Scenario 4: Introduction of alternative land use systems scenario
In this scenario a completely new set of alternative land use systems is added to the
former set with only actual cropping systems, a total of 128 land use systems, see worksheet
MODEL2. To study the feasibility of using fertilizer to compensate for soil nutrient depletion
(and thus to produce in a sustainable way) the same crops with the same management options
were generated with LUCTOR as for actual land use systems used in the previous scenarios.
The production level of alternative land use systems was set at 100% of the maximum
attainable level and are therefore higher than the current attained yields.
 View briefly the model-worksheet and recognize that alternative land use systems have
been added to the technical coefficients compared to the previous scenarios (compare
worksheet MODEL1 and MODEL2).
 Press [Ctrl+r] to open a dialog box with scenario options and select ‘Introduction of
alternative systems scenario ’. Press [OK] when the scenario is selected.
 The LP-model optimizes the net return of the farm in the same way as in the previous
scenarios.
 When an optimal solution is found press the OK button or [Return]. The model writes the
results to the worksheet alternative_run, which will be the active worksheet when
finished.
 View the contents of this worksheet and fill in Table 1 (at the end of the document). Note
the differences with the previous scenarios, as well as the trade-offs between indicator
values.
Although the costs (without labor and fertilizer costs) of alternative land use systems are
twice as high as those of actual land use systems, it is profitable to choose for alternative land
use systems. The net revenue can be tripled by selecting high yielding alternative land use
systems compared to the base run of scenario 1. In terms of crop choice this scenario
resembles the base run scenario: cassava, pineapple and palmheart are the most preferred
crops that each attain their crop rotation constraint of 2 ha. Note that labor availability in this
scenario limits further increase of the net revenue. Note also the high input of biocides
required to realize the high yields of alternative land use systems.
27/06/2016 612930688
9
Scenario 5: Reduced credit scenario
The previous scenario showed that farm profit can be increased considerably through the
introduction of alternative (and 100% sustainable!!) land use systems. However, costs for
machinery, biocides, plant material etc. are doubled compared to the base run (scenario 1).
These investments are even much higher as the costs for fertilizer and labor, - which are
substantial for alternative land use systems and which are not accounted for in the costs as
shown!-, are taken into account. It is unlikely that a farmer has the financial sources to realize
these investments. In this scenario it is assumed that the farm has a credit restriction at the
amount of the costs of the first scenario, i.e. 744857 col. for the entire farm (see results
scenario 1 in Table 1). This is almost half of the investments required in scenario 4.
 Press [Ctrl+r] to open a dialog box with scenario options and select ‘Reduced credit
scenario ’. Press [OK] when the scenario is selected.
 The scenario results are written to the worksheet credit_run. When finished this
worksheet is the active sheet with results of the scenario.
 View the contents of this worksheet and fill in Table 1 (at the end of the document). Note
the differences with scenario 4, as well as the trade-offs among indicator values.
Note that net return drops almost 25% while investment costs are 50% lower than in
scenario 4. The production has shifted towards less expensive (less input demanding)
cropping systems. The area with pineapple (the most expensive crop) is sharply reduced while
for all land use systems the low herbicide option is preferred since these are a little bit more
profitable than the high herbicide options. These low herbicide options require fewer
herbicides but more labor, which is also shown by the reduction in biocide use with 45%,
compared to scenario 4. Apparently, the credit constraint is restricting the objective value
more than the labor constraint. In the previous scenario (scenario 4) only labor was restricting
a further profit increase. Therefore, in that scenario labor extensive management options were
selected with high herbicide and some high mechanization options since these require less
labor (see results scenario 4 in Table 1). More area could be taken in production, 6.7 ha
compared with 5.92 ha in the credit scenario, which allowed raising farm profits.
Scenario 6: Reduced labor availability scenario
In this scenario, the same model as scenario 4 is run, the only difference consisting of a
restriction on the availability of labor. It is assumed that the farmer can work a part of his time
27/06/2016 612930688
10
at a nearby banana plantation reducing his total labor availability at the farm at 200 mnd per
year (compared to the 300 mnd per year in other scenarios).
 Press [Ctrl+r] to open a dialog box with scenario options and select ‘Reduced labor
availability scenario ’. Press [OK] when the scenario is selected.
 The scenario results are written to the worksheet labor_run. When finished this worksheet
is the active sheet with results of the optimization procedure.
 View the contents of this worksheet and fill in Table 1 (at the end of the document). Note
the differences with scenario 4, as well as the trade-offs between indicator values.
