Directory UMM :Data Elmu:jurnal:A:Agricultural Systems:Vol62.Issue3.Dec1999:

Agricultural Systems 62 (1999) 169±188
www.elsevier.com/locate/agsy

Bio-economic evaluation of dairy farm management scenarios
using integrated simulation and multiple-criteria models
M. Herreroa,*, R.H. Fawcetta, J.B. Dentb
a

Institute of Ecology and Resource Management, School of Agriculture Building, University of Edinburgh, Kings Buildings,
West Mains Road, Edinburgh EH9 3JG, UK
b
Royal Agricultural College, Cirencester, Gloucestershire GL7 6JS, UK
Received 1 September 1999; received in revised form 20 September 1999; accepted 8 October 1999

Abstract
Appropriate selection of holistic management strategies for livestock farming systems requires: (1) understanding
of the behaviour of, and interrelations between, the di€erent parts of the system; (2) knowledge of the basic objectives of
the decision maker managing such enterprise; and (3) understanding of the system as a whole in its agro-ecoregional
context. A decision-support system based on simulation and mathematical programming techniques has been built to
represent pastoral dairy production systems. The biological aspects (grass growth, grazing, digestion and metabolism,
animal performance) are represented by simulation studies under a variety of management regimes. The outputs from

the simulation runs (such as pasture utilisation, stocking rates, milk yields, fertilizer use, etc.) are used as data input to
the multi-criteria decision-making models, and the latter have been used to select the management strategies which
make the most ecient use of the farm's resources (i.e. land, animals, pastures). The paper discusses the e€ects and
implications of di€erent management scenarios and policies on the bio-economic performance of highland dairy farms
in Costa Rica. Nevertheless, the model frameworks are generic and can be adapted to di€erent farming systems or
ruminant species. The e€ect of model formulation and sensitivity, di€erent decision-maker objectives, and/or activity
or constraint de®nitions on management strategy selection are also analysed. # 2000 Elsevier Science Ltd. All rights
reserved.
Keywords: Dairy farming; MCDM; Simulation; Farm management; Costa Rica; Systems analysis

1. Introduction
Appropriate selection of holistic management
strategies for livestock farming systems requires:
(1) understanding of the system as a whole in its
agro-ecoregional context; (2) understanding of the
* Corresponding author. Tel.: +44-131-535-4384; fax: +44131-667-2601.
E-mail address: mario.herrero@ed.ac.uk (M. Herrero).

behaviour of, and interrelations between, the different parts of the system; and (3) knowledge of
the basic objectives of the decision maker managing such an enterprise.

Validated simulation models provide a coste€ective means of representing the biological
dynamics of the system and its components, while
multiple-criteria decision-making (MCDM) models allow for appropriate selection of resource
allocation strategies depending on the di€erent

0308-521X/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.
PII: S0308-521X(99)00063-3

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M. Herrero et al. / Agricultural Systems 62 (1999) 169±188

objectives and management `styles' of particular
individuals or households. Integration of both
mechanisms provides the necessary elements for
ecient decision-support at farm or ecoregional
level (Veloso et al., 1992; van Keulen, 1993; Fawcett, 1996; Herrero et al., 1996, 1997).
A decision-support system (DSS) based on these
techniques has been built to represent pastoral
cattle production systems. The biological aspects

(grass growth, grazing, digestion and metabolism,
animal performance, herd dynamics) are represented by simulation studies under a variety of
management regimes using the models described
by Herrero (1997) and Herrero et al. (1999a, b).
The outputs from the simulation runs (such as
pasture utilisation, stocking rates, milk yields, fertiliser use, etc.) are part of the data input to the
MCDM models, and the latter have been used to
select the management strategies which make the
most ecient use of the farm's resources (i.e. land,
animals, pastures, other inputs, etc.).
This paper describes the MCDM models and
the whole DSS, and demonstrates how they can be
used in farm management and policy development. Examples are given with reference to highland dairy farming in Costa Rica. The e€ects of
di€erent decision-maker objectives, and/or activity
or constraint de®nitions on management strategy
selection are analysed and discussed.

