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An MCDM approach to production analysis: An application to irrigated farms in Southern Spain
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
ELSEVIER
European Journal of Operational Research 107 (1998) 108-I 18
Theory and Methodology
An MCDM approach to production analysis: An application to irrigated farms in Southern Spain J. Berbel aj*, A. Rodriguez-Ocafia b a Dpto. de Agrarias Economia, Universidad de Cordoba, P.O. Box 3048, 14080 Cordoba, Spain b Consejeria de Agricultura y Pesca, Junta de Andalucia, Delegacidn de Sevilla, Spain
Received 11 February 1997; accepted 14 May 1997
Abstract The analysis of the decision-making process in agricultural enterprises is approached with the development of a methodology based upon two stages: firstly we enlarge our knowledge of the system under study by performing grouping operation - cluster analysis - of the farm enterprises. The result of this stage is to classify farms according to crop pattern, which is the basis for the second stage of analysis: the system is studied by solving a weighted goal programming to approach the weights given by different farmers to the objectives of the decision process. This methodology is applied to two nearby but different irrigation units in Southern Spain, and we found that there was an important degree of heterogeneity in production plans explained by differences in objective weights. 0 1998 Elsevier Science B.V. All rights reserved. Keywords: Multicriteria
analysis; Irrigated agriculture; Goal programming;
1. Introduction Self-employed farmers frequently manage agricultural enterprises; therefore, the owner-operator takes into account his objectives, goals and constraints, and decides production plans. Differences in the availability of material resources (land area, water supply, quality of soil, etc.) or economic resources (marketing channels, production quotas,
Corresponding author. Fax: +34-957-218-563; e-mail: [email protected]. ??
Cluster analysis
etc.) are not the only source of heterogeneous production decisions, because farms also differ from each other in their socio-economic characteristics. Variations in socio-economic and technical characteristics of farms may cause differences in risk preferences or time allocation between farm work and off-farm work. These differences in the operators’ behaviour will lead to diverse production decisions. Successful simulation models of agricultural systems and the design of agricultural or environmental policies should integrate the rules governing this heterogeneity, but unfortunately a great number of models ignore this
SO377-2217/98/$19.00 0 1998 Elsevier Science B.V. All rights reserved. PIISO377-2217(97)00216-6
J. Berbel, A. Rodriguez-Ocafia I European Journal of Operational Research 107 (1998)
heterogeneity. Moreover, the question arises as to which factor will be more influential on farm decisions: technical and natural resources or human capital and socio-economic characteristics of the decision-maker. This paper is in the field of the applied economics searching for a deeper empirical understanding of individual and collective behaviour. The major objective of this paper is to develop a methodology for the analysis of decision criteria and the effect of the decision making process in production plans. It will apply the methodology to a case study of irrigated farms in Southern Spain where we find an almost perfect competition context. There is general consensus among economists on the hypothesis that managers take into account many conflicting criteria in the process of decision making both in private enterprises and institutional agencies. This hypothesis is the basis of the multiple criteria decision-making theory (MCDM). According to Barnett et al. (1982) MCDM research can be characterised as “descriptive”, “operational” or “combined”. A descriptive approach concerns whether or not decision-makers possess multiple objectives, and develop relative rankings of them. The operational approach uses hypothesised objective weights and examines their impact upon a decision model. Finally, the combined approach embodies an attempt to discover objectives and their weights and then to use them in a decision model. The present paper may be included in the combined approach type, which may identify weights and use them simultaneously or iteratively as in Barnett et al. (1982) which is the type of application we aim to explain. The first step in our methodology is to sort farmers according to their socioeconomic characteristics and technical and natural production resources. From this grouping will be selected some “clusters” or farm-types with the innovation that the farm types will incorporate both technical and socio-economic elements. Secondly we will try to find relationships between the type of farm operator and the production plans; this is done as an application of weighted goal programming to approach the weights given by the different types of farmers to the objectives in the decision process.
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109
2. Goals and values of farmers in previous works There are works on empirical research in decision criteria of farmers with some years in anticipation of the MCDM theory and methodological approaches. A pioneering work is the research conducted by Gasson (1967) among farmers in Cambridge (UK). In this work Gasson argues that we should distinguish between values which are defined as observable subjective beliefs related to the way of life of an economic agent and management criteria that are observable values that guide the management decision. Values are cultural products held by members of a social system. Values do not exist in isolation but are organised in systems of value orientations. Values are a more permanent property of the individual, less liable to change with time and circumstances. Values are abstract criteria and they can only be approached indirectly through observed behaviour or verbal responses. Gasson classified “for convenience” value orientations in the following four headings: (1) Instrumental making a maximum income; making a satisfactory income; safeguarding income for the future; expanding the business; providing congenial working conditions (hours, security). belonging to (2) Social gaining recognition; farming community; continuing farming tradition; working with other members of the family; maintaining good relations with workers. (3) Expressive feeling pride of ownership; gaining self-respect for doing a worthwhile job; exercising special abilities; meeting a challenge. (4) Intrinsic enjoyment of work task; preference for healthy, outdoor job; value of hard work; independence-freedom; control of a variety of situations. In the research about farmers in Cambridgeshire, Gasson found that the farmers’ value orientations are related to business size. We find the setting of value orientation types as a very interesting approach to simplify the second stage of the analysis, i.e. the development of a decision model for each of the important types found in the descriptive analysis.