Note that the net revenue is reduced with 17% compared to scenario 4, although the labor
availability is reduced with a third. Because the labor availability is limited in this scenario,
only two land use systems are selected both with high input of capital goods (biocides and
mechanization) which require relatively little labor. With the little labor available the farmer
cannot cultivate much has, even a part of the fertile well-drained soils are taken out of
production.
When finished with scenario 6, close the file LP_MOD.XLS. Do not save the file.
Conclusions
The results of the scenarios (as summarized in Table 1) indicate the ‘playground’ for
sustainable development of this particular farm type. By running different scenarios, tradeoffs between socio-economic, sustainability and environmental objectives are quantified. The
remarks made at the end of scenario 1 are valid for all other scenarios; I.e. at an aggregate
level of analysis, e.g. a region, product prices will become endogenous and will affect the
outcome of a scenario. The highest profits are realized with sustainable (alternative) land use
systems as is shown in the last three scenarios. The higher yields that can be attained with a
well-balanced mix and high level of inputs (and associated high costs!) will pay off. However,
The selected land use systems do not account for yield risks caused by e.g. adverse weather
conditions. Moreover, it assumes that farmers timely apply the required inputs and carry out
the required operations. This requires a well-educated and precise farm management. Based
on the current production systems a reduction in the use of biocides or in N-depletion of 50%,
both have a ‘financial trade-off’ of about 15% on farmers profit (while still using
unsustainable cropping systems), as is shown in scenario 2 and 3.
27/06/2016 612930688
11
Table 1 Summary of scenario results.
SCENARIO:
Base scenario
Net
revenue
1619192
Land use systems (type +ha) SFW (ha) SIW (ha) labor (mnd/yr) costs (col/yr) N-balance (kg N/ha) Biocide (kg ai/ha)
SFW.ME.F0HHL = 2
SFW.ZC.F0HHL = 1
SIW.AM.F0HLH = 2
SIW.BG.F0HLL = 2
5
2
228
744857
Reduced N depletion
scenario
Reduced biocide
scenario
Introduction of
alternative systems
scenario
Reduced credit
scenario
Reduced labor
availability scenario
27/06/2016 612930688
-157
12
12
27/06/2016 612930688
13
Annex I
Technical Coefficients of land use systems
Description of technical coefficient
Unit
Code
Export quality product
kg/ha/yr
EXP
Domestic quality product
kg/ha/yr
DOM
Refuse product
kg/ha/yr
REF
Labor requirements – discounted annuity
mnd/yr
CLABA
Labor requirements – mean
mnd/yr
CLABM
Costs
col/yr
CCOST
N-balance
kg N/ha/yr
NBAL
P-balance
kg P/ha/yr
PBAL
K-balance
kg K/ha/yr
KBAL
Volatilisation
kg N/ha/yr
NVOL
Denitrification
kg N/ha/yr
NDEN
N-Leaching
kg N/ha/yr
NLEA
Biocide index
BIOI
Biocide use
kg ai/ha/yr
BIOA
Fertilizer N-input
kg N/ha/yr
FIN
Fertilizer P-input
kg P/ha/yr
FIP
Fertilizer K-input
kg K/ha/yr
FIK
P-fixation
kg P/ha/yr
PFIX
K-leaching
kg K/ha/yr
KLEA
Tractor use
trdays/yr
TRAC
Sowing equipment use
seqdays/yr
SOWE
Multicultivator equipment use
meqdays/yr
MULT
Fertilizer spreader use
feqdays/yr
FEQ
Knapsack sprayer use
keqdays/yr
BOMB
Seedlings/seed
#/ha or kg/ha
SEED
27/06/2016 612930688
14
Annex II
Identification codes of land use systems
Land use systems have an identification code, for example: SFP.ZM.F9HHL
code 1: Land units can be:
SFW = Soil fertile well drained
SIW = Soil infertile well drained
SFP = Soil fertile poorly drained
code 2: Crop type can be:
AM = pineapple for local market
BG = palmheart
ME = cassava
PV = beans
ZM = maize grain
ZC = maize fresh cobs
code 3: Combination of type of land use system, target yield level, pesticide level, herbicide
level and mechanization level.
First letter plus number: type of land use system plus yield level. F0 stands for actual land use
systems, F1…F9 stand for alternative land use systems in which F9 is the maximum level and
F1 is 10% of this level.
Second letter: pesticide level (L = low, H = high)
Third letter: herbicide level (L = low, H = high)
Fourth letter: mechanization level (L = low, H = high)
27/06/2016 612930688