2. Multiple-criteria model de®nition
2.1. General characteristics
Any model derived from linear optimisation

(i.e. MCDM models) has three basic elements
(Dent et al., 1986; Romero and Rehman, 1989):
(1) an objective function, which minimises or
maximises a function of the set of activity levels; (2) a description of the activities within the
system, with coecients representing their productive responses; and (3) a set of constraints
that de®ne the operational conditions and the
limits of the model and its activities. A number of
examples referring to the basis and application
of these modelling techniques can be found in
the literature (Zeleny, 1982; Dent et al., 1986;

Romero and Rehman, 1989; Romero, 1991; Williams, 1993).
Interaction between the simulation models
(Herrero, 1997; Herrero et al., 1999a, b) and the
MCDM model occurs by generating the coecients (values) for the di€erent activities of the
system, in this case a dairy farm. The MCDM
model reads a series of ASCII ®les containing
data from simulations carried out under a variety
of di€erent management practices, and `chooses'
from the simulated runs, which maximises or

minimises an objective function, subject to the set
of constraints speci®ed. A generalised ®gure of
this methodology was presented by Herrero et al.
(1996, 1997). This mode of interaction has the
enormous advantage that, since activity coecients are not constant, usually non-linear, and are
generated from the simulation models, di€erent
objectives can be met, while at the same time taking into account the biological and managerial
feasibility of the range of options available. It also
provides the ¯exibility for tailor-made decisionsupport for individual farmers, since management
practices can be re¯ected in the simulations. This
does not happen often in conventional application
of linear programming models, which are often
too aggregated. In most cases activity coecients
do not represent the management strategies commonly practised by farm households, and/or the
biological feasibility of the alternatives proposed
for the system under study (Veloso et al., 1992;
Fawcett, 1996). Therefore, model outcomes represent optimal solutions, but do not represent realistically viable options, which may lead to their
lack of adoption (Fawcett, 1996).
The aim of the MCDM model is to select the
best combination of resources to produce milk in a

highland dairy farm of Costa Rica with a ®xed
grasslands area, with or without milk quota, and
year-round calving patterns and grazing. The
model assumes that forest areas within the farm
cannot be cleared for milk production, and therefore it is constrained to using only the existing
grazing land. Resources available consist of animals, pastures, labour, and purchased inputs,
namely concentrates and nitrogen fertiliser.
The model calculates herd sizes and structures,
pasture management strategies (paddock sizes,

M. Herrero et al. / Agricultural Systems 62 (1999) 169±188

rest periods, utilisation intensities, N fertiliser use),
number of farm personnel, and the supplementation strategies for the lactating dairy cows (concentrates use and method of allocation), required
for milk production. Alternative youngstock supplementation practices were not tested in this version of the model.
The model was de®ned for a single day but
results can be aggregated to a monthly basis if
required. This was done for the following reasons:
1. Since all farms operate in a continuous calving pattern, herds are managed on a `steadystate'. Therefore, herd dynamics (i.e. lactating
vs. dry cows), and the reproductive (i.e. days

open) and productive parameters (i.e. average
days in lactation, milk production per cow)
do not show marked seasonal ¯uctuations
(van der Grinten et al., 1992; Camacho et al.,
1995), and are relatively similar from day to
day. This is largely caused by the stable
environmental conditions of the region under
study (rainfall 3500 mm/year, average temperature 17‹1.5 C year round, evapotranspiration rarely exceeding rainfall in the
driest months; Babbar and Zak, 1994).
2. Dairy farm management practices in the
PoaÂs region of Costa Rica do not present
marked seasonal ¯uctuations (van der Grinten et al., 1992; Solano, 1993).
3. Grass production and quality are barely or
not a€ected at all by the mild dry season
(Herrero, 1997).
4. Milk quotas in Costa Rica operate on a daily
basis, presumably partly because of the lack
of extreme environmental conditions and the
continuous calving patterns.
5. A daily time step permits the most precise

integration between the simulation models
and the general operational management
practices of the farm. Cows eat grass, are fed
concentrate, and produce milk on a daily
basis. Linear programming models representing dairy farms (i.e. Conway and Killen,
1987) usually use longer time steps than a
day, perhaps because a day would not represent properly the management dynamics of
the production systems in their studies. This