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A second approach to ranking goals of farmers is quoted in Patrick and Blake (1980) describing an unpublished work by Hesselbach and Eisgruber who considered nine goals such as living standard, farming as a way of life, farm ownership, nurture of children, realisation of standards, retirement, work as a goal, risk aversion and decision making readiness. By means of verbal indicators goals were developed and a decision model based upon this information was built. A third approach is the paired comparison technique exemplified by Harper and Eastman (1980) who rank a goal hierarchy from a randomly selected sample of small farm operators in New Mexico. Two sets of goals were evaluated: goals for the family unit and goals for the agricultural enterprise. Having established a correspondence between both types of goals within the sample, their analysis evaluated the symmetry between the hierarchy and a similar study conducted in Oklahoma and Texas concluded that there was a lack of correspondence. Harman et al. (1972) uses this approach to determine the goal hierarchy and factors affecting goals for use in a simulation model. Hatch et al. (1974) included goals to control more acreage, to avoid being forced out of business, etc. They found that the dominant goals changed frequently and that trade-offs should be included. Barnett (1979) who started with paired comparison data later introduced multidimensional preference scaling (MDS) as a fourth approach. The goal scores obtained from MDS are assumed to be on a ratio scale. In this section we have only reviewed some works on empirical studies, but the work of Patrick and Kliebestein (1983) makes a more complete review on the subject, methodologies and cases. Finally, we wish to comment on the work of Patrick (1978) who developed a simulation model that uses the “goals orientation”. The concept of “goals orientation” is similar to Gasson’s “value orientation”. This type of analysis based upon type definition will be the approach of our analysis. The reason for the determination of types is that it is quite difficult to establish a unique goal hierarchy for a heterogeneous group of farmers or decision-makers, even in the case of a common
Research 107 (1998) 108-118
cultural background and similar resource availability. It is interesting to see that previous research into values such as Gasson (1973) or Kerridge (1977) found different distribution of value orientations among farmers. Table 1 shows that farmers are quite heterogeneous worldwide and socio-economic characteristics influence values, which in the end will determine production decisions. Unfortunately, information regarding the effect of socio-economic characteristics on decision-making is limited.
3. Models of irrigated agriculture Today business environment is frequently composed by a limited number of firms trying to maintain competition from other firms as low as possible, it is not usual to find the classical “perfect competition” conditions. Agricultural production firms usually are too small to influence markets and technologies, inputs and outputs are commodities where it is not possible to gain a superior role in any market, or try any differentiation strategies. The fact that agricultural production may be characterised as “perfect competition” makes it an interesting field to test empirical models of decision making. Irrigated agriculture uses 85% of water consumed in Mediterranean climates as in Southern Spain, and produces over 50% of the agricultural output. As residential, industrial and environmental demands for water increase, the analysis of irrigated agriculture and water demand becomes a strategic research problem. Water demand for irrigation depends upon farmers’ decisions, which Table 1 Summary Author
Intrinsic Expresive Instrumental Social
of values orientation Gasson
(1973)
Small (%)
Large (“Yo)
27 16 27 39
24 20 33 23
Kerridge
41% 18% 38% 3%
( 1977)
J. Berhel, A. Rodriguez-Ocmia I European Journal of Operational Research 107 (1998)
is the objective of our research. Irrigated agricultural enterprises are an interesting empirical field as they are composed of relatively homogeneous decision-makers of a price-taker nature, therefore in a relatively “perfect competition” world. Models of applied irrigated agriculture have used linear programming to study the effects of changing water price and supply in optimal cropping patterns and later efforts have incorporated quadratic programming, dynamic programming or discrete sequential programming (Taylor and Young, 1995). But generally these models on a regional scale may suffer from aggregation problems and the objective function - usually regional agricultural income - may not capture the real underlying decision process. The typical decision-maker owns and operates a family farm, where production and consumption decisions are determined simultaneously. Socioeconomic factors enter through value orientations into the farmer’s preference or multiattribute utility function. Variations in socio-economic characteristics affect production choices in various ways. Firstly, it may affect the farmer’s rate of substitution between income and leisure, or may change his opportunity cost and the way time is distributed between on farm and off-farm work. The effects have been investigated extensively, but we should mention the research of Kimhi (1996) where results found are to the effect that off-farm participation is highly sensitive to personal characteristics, followed by age, farm tenure and other factors. Another way of influencing criteria weights is that a change in socio-economic characteristics may affect decisions via risk attitudes. We would like to highlight a recent paper by Feinerman and Finkelshtain (1996) who introduce socio-economic characteristics into production analysis under risk. When we consider the risk-return model as a two criteria model it can be treated as a member of general Multicriteria models. These authors conclude that risk attitude is influenced by farm size and technical characteristics and also family size, age, education affect quite significantly risk attitude and, consequently, production plans. Many authors have built MCDM models of farm-decisions paying special detail to heterogeneous farms; we can quote Berbel (1993) or Zekri
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Ill
and Romero (1993) as examples in the field of Multicriteria analysis of irrigated agriculture. We recommend the book by Romero and Rehman (1989) as a comprehensive reference of the stateof the-art of these techniques, with special reference to agricultural problems. Models found in the literature usually try to avoid the “aggregation problem” when modelling regional systems by dividing the farms according to size and technical characteristics. Generally, the results of MCDM prove to be closer to real decisions than simple profit-maximising linear programming. Nevertheless, we should mention that the methodology that will be explained in this paper might be applied to any other economic sector and in many decision contexts (financial, manufacture, administration, etc.). The results of the methodology are not limited to this type of firm.
4. Analysis of irrigated firms in Andalusia Our approach to model decision making in irrigated agriculture will be based upon MCDM theory, but we are interested in obtaining models, which may be used as tools for water management policy formulation. We decide that practical models should be built at a “middle-level”, which is a compromise between a single model for all the river management and exhaustive micro level by single farm, which is too detailed for practical policy making. Therefore, for this reason, we need to analyse an area large enough to contain a significant number of farmers, but not too large as to introduce sources of variation in soil, climate or market conditions, and this level is the “irrigation unit”. Furthermore, from the economic point of view, when the region is not perfectly homogeneous, the result may suffer some “aggregation bias”. Consequently, our methodology will make an intermediate approach: it will analyse a small region, but it will divide the complete set of farmers into “cluster” or homogeneous groups reducing it to a manageable figure. Research will be conducted in two stages: (1) descriptive analysis and grouping of types of decision-maker and (2) development of a simulation model.
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Result of the first stage will be the sorting of farmers in different types of decision-makers by using cluster techniques. The term “cluster analysis” embraces a loosely structured body of algorithms, which are used in the exploration of data from the measurement of a number of characteristics for a collection of individuals. Cluster analysis is concerned with the discovering of the groups. The word “cluster” or “group” should be interpreted as a collection of “similar” objects. The sample is based upon a random choice of 115 farmers in the Mid Guadalquivir Valley (Southern Spain) from two nearby irrigation sectors (68 farmers in area 1 “Campifia Baja” and 47 in area 2 “Las Colonias”). The variables were a number of 101 and were grouped in 10 categories (socioeconomic, structure, etc.) In this paper, results are shown in Table 2 about six relevant categories. Each of these categories is formed with the observations (answers) taken from each individual farmer. We grouped by cluster technique the farmers in the following clusters of groups as shown in Table 2.