171

is probably related to the fact that these
techniques have been mostly applied in temperate conditions, where seasonal impacts
are severe. Therefore, carry-over e€ects of
previous seasons, forage conservation and
uneven calving patterns directly a€ect the
yearly milk quotas, and become of paramount importance in the calculations. The
same applies where linear programming has
been applied to study the economics of
reproductive policies in temperate dairy systems (i.e. Jalvingh, 1994). Nevertheless, an

advantage of using daily models is that, if
necessary, they have the ¯exibility of aggregating data for representing longer time
steps.
The matrix of the model consists of 1336 rows
and 2047 columns, representing constraints and
activities, respectively. It has 8534 matrix elements, 31 right hand-side elements, 939 bound
elements, 18 integer plus 921 binary variables,
respectively. The matrix was generated and implemented using the industrial version of XPRESSMP mathematical programming software (Dash
Associates, 1994).
2.2. De®ning the herd
The model describes a dairy herd composed of
lactating and dry cows, and female youngstock.
The model treats individual animals as integers.
This is especially important in small herds, where
the value of an individual animal acquires a higher
relative signi®cance in model outcomes than in
bigger herds, since these can vary substantially
depending on the total number of animals (i.e.
integerising a model solution of 5.6 cows to 6 cows
in a herd of 10 or 100 cows does not have the same

relative importance on model outcomes).
Lactating cows (TOTLAC), of a similar bodyweight, are described by three variables: lactation
number (i ), potential milk production (g) and
stage of lactation (s). The description of cows
based on three lactation numbers has been shown
to be adequate in lactation curve studies (Wilmink, 1987), and had been previously applied to
lactation records from the PoaÂs region (Camacho

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M. Herrero et al. / Agricultural Systems 62 (1999) 169±188

et al., 1995; Vargas and Solano, 1995). The de®nition of three milk production potentials and three
stages of lactation is standard practice, and is
useful from a managerial perspective. Therefore,
the model described 27 possible cow states:
TOTLACigs ;

…1†

where i:imax=3; 1, ®rst calving; 2, second calving;
3, three or more calvings; g:gmax=3; 1, high; 2,
average; 3, low milk production potential;
s:smax=3; 1, early; 2, mid; 3, late lactation.

NL2…g ˆ 1 : g max† : LAC2g
ÿ 0:5LAC3g > 0:

3. The number of 3+ calvers is always greater
than the number of ®rst calvers (NL3):
NL3…g ˆ 1 : g max† : LAC3g
ÿ LAC1g > 1:

ÿ LAC2g > 1:

3. Constraints on the herd structures

3.1. Lactation number constraints
An analysis of the raw data demonstrated that
realistic herd structures were obtained by using the
following simple rules:
1. The sum of the ®rst and second calvers is
greater than the number of animals with
more than three or more calvings (3+)
(NL1):
NL1…g ˆ 1 : g max† : LAC1g
‡ LAC2g ÿ LAC3g > 1;

…2†

where LACi=1:imax,g represent the cows in
the ith lactation across all levels of potential
milk production (g).
2. The number of second calvers is always
greater than half the number of 3+ calvers
(NL2):

…4†

4. The number of ®rst calvers is always greater
that the number of second calvers (NL4):
NL4…g ˆ 1 : g max† : LAC1g

Several constraints were used to estimate the
appropriate number of animals in each category.
The values of the coecients are herd dependent;
therefore they can be modi®ed to represent herds
under di€erent management regimes or in other
environmental conditions. These coecients can
be derived from existing farm monitoring services
or farm records (Herrero et al., 1997). In this case
they were derived from the VAMPP database of
19 farms from the PoaÂs region, previously used by
van der Grinten et al. (1992).

…3†

…5†

3.2. Potential milk production constraints
Milk yield per cow per lactation is usually a
normally distributed variable within a herd. Cows
with average milk production potential represent
the largest proportion of the herd, and those with
low or high potential are generally fewer. The
proportions of animals in each category are subjective, since they depend on the di€erent perceptions of individual farmers and/or managers of
`high', `medium' or `low' potential, relative to the
mean and the variance of milk yield. De®nition of
basic constraints to realistically describe this distribution was also required [GEN1±3]. Cows with
average potential milk production, GP2, were
considered to be at least 50% of all lactating cows,
while cows with high [GP1] or low [GP3] milk
production potential represented at least 20 and
10%, respectively. Since all animals were treated
as integers, a 20% slack value on the number of
lactating cows was left in the de®nition of this
distribution to prevent over constraining the
model for ®nding feasible global solutions:
GEN…1† : ÿGP1 ‡ 0:1TOTLACT < 0

…6†

GEN…2† : ÿGP2 ‡ 0:5TOTLACT < 0

…7†

GEN…3† : ÿGP3 ‡ 0:2TOTLACT < 0;

…8†

where:
TOTLAC ˆ

X
GPg :
g

…9†

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M. Herrero et al. / Agricultural Systems 62 (1999) 169±188

Dry cows were also assumed to be equally distributed across genetic potentials and lactation
numbers. Theoretically, a farm with a continuous
calving pattern, a 365-day calving interval and
a 60-day dry period, should have close to 17%
of dry cows at any point in time. Analysis of
the VAMPP database demonstrated that with the
reproductive standards of farms in the PoaÂs
region, in an average farm, the dry cows represented at least 20±25% of the total number of
cows (TOTCOWS). Therefore, the constraint
determining the number of dry cows (DSIZE) was
written:
DSIZE : ÿ0:25TOTCOWS ‡ DRY > 0:

…10†

This ®gure is dependent on the reproductive
policies of the herd and its dry period. Farms with
longer calving intervals usually tend to have longer
dry periods and a higher proportion of dry cows.
Youngstock [YSz] were divided in three categories
to represent animals at di€erent stages of growth.
YS1 represented animals from 0 to 1 year, while YS2
and YS3 were heifers from 1 to 2 years and pregnant replacement heifers, respectively. These represented at least 0.2, 0.4, and 0.2 of the total number
of cows, respectively. Again, a slack value of 20%
was left to satisfy the integer constraints:
YSTK…1† : ÿYS1 ‡ 0:2TOTCOWS < 0

…11†

YSTK…2† : ÿYS2 ‡ 0:4TOTCOWS < 0

…12†

YSTK…3† : ÿYS3 ‡ 0:2TOTCOWS < 0

…13†

In farms of the PoaÂs region, youngstock represent close to 50% of the total herd size (van der
Grinten et al., 1992; Solano, 1993). Therefore, a
constraint (YSIZE) was applied so the number
of youngstock had to be equal to the number of
mature cows (TOTCOWS):
X
YSZ ˆ 0;
…14†
YSIZE : TOTCOWS ÿ

4. Lactating cows and milk production
Calculation of the number of lactating cows is
dependent on their pasture intake, their productive responses to concentrate supplementation,
and their state, relative to the characteristics of the
system (i.e. land, costs, milk quota, grazing management). Hence, it is largely dependent on the
coecients obtained from the simulation models.
The number of simulation runs is dependent on
the number of nutritional strategies and supplementation levels that want to be evaluated, and
these are user de®ned. For each nutritional strategy, an ASCII ®le (*.dat) was produced that
contained three simulated output variables (one
column per variable): pasture intake, supplements
intake, milk production for each of the 27 cow
states described before. For the present example,
three strategies were used: grazing only and grazing plus a commercial concentrate but with
two di€erent methods of allocation (¯at rate or
based on milk±concentrate relations). Additionally, within each concentrate regime there were
three di€erent levels of supplementation ( j );
therefore, each of these ASCII ®les contained 81
rows of data (27 states3 levels of supplementation=81 rows). The ®le containing the data for
the grazing only regime had 27 rows. The model
calculated, subject to the constraints imposed, the
numbers of animals in each nutritional strategy
and level of supplementation, according to lactation number, potential milk production, and stage
of lactation, or a combination of these, to meet the
milk quota according to the di€erent objectives.
For strati®cation according to potential milk production, the model de®ned the following:

ÿ

i gˆ1 s

i gˆ1 s

i gˆ1 s

ÿ

…15†

…16†

j

XXX
XXXX
W5Aigsj
W5Pigs ÿ
i gˆ2 s

where the total number of cows is:

j

XXXX
W5Bigsj ‡ GP1 ˆ 0
ÿ

z

TOTCOWS ˆ TOTLACT ‡ DRY:

XXXX
XXX
W5Aigsj
W5Pigs ÿ

i gˆ2 s

j

XXXX
ÿ
W5Bigsj ‡ GP2 ˆ 0
i gˆ2 s

j

…17†

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M. Herrero et al. / Agricultural Systems 62 (1999) 169±188