Table 2 Results of cluster
analysis
Variable County-irrigation Socio-economic
Structure
Decision
Criteria
Values
This stage of the analysis uses conventional statistical techniques in order to get a qualitative and cardinal aggregation of raw data. It is not the aim of this stage of descriptive analysis to apply multivariate techniques in order to explore the system, as we mentioned previously, our goal is to reduce the number of farms to a manageable figure through grouping techniques. The aim of cluster techniques is to get the information ready for the second stage, which is the application of Multicriteria models in a selected number of farm types which represent the complete system analysed as closely as possible. The second stage in the cluster analysis is the application of Group Analysis to the different categories. The analysis of this information is quite interesting for an understanding of the relationship between individual socio-economic characteristics and the values and criteria orientations. Finally it is interesting to seek relationships between individual socio-economic characteristics and final production decisions.
unit
Group
%
Definition
Zl 22 Al A2 A3 A4 Bl B2 B3 B4 Dl D2 D3 Fl F2 F3 F4 F5 Hl H2 H3 H4
59 41 17 63 10 10 43 35 12 10 26 17 57 17 14 12 37 21 43 36 11 10
Campiiia Baja Las Colonias Farm income below 50% older, low qualification Full-time, medium age, low qualification Full-time, younger, high qualification Farm income around 50%, medium age, low qualification Medium farms, irrigated below 20% Small farm, 100% irrigated, no wells Small farm, mostly irrigated, own wells Large farms, mostly irrigated, own wells ~50% water supply Cotton around 50%, rest sunflower and various Cotton around 50%, rest mainly corn Cotton almost 100% (1) Max profit; (2) Max production (sales) (1) Max profit; (2) Max resource use (1) Max profit; (2) Max family labour (1) Max profit; (2) Min cost (1) Max production (sales); (2) Max profit Instrumental: (1) income; (2) independence Expressive-intrinsic: (1) to own land; (2) independence Expressive: (1) creativity; (2) independence Intrinsic: (1) Farm work; (2) creativity
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Unfortunately, we also found that “criteria” (variable F) was independent from “decision” (variable D) and this was not a desired result. We should explain that because verbal questioning about management criteria is not well understood by farmers; on the contrary, farmers more easily understand questions on values that are based upon cultural beliefs than criteria questions (profit, risk, etc.). A more intense research should be conducted in the analysis of management criteria with the help of direct methods, and the use of multivariate statistics will help to examine fully the original data, but this is not the goal of our research which is to develop an analysis method based upon Multicriteria analysis at an intermediate level. Deffontaines and Petit (1985) affirmed that farmers’ criteria are better observed by indirect methods than by direct verbal questioning, therefore, arriving to a similar conclusion.
According to values orientation of farmers (answers to question: “reasons for being a farmer”), we find four values orientation (groups Hl-H4, Table 2) it may be seen that value orientations percentages differ from Table 1. The year 1995 when our field research and questioning was conducted, Southern Spain was suffering a severe drought, which affected farmers’ production plans. The anomalous scarcity of water led us to ask questions about the “projected crop plan” with the known supply of water and we also include questioning about the “desired crop plan” without a water shortage. It is not the objective of this paper to analyse in depth the description of individual farmer’s types and orientations, as more information on this can be found in RodriguezOcafia et al. (1996), where log-linear analysis is applied to the analysis of dependence between variables. The analysis of dependence between couples of clusters is conducted through a Chi Square Pearson test of Independence. Table 3 shows the analysis of dependence, and we can hypothesise that variable i and j are not independent when c1 < 0.05. Each variable represents the different groups produced by cluster analysis. We can draw practical consequences from Table 3 and it can be seen that decision plans (variable 0) are related to socio-economic characteristics of farmer (variable A), values of farmer (variable H), and county (variable Z). On the other hand, the decision does not depend upon structure or technical and natural characteristics on the farm (variable B). This is an important finding of our research, as most of the previous works have used farm size and technical characteristics as the main source of heterogeneity in production decisions. Table 3 Chi Square
A: B: D: F: H: Z:
Pearson
Socio-economic Structure Decision Criteria Values County
5. Multicriteria decision model As we mention above, traditional mathematical programming based on the optimisation of a single objective should be replaced by Multicriteria analysis. There are two streams of Multicriteria analysis: Multiobjective programming which optimises several objectives (many of them usually in conflict) and Goal programming which tries to satisfy as far as possible a set of goals compatible with the preference revealed by farmers. Sumpsi et al. (1997) propose a model in the weighted goal programming approach fully described in a recent paper, and which is applied as described in the simplified and most frequent case, i.e.
test of independence A
B
D
F
H
Z
_ 0 0.0038 0.0821 0.1905 0
0
0.0038 0.7686 _ 0.6976 0.0150 0.0015
0.0821 0.1181 0.6976 _ 0.0932 0.1509
0.1905 0.0262 0.0150 0.0932
0 0.0027 0.0015 0.1509 0.0131
0.7686 0.1181 0.0262 0.0027
0.0131
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Step 1: After an initial interaction with farmers (questionnaire and descriptive research explained above) a tentative set of objectives are established. Step 2: Determine the pay-off matrix of the above set of objectives. As the matrix is unique, then go to step 3’. Step 3’: (Please, note that this is step no. 4 in general algorithm of Sumpsi et al.). Formulate and solve a weighted goal programming which will provide a set of weights that surrogate the preferences of farmers. When weights are satisfactory, then stop. Step 4’: (Step 5 in Sumpsi et al.) The initial solution (set of weights) obtained is improved by resorting to an iterative structured trial and error procedure until a satisfactory solution is obtained. In their paper Sumpsi et al. work with individual farmers, finding for each case a set of weights that are a surrogate of individual preferences. In a similar approach, Mendez-Barrios (1995) and Gomez-Limon and Berbel (1995) use the methodology for analysing a small area but on an aggregate level, finding a surrogate for the “collective decision-maker”, probably when the region is not perfectly homogeneous, the result may suffer some “aggregation bias”. The present paper will make an intermediate approach: it will analyse a small region homogeneous in technical aspects but sorting the complete set of farmers into “cluster” or homogeneous groups. Cluster techniques are therefore used as a help to avoid aggregation problems on one hand and on the other to avoid an excessive amount of data, as it will imply using individual information. Results on cluster analysis allow us to classify farmers in small and manageable relatively homogeneous groups. The descriptive analysis explained above, shows that production plans in each of both irrigation units might be classified in three clusters. Also we could see (Table 3) that decisions were more dependent on socio-economic characteristics than on other sources of variation. We will therefore try to understand weights given to different criteria by each of the decision types by using the model developed by Sumpsi et al. (1997). According to experience gained in the first stage of research, when questioning farmers directly
Research IO7 (1998) 108-118
about criteria, we propose that the following criteria be analysed: (Wi) maximisation of net income; (WJ minimisation of hired labour; (Ws) minimisation of working capital requirements; and ( W,) optimising the MAXIMIN for the period 198881992. Net income is simulated according to data gathered on yields and prices in the area, and cost of production, and complemented by direct payments due to Common Agricultural Policy (CAP) rules. Farmers try to avoid hired labour because they prefer to get as much as possible out of family labour. Cash requirements for working capital are minimised because a great need of capital implies external financing via a bank debt and, simultaneously working capital invested in a production plan is associated with risk. Risk itself was modelled with different parameters suggested in the literature but MAXIMIN was selected because of its simplicity and good results with our data set. Nine crops are included in the analysis covering 99% of production in the area of study: soft wheat; vitreous (durum) wheat; corn; potatoes; sugar beet; cotton; onion; watermelon and sunflower. The set-a-side (no cultivation) area is included in the scheme in accordance with European Common Agricultural Policy regulations. After objectives and decision variables are defined, it is necessary to explicit the acreage, soil quality, technical, irrigation water constraints and administrative and marketing quotas which define the feasible set. As we have defined three decision types for each irrigation unit we have six feasible sets, where technical coefficients are always the same but different resources availability is supposed for land, water, and labour resource level. The weighted goal programming (WGP) proposed by Sumpsi et al. (1997) aims to find weights that make the decision making plan as close as possible to the real decision plan. Applying the above mentioned algorithm to our model is solved as follows: Step 1: To formulate the four hypothesised objectives h(x), i = 1,4. Step 2: To obtain the pay-off matrix by solving the program:
J. Berhel, A. Rodriguez-Ocaria I European Journal of Operational Research 107 (1998) 108-I 18
subject to x E F.
maximise j”t(x) ,
(1)
The optimum of Eq. (1) f; = ftt is the first entry of the matrix. To obtain the other terms of the first column we only need to substitute the optimum vector of decisional variables provided by Eq. (1) in the remaining i = 2,4 objectives. By implementing the same calculation we obtain a squared matrix shown in Table 3 for County or irrigation unit number 1. Easily we find a similar matrix for area 2, but we show only the first one to illustrate the procedure. Step 3: To solve the problem: min
[
1
1 (no +pl)z+...+(ni+pi’fi
f...
+Pq$ 1
h
+
(2)
115
pay-off matrix (J ,fn), these values depend upon what farmers are doing in the real world. A theoretical problem of this methodology maybe the possibility of some objectives closely correlated in the sense that maximising one objective implies the simultaneous achievement of the rest. An advice may be to be very selective in the number of objectives, avoiding those closely related, (e.g. in agricultural production, sales are closely related to gross margin). Pay-off matrix shows the degree of conflict among criteria, and in the hypothetical case that all objectives are closely related (maximisation of an objective implies almost optima for the rest), we conclude that there is not a Multicriteria problem. Nevertheless real decision system almost always shows conflict between decision criteria.
4
s.t.
Wjfil + “6,
+n1
Wlfj] .fiq
”
+
W]f,l
’ +
-PI
+
.
ni
-
wj
+
Wi
”
fii
+
”
’ +
’ ‘.
+
6. Empirical findings
Wq
Wq
Pl = fi
(3)
+“.+Wi
+
+
=f1
fqi+‘..+Wq
fqq+nq-pq WI
f,i
=fq +
Wi
+
”
+
Wq
=
1
(4)
Step 4: The initial solution (set of weights) obtained is improved by resorting to an iterative trial and error procedure as Sumpsi et al.
Results are shown in Section 6. We should comment that pay-off matrix results from technical characteristics of the system, and the observed behaviour may be seen in the added column to the
Table 4 Pay-off matrix,
County
The result of the descriptive analysis by cluster techniques was the definition for each of the irrigation units analysed three crops orientations, which is to say, three farm enterprises decision groups (Variable D, Tables 2 and 4). According to MCDM theory each of these three groups selected according to crop plan should have similar ‘values orientation’ and consequently similar objective weights. As we mentioned before it was not possible to find a relationship between decisions and elicited criteria, because we suppose that there are some linguistic and psychological problems that we have not solved yet. Therefore, we shall seek the objective weights with the help of the weighted goal programming (WGP) methodology explained above. The final output of Sumpsi et al. algorithm gives the objective weights shown in Table 5 for
1
Objective
Zl
22
23
24
Zl: 22: 23: 24:
345.590 46.064 332.009 9.083
68.589 10.605 63.699 7.090
335.636 37.919 336.799 27.066
74.013 11.503 70.183 0
Max income Min hired labor Maxmin Min working capital
J. Berbel, A. Rodriguez-OcaCa I European Journal of Operational Research IO7 (1998) 108-118
116
farmer groups D1, D2 and Dj. When applying the WGP to the three cluster distributions we found that group D1 of irrigation unit 1 seems to take into account three criteria in decision making: maximising income (56%) minimising working capital (35%) and minimising hired labour (g%). Group D2 is quite different as the main criteria is minimising labour (60%) minimising risk (31%) and thirdly maximising profit (6%). Finally group 03 seems to seek a risk minimisation (64%) and, secondly, minimising hired labour (35%). We can draw the conclusion that the study area is quite heterogeneous in production plans as a consequence of variations in socio-economic and technical characteristics of farm enterprises. Three orientations may explain the production plans: D1 instrumental values orientation (maximising income, expanding business); 02 and 03 seems to be expressive or intrinsic orientation, with different degrees of risk aversion. Results for irrigation unit 2 are similar when we proceed to apply the methodology, and differences may be explained by different technical characteristics (soil quality, water supply, climate) and socio-economic characteristics. Nevertheless, as the counties are quite close to each other (25 km) we expected to have similar results as could be seen in Table 5. Relative weights given to decision criteria in clusters Dl-D3 are remarkably similar in both irrigation units, showing that the WGP method when applied to a region where a previous sorting in of
Table 5 Objective
weights
by type of decision
cluster
farm operators is made, may be an appropriate methodology for analysing real decision making. Table 6 shows for irrigation unit #l the result of applied weights to objectives and projected real area of crops. It can be seen that crop distribution is fairly heterogeneous according to farm-type. On the other hand, results are remarkably close to real crop plans, but it should be noted as model approximates behaviour in the objectives space and not in decision space and there is not perfect correlation between both spaces.
7. Concluding remarks The analysis of the decision-making process in agricultural enterprises is approached in this paper with the development of a methodology based upon a combination of techniques that allow a deep understanding of the influence of socio-economic and technical heterogeneity on production decisions. A major advantage of the proposed method is that it is composed of two stages, in the first of which we enlarge our knowledge of the system under study by cluster analysis of the farm enterprises. Once the farms are classified according to productive behaviour, we may also reach a deeper understanding of the agricultural system analysed. The result of this stage is to classify farms according to crop pattern, which is the basis for the second stage. WGP is selected as the methodology
and County
D1 (“/I
D2
County 1 Campiiia Baja W, (MAX income) w2 (MIN hired labour) w3 (MAXIMIN) w4 (MIN working capital)
56.5 8.1 0.0 35.4
6.0 60.7 31.1 2.2
35.4 64.6 0.0
County 2 Las Colonias W, (MAX income) ~2 (MIN hired labour) w3 (MAXIMIN) w4 (MIN working capital)
51.7 6.1 0.0 42.1
5.0 59.5 33.0 2.4
0.0 36.6 63.4 0.0
(“/I
D3
(“4
0.0
J. Berbel, A. Rodriguez-Ocaria I European Journal of Operational Research IO7 (1998)
Table 6 Projected
values for crop areas by farm cluster Simulated
Income Hired labor Maximin Working capital Soft wheat Durum wheat Corn Potatoes Sugar beet Cotton Onion Watermelon Sunflower Set-a-side
and irrigation
117
108-118
area 1 vs. real
crop plan
Actual
crop plan
Dl
D2
D3
Dl
D2
D3
273.079 42.349 271.363 0
196.697 23.860 197.432 0
317.722 3 1.204 323.366 49.550
254.007 54.786 238.530 0
234.107 40.861 216.508 15.992
314.337 37.012 316.539 46.490
0
33.2% 1.4% 0 0 1.8% 48.6% 0 0 7.6% 7.4%
6.9% 5.4% 2.7% 4.7% 6.0% 5 1.3% 3.2% 4.1% 11.2% 4.6%
0 1.4% 41.2% 0.5% 1.8% 44.3% 1.2% 1.6% 0.5% 7.6%
5.4% 6.2% 7.1% 6.0% 59.3% 0 0.3% 11.6% 4.1%
that approaches the weights given by different farmers to the objectives of the decision process. As we applied this methodology to two different irrigation units, we found that there was an important degree of heterogeneity in production plans, and that the variation of crop plans could be explained by differences in objective weights caused by differences in the farmers’ value orientation. Also, we should point out that it was not possible to directly link value orientation to criteria by direct questioning, and this opens up an interesting field of research. This framework combined with empirical models can be a useful tool for the analysis of policies such as stabilisation programs, water management schemes, direct or indirect regulations or agricultural support programs. Also, it shows that human capital (experience, education, and age) is at least as important to explain agricultural output as technical and natural capital availability. Finally, we hope that this paper has contributed to extend the field of applications of MCDM techniques, as well as to have enlarged our knowledge of a real decision making process and decision-maker’ objectives, especially in the field of agricultural enterprises.
0 0 0
0 0 100.0 0 0 0 0
0 0
0 0 0
98.4% 1.6% 0 0 0
There are some interesting avenues of research, as to study the evolution of weights in a period of time. In the specific case of irrigated agriculture, it may be applied to analyse the projected demand on natural resources (i.e. water, fertiliser) using the weighted goal programming approach instead of the classical profit-maximising hypothesis. Also for the MCDM community, some discussion on the meaning of weights and uses of weights for economic and management models is convenient. Acknowledgements
Comments and suggestions of Dr. Pedro RuizAviles, Dr. Carlos Romero and anonymous referees is acknowledged. The authors have received the financial support of Spanish CICYT project HID96-1294. References Barnett, D., 1979. Farmer’s goals and constraints: Their effects on the cultivation of crops in sine saloum, Senegal. Unpublished M.S. Thesis, Purdue University.
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Bamett, D., Blake, B., McCarl, B., 1982. Goal programming via multidimensional scaling applied to senegalese subsistence farms. Amer. J. Agric. Econ. 9, 720-727. Berbel, J. 1993. Risk programming in agricultural systems: A multiple triter decision analysis. Agricultural Systems 41 (3) 275-288. Bernardo, D.J., Whittlesey, N.K., Saxton, K.E., Basset, D.L., 1987. An irrigation model for management of limited water supplies. West. J. Agr. Econ. 12, 164-173. Deffontaines, J.P., Petit, M., 1985. Comment Ctudier les explotations agricoles d’une region. Presentation d’un ensemble methodologique. Etudes et recherches (4) INRA, Dijon. Feinerman, E., Finkelshtain, I., 1996. Introducing socioeconomic characteristics into production analysis under risk. Agr. Econ. 13, 149-161. Gasson, R. 1973., Goals and Values of Farmers J. Agr. Econ. 24, pp. 521-537. Gomez-Limon, J.A., Berbel, J., 1995. Aplicacion de una metodologia multicriterio para la estimacibn de 10s objetivos de 10s agricultores de1 regadio cordobes. Invest. Agr. Econ. 10 (1). Harman, W.L., Hatch, R.E., Eidman, V.R., Claypool, P.L., 1972. An evaluation of factors affecting the hierarchy of multiple goals. Okla. Agr. Exp. Sta. Tech. Bull. T-134. Harper, W.M., Eastman, C., 1980. An evaluation of goal hierarchies for small farm operators. Amer. J. Agric. Econ. Hatch, R.E., Harman, W.L., Eidman, V.R., 1974. Incorporating multiple goals into the decision-making process, a simulation approach for firm growth analysis. S. J. Agr. Econ. 7, 103-110. Kerridge, K.W., 1977. An exploratory analysis of the value orientation of farmers in the wheat-sheep zone of Western Australia. Bureau of Agricultural Economics, Australia.
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Kimhi, A., 1996. Farmers’ time allocation between farm work and off-farm work and the importance of unobserved group effects: Evidence from Israeli cooperatives. Agr. Econ. 14, 1355142. Mendez-Barrios, J.C., 1995. Intensification de la cafeiculture chez les petits producteurs du Guatemala. Diplome de Doctorat, Ecole National Superieure Agronomique de Montpellier. Patrick, G.F., 1978. Some impacts of inflation on farm firm growth. Southern J. Agr. Econ., 10, 9-14. Patrick, G.F., Kliebenstein, J.B., 1980. Multiples goals in farm decision-making: A social perspective. Department of Agricultural Economics, Agricultural Experimental Station, Mimeo, Pardue University. Patrick, F., Blake, B.F., 1980. Measurement and modelling of farmers’ goals: An evaluation and suggestions. Southern J. Agr. Econ. 1. Rodriguez-Ocaria, A., Berbel, J., y Ruiz-Aviles, P., 1996. Methodology for analysis of decision criteria: An application to irrigated farms in Southern Spain, en II Intemationa M.O.P.G.P. Conference, Torremolinos, Spain, May 1996. Romero, C., Rehman, T., 1989. Multiple Criteria Analysis for Agricultural Decisions, Elsevier, Amsterdam. Sumpsi, J.M., Amador, F., Romero, C., 1997. On farmers’ objectives: A multi-criteria approach. Eur. J. Oper. Res. 96 (I), 64-71. Taylor, R.G., Young, R.A., 1995. Rural-to-urban water transfers: Measuring direct foregone benefits of irrigation water under uncertain water supplies. J. Agr. Resource Econ. 20 (2) 247-262. Zekri, S., Romero, C., 1993. Public and private compromise in agricultural water management. J. Envir. Mgmt. 37, 281290.
ELSEVIER
European Journal of Operational Research 107 (1998) 108-I 18
Theory and Methodology
An MCDM approach to production analysis: An application to irrigated farms in Southern Spain J. Berbel aj*, A. Rodriguez-Ocafia b a Dpto. de Agrarias Economia, Universidad de Cordoba, P.O. Box 3048, 14080 Cordoba, Spain b Consejeria de Agricultura y Pesca, Junta de Andalucia, Delegacidn de Sevilla, Spain
Received 11 February 1997; accepted 14 May 1997
Abstract The analysis of the decision-making process in agricultural enterprises is approached with the development of a methodology based upon two stages: firstly we enlarge our knowledge of the system under study by performing grouping operation - cluster analysis - of the farm enterprises. The result of this stage is to classify farms according to crop pattern, which is the basis for the second stage of analysis: the system is studied by solving a weighted goal programming to approach the weights given by different farmers to the objectives of the decision process. This methodology is applied to two nearby but different irrigation units in Southern Spain, and we found that there was an important degree of heterogeneity in production plans explained by differences in objective weights. 0 1998 Elsevier Science B.V. All rights reserved. Keywords: Multicriteria
analysis; Irrigated agriculture; Goal programming;
1. Introduction Self-employed farmers frequently manage agricultural enterprises; therefore, the owner-operator takes into account his objectives, goals and constraints, and decides production plans. Differences in the availability of material resources (land area, water supply, quality of soil, etc.) or economic resources (marketing channels, production quotas,
Corresponding author. Fax: +34-957-218-563; e-mail: [email protected]. ??
Cluster analysis
etc.) are not the only source of heterogeneous production decisions, because farms also differ from each other in their socio-economic characteristics. Variations in socio-economic and technical characteristics of farms may cause differences in risk preferences or time allocation between farm work and off-farm work. These differences in the operators’ behaviour will lead to diverse production decisions. Successful simulation models of agricultural systems and the design of agricultural or environmental policies should integrate the rules governing this heterogeneity, but unfortunately a great number of models ignore this
SO377-2217/98/$19.00 0 1998 Elsevier Science B.V. All rights reserved. PIISO377-2217(97)00216-6
J. Berbel, A. Rodriguez-Ocafia I European Journal of Operational Research 107 (1998)
heterogeneity. Moreover, the question arises as to which factor will be more influential on farm decisions: technical and natural resources or human capital and socio-economic characteristics of the decision-maker. This paper is in the field of the applied economics searching for a deeper empirical understanding of individual and collective behaviour. The major objective of this paper is to develop a methodology for the analysis of decision criteria and the effect of the decision making process in production plans. It will apply the methodology to a case study of irrigated farms in Southern Spain where we find an almost perfect competition context. There is general consensus among economists on the hypothesis that managers take into account many conflicting criteria in the process of decision making both in private enterprises and institutional agencies. This hypothesis is the basis of the multiple criteria decision-making theory (MCDM). According to Barnett et al. (1982) MCDM research can be characterised as “descriptive”, “operational” or “combined”. A descriptive approach concerns whether or not decision-makers possess multiple objectives, and develop relative rankings of them. The operational approach uses hypothesised objective weights and examines their impact upon a decision model. Finally, the combined approach embodies an attempt to discover objectives and their weights and then to use them in a decision model. The present paper may be included in the combined approach type, which may identify weights and use them simultaneously or iteratively as in Barnett et al. (1982) which is the type of application we aim to explain. The first step in our methodology is to sort farmers according to their socioeconomic characteristics and technical and natural production resources. From this grouping will be selected some “clusters” or farm-types with the innovation that the farm types will incorporate both technical and socio-economic elements. Secondly we will try to find relationships between the type of farm operator and the production plans; this is done as an application of weighted goal programming to approach the weights given by the different types of farmers to the objectives in the decision process.
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2. Goals and values of farmers in previous works There are works on empirical research in decision criteria of farmers with some years in anticipation of the MCDM theory and methodological approaches. A pioneering work is the research conducted by Gasson (1967) among farmers in Cambridge (UK). In this work Gasson argues that we should distinguish between values which are defined as observable subjective beliefs related to the way of life of an economic agent and management criteria that are observable values that guide the management decision. Values are cultural products held by members of a social system. Values do not exist in isolation but are organised in systems of value orientations. Values are a more permanent property of the individual, less liable to change with time and circumstances. Values are abstract criteria and they can only be approached indirectly through observed behaviour or verbal responses. Gasson classified “for convenience” value orientations in the following four headings: (1) Instrumental making a maximum income; making a satisfactory income; safeguarding income for the future; expanding the business; providing congenial working conditions (hours, security). belonging to (2) Social gaining recognition; farming community; continuing farming tradition; working with other members of the family; maintaining good relations with workers. (3) Expressive feeling pride of ownership; gaining self-respect for doing a worthwhile job; exercising special abilities; meeting a challenge. (4) Intrinsic enjoyment of work task; preference for healthy, outdoor job; value of hard work; independence-freedom; control of a variety of situations. In the research about farmers in Cambridgeshire, Gasson found that the farmers’ value orientations are related to business size. We find the setting of value orientation types as a very interesting approach to simplify the second stage of the analysis, i.e. the development of a decision model for each of the important types found in the descriptive analysis.
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A second approach to ranking goals of farmers is quoted in Patrick and Blake (1980) describing an unpublished work by Hesselbach and Eisgruber who considered nine goals such as living standard, farming as a way of life, farm ownership, nurture of children, realisation of standards, retirement, work as a goal, risk aversion and decision making readiness. By means of verbal indicators goals were developed and a decision model based upon this information was built. A third approach is the paired comparison technique exemplified by Harper and Eastman (1980) who rank a goal hierarchy from a randomly selected sample of small farm operators in New Mexico. Two sets of goals were evaluated: goals for the family unit and goals for the agricultural enterprise. Having established a correspondence between both types of goals within the sample, their analysis evaluated the symmetry between the hierarchy and a similar study conducted in Oklahoma and Texas concluded that there was a lack of correspondence. Harman et al. (1972) uses this approach to determine the goal hierarchy and factors affecting goals for use in a simulation model. Hatch et al. (1974) included goals to control more acreage, to avoid being forced out of business, etc. They found that the dominant goals changed frequently and that trade-offs should be included. Barnett (1979) who started with paired comparison data later introduced multidimensional preference scaling (MDS) as a fourth approach. The goal scores obtained from MDS are assumed to be on a ratio scale. In this section we have only reviewed some works on empirical studies, but the work of Patrick and Kliebestein (1983) makes a more complete review on the subject, methodologies and cases. Finally, we wish to comment on the work of Patrick (1978) who developed a simulation model that uses the “goals orientation”. The concept of “goals orientation” is similar to Gasson’s “value orientation”. This type of analysis based upon type definition will be the approach of our analysis. The reason for the determination of types is that it is quite difficult to establish a unique goal hierarchy for a heterogeneous group of farmers or decision-makers, even in the case of a common
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cultural background and similar resource availability. It is interesting to see that previous research into values such as Gasson (1973) or Kerridge (1977) found different distribution of value orientations among farmers. Table 1 shows that farmers are quite heterogeneous worldwide and socio-economic characteristics influence values, which in the end will determine production decisions. Unfortunately, information regarding the effect of socio-economic characteristics on decision-making is limited.
3. Models of irrigated agriculture Today business environment is frequently composed by a limited number of firms trying to maintain competition from other firms as low as possible, it is not usual to find the classical “perfect competition” conditions. Agricultural production firms usually are too small to influence markets and technologies, inputs and outputs are commodities where it is not possible to gain a superior role in any market, or try any differentiation strategies. The fact that agricultural production may be characterised as “perfect competition” makes it an interesting field to test empirical models of decision making. Irrigated agriculture uses 85% of water consumed in Mediterranean climates as in Southern Spain, and produces over 50% of the agricultural output. As residential, industrial and environmental demands for water increase, the analysis of irrigated agriculture and water demand becomes a strategic research problem. Water demand for irrigation depends upon farmers’ decisions, which Table 1 Summary Author
Intrinsic Expresive Instrumental Social
of values orientation Gasson
(1973)
Small (%)
Large (“Yo)
27 16 27 39
24 20 33 23
Kerridge
41% 18% 38% 3%
( 1977)
J. Berhel, A. Rodriguez-Ocmia I European Journal of Operational Research 107 (1998)
is the objective of our research. Irrigated agricultural enterprises are an interesting empirical field as they are composed of relatively homogeneous decision-makers of a price-taker nature, therefore in a relatively “perfect competition” world. Models of applied irrigated agriculture have used linear programming to study the effects of changing water price and supply in optimal cropping patterns and later efforts have incorporated quadratic programming, dynamic programming or discrete sequential programming (Taylor and Young, 1995). But generally these models on a regional scale may suffer from aggregation problems and the objective function - usually regional agricultural income - may not capture the real underlying decision process. The typical decision-maker owns and operates a family farm, where production and consumption decisions are determined simultaneously. Socioeconomic factors enter through value orientations into the farmer’s preference or multiattribute utility function. Variations in socio-economic characteristics affect production choices in various ways. Firstly, it may affect the farmer’s rate of substitution between income and leisure, or may change his opportunity cost and the way time is distributed between on farm and off-farm work. The effects have been investigated extensively, but we should mention the research of Kimhi (1996) where results found are to the effect that off-farm participation is highly sensitive to personal characteristics, followed by age, farm tenure and other factors. Another way of influencing criteria weights is that a change in socio-economic characteristics may affect decisions via risk attitudes. We would like to highlight a recent paper by Feinerman and Finkelshtain (1996) who introduce socio-economic characteristics into production analysis under risk. When we consider the risk-return model as a two criteria model it can be treated as a member of general Multicriteria models. These authors conclude that risk attitude is influenced by farm size and technical characteristics and also family size, age, education affect quite significantly risk attitude and, consequently, production plans. Many authors have built MCDM models of farm-decisions paying special detail to heterogeneous farms; we can quote Berbel (1993) or Zekri
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Ill
and Romero (1993) as examples in the field of Multicriteria analysis of irrigated agriculture. We recommend the book by Romero and Rehman (1989) as a comprehensive reference of the stateof the-art of these techniques, with special reference to agricultural problems. Models found in the literature usually try to avoid the “aggregation problem” when modelling regional systems by dividing the farms according to size and technical characteristics. Generally, the results of MCDM prove to be closer to real decisions than simple profit-maximising linear programming. Nevertheless, we should mention that the methodology that will be explained in this paper might be applied to any other economic sector and in many decision contexts (financial, manufacture, administration, etc.). The results of the methodology are not limited to this type of firm.
4. Analysis of irrigated firms in Andalusia Our approach to model decision making in irrigated agriculture will be based upon MCDM theory, but we are interested in obtaining models, which may be used as tools for water management policy formulation. We decide that practical models should be built at a “middle-level”, which is a compromise between a single model for all the river management and exhaustive micro level by single farm, which is too detailed for practical policy making. Therefore, for this reason, we need to analyse an area large enough to contain a significant number of farmers, but not too large as to introduce sources of variation in soil, climate or market conditions, and this level is the “irrigation unit”. Furthermore, from the economic point of view, when the region is not perfectly homogeneous, the result may suffer some “aggregation bias”. Consequently, our methodology will make an intermediate approach: it will analyse a small region, but it will divide the complete set of farmers into “cluster” or homogeneous groups reducing it to a manageable figure. Research will be conducted in two stages: (1) descriptive analysis and grouping of types of decision-maker and (2) development of a simulation model.
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Result of the first stage will be the sorting of farmers in different types of decision-makers by using cluster techniques. The term “cluster analysis” embraces a loosely structured body of algorithms, which are used in the exploration of data from the measurement of a number of characteristics for a collection of individuals. Cluster analysis is concerned with the discovering of the groups. The word “cluster” or “group” should be interpreted as a collection of “similar” objects. The sample is based upon a random choice of 115 farmers in the Mid Guadalquivir Valley (Southern Spain) from two nearby irrigation sectors (68 farmers in area 1 “Campifia Baja” and 47 in area 2 “Las Colonias”). The variables were a number of 101 and were grouped in 10 categories (socioeconomic, structure, etc.) In this paper, results are shown in Table 2 about six relevant categories. Each of these categories is formed with the observations (answers) taken from each individual farmer. We grouped by cluster technique the farmers in the following clusters of groups as shown in Table 2.
Table 2 Results of cluster
analysis
Variable County-irrigation Socio-economic
Structure
Decision
Criteria
Values
This stage of the analysis uses conventional statistical techniques in order to get a qualitative and cardinal aggregation of raw data. It is not the aim of this stage of descriptive analysis to apply multivariate techniques in order to explore the system, as we mentioned previously, our goal is to reduce the number of farms to a manageable figure through grouping techniques. The aim of cluster techniques is to get the information ready for the second stage, which is the application of Multicriteria models in a selected number of farm types which represent the complete system analysed as closely as possible. The second stage in the cluster analysis is the application of Group Analysis to the different categories. The analysis of this information is quite interesting for an understanding of the relationship between individual socio-economic characteristics and the values and criteria orientations. Finally it is interesting to seek relationships between individual socio-economic characteristics and final production decisions.
unit
Group
%
Definition
Zl 22 Al A2 A3 A4 Bl B2 B3 B4 Dl D2 D3 Fl F2 F3 F4 F5 Hl H2 H3 H4
59 41 17 63 10 10 43 35 12 10 26 17 57 17 14 12 37 21 43 36 11 10
Campiiia Baja Las Colonias Farm income below 50% older, low qualification Full-time, medium age, low qualification Full-time, younger, high qualification Farm income around 50%, medium age, low qualification Medium farms, irrigated below 20% Small farm, 100% irrigated, no wells Small farm, mostly irrigated, own wells Large farms, mostly irrigated, own wells ~50% water supply Cotton around 50%, rest sunflower and various Cotton around 50%, rest mainly corn Cotton almost 100% (1) Max profit; (2) Max production (sales) (1) Max profit; (2) Max resource use (1) Max profit; (2) Max family labour (1) Max profit; (2) Min cost (1) Max production (sales); (2) Max profit Instrumental: (1) income; (2) independence Expressive-intrinsic: (1) to own land; (2) independence Expressive: (1) creativity; (2) independence Intrinsic: (1) Farm work; (2) creativity
113
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Unfortunately, we also found that “criteria” (variable F) was independent from “decision” (variable D) and this was not a desired result. We should explain that because verbal questioning about management criteria is not well understood by farmers; on the contrary, farmers more easily understand questions on values that are based upon cultural beliefs than criteria questions (profit, risk, etc.). A more intense research should be conducted in the analysis of management criteria with the help of direct methods, and the use of multivariate statistics will help to examine fully the original data, but this is not the goal of our research which is to develop an analysis method based upon Multicriteria analysis at an intermediate level. Deffontaines and Petit (1985) affirmed that farmers’ criteria are better observed by indirect methods than by direct verbal questioning, therefore, arriving to a similar conclusion.
According to values orientation of farmers (answers to question: “reasons for being a farmer”), we find four values orientation (groups Hl-H4, Table 2) it may be seen that value orientations percentages differ from Table 1. The year 1995 when our field research and questioning was conducted, Southern Spain was suffering a severe drought, which affected farmers’ production plans. The anomalous scarcity of water led us to ask questions about the “projected crop plan” with the known supply of water and we also include questioning about the “desired crop plan” without a water shortage. It is not the objective of this paper to analyse in depth the description of individual farmer’s types and orientations, as more information on this can be found in RodriguezOcafia et al. (1996), where log-linear analysis is applied to the analysis of dependence between variables. The analysis of dependence between couples of clusters is conducted through a Chi Square Pearson test of Independence. Table 3 shows the analysis of dependence, and we can hypothesise that variable i and j are not independent when c1 < 0.05. Each variable represents the different groups produced by cluster analysis. We can draw practical consequences from Table 3 and it can be seen that decision plans (variable 0) are related to socio-economic characteristics of farmer (variable A), values of farmer (variable H), and county (variable Z). On the other hand, the decision does not depend upon structure or technical and natural characteristics on the farm (variable B). This is an important finding of our research, as most of the previous works have used farm size and technical characteristics as the main source of heterogeneity in production decisions. Table 3 Chi Square
A: B: D: F: H: Z:
Pearson
Socio-economic Structure Decision Criteria Values County
5. Multicriteria decision model As we mention above, traditional mathematical programming based on the optimisation of a single objective should be replaced by Multicriteria analysis. There are two streams of Multicriteria analysis: Multiobjective programming which optimises several objectives (many of them usually in conflict) and Goal programming which tries to satisfy as far as possible a set of goals compatible with the preference revealed by farmers. Sumpsi et al. (1997) propose a model in the weighted goal programming approach fully described in a recent paper, and which is applied as described in the simplified and most frequent case, i.e.
test of independence A
B
D
F
H
Z
_ 0 0.0038 0.0821 0.1905 0
0
0.0038 0.7686 _ 0.6976 0.0150 0.0015
0.0821 0.1181 0.6976 _ 0.0932 0.1509
0.1905 0.0262 0.0150 0.0932
0 0.0027 0.0015 0.1509 0.0131
0.7686 0.1181 0.0262 0.0027
0.0131
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I European Journal of Operational
Step 1: After an initial interaction with farmers (questionnaire and descriptive research explained above) a tentative set of objectives are established. Step 