XXX
XXXX
W5Aigsj
ÿ
W5Pigs ÿ
i gˆ3 s

i gˆ3 s

j

XXXX
W5Bigsj ‡ GP3 ˆ 0;
ÿ
i gˆ3 s

W5Pig3 ‡

j

j

X
ÿ W5Pig2 ÿ
W5Aig2j

…18†

j

j

where W5Pigs, are the number of lactating cows
under a `grazing only' nutritional regime, across
potential milk production levels GPg; W5Aigsj are
the number of lactating cows under a `grazing
plus concentrates' ¯at rate (nutritional regime A),
across potential milk production levels GPg;
W5Bigsj, are the number of lactating cows under a
`grazing plus concentrates' feeding strategy, with
concentrates allowance based on a milk±concentrate relationship (nutritional regime B), across
potential milk production levels GPg; and j=level
of supplementation within the nutritional regime,
where jmax=3.
The strati®cation of lactating animals by a
combination of lactation number X genetic
potential [LRig] then becomes, for i=1:imax,
g=1:gmax:
XX
X
W5Aigsj
ÿ
W5Pigs ÿ
s

j

XX
W5Bigsj ‡ LACig ˆ 0
ÿ
s

X
X
W5Big3j
W5Aig3j ‡

…19†

…22†

X
W5Big2j > 0
ÿ
j

2. Theoretically, the model could calculate
separate feeding strategies for the 27 groups
of lactating animals. However, from a practical standpoint, it would be extremely complicated to apply them at farm level, since
farmers rarely stratify lactating cows in more
than three or four groups for feeding. The
model was designed to select the single best
nutritional management strategy for each
stage of lactation (i.e three groups), which is
one of the common systems for supplementing dairy cows in the highlands of Costa Rica
(Campabadal, 1988; van der Grinten et al.,
1992). For i=1:imax, g=1:gmax; the constraints were de®ned as:
ÿW5Aig13 ‡ W5Aig23 ÿ W5Big13
‡ W5Big23 < 0

…23†

j

Two further constraints were applied to the distributions of the lactating herd:
1. In farms with continuous calving patterns,
the distribution of lactating cows across
stages of lactation is similar (30±35% in each
stage). Therefore, for i=1:imax, g=1:gmax:
X
X
W5Big1j
W5Aig1j ‡
W5Pig1 ‡
j

ÿ W5Pig3 ÿ

j

X
W5Aig3j
j

j

j

X
W5Big1j > 0
ÿ
j

X

W5Big2j ÿ

W5Aig1j ‡

X

W5Big2j < 0

X

W5Big1j ÿ

jˆ1:3

…21†

X

W5Aig2j ‡

jˆ2:3

ÿ

X

X

W5Big2j < 0

…25†

jˆ1:3

X

W5Big2j ÿ

…26†

W5Aig3j

jˆ2:3

jˆ2:3

…24†

W5Aig2j

jˆ1:3

jˆ1:3

ÿ

X

jˆ2:3

jˆ2:3

X

W5Aig2j

jˆ2:3

‡ W5Big33 < 0

X
X
W5Big2j
W5Aig2j ‡

X
ÿ W5Pig1 ÿ
W5Aig1j

ÿ

X

ÿ W5Aig23 ‡ W5Aig33 ÿ W5Big23

j

j

W5Aig1j ‡

jˆ2:3

…20†

X
W5Big3j > ÿ1
ÿ
W5Pig2 ‡

X

X

W5Big3j < 0

jˆ2:3

…27†

M. Herrero et al. / Agricultural Systems 62 (1999) 169±188

X

W5Aig2j ‡

X

W5Big2j ÿ

X

W5Big3j < 0

…28†

jˆ1:3

jˆ1:3

Milk production was estimated from the number of cows calculated by the model multiplied
by the respective columns from the ASCII ®les
containing the milk production data for each
nutritional strategy and each cow state. In this
case, the ASCII ®les were named C5WP, C5W,
B5W for the grazing only, nutritional regime A,
and nutritional regime B, respectively. The milk
production data was the third data item in the
®les. Therefore:
XXX
C5WPigs3 W5Pigs
ÿ
i

g

s

i

g

s

j

i

g

s

j

XXXX
ÿ
C5Wigsj3 W5Aigsj
XXXX
B5Wigsj3 W5Bigsj
ÿ

…29†

‡ QMILK ‡ XSMILK < 0;
where QMILK is the daily milk quota (kg/day)
and XSMILK is milk produced over the quota
limit (kg/day). XSMILK was included as a variable since, in Costa Rica, milk produced above
the quota limit is paid at 25% less than the price
of milk, and farmers are not penalised in the long
term for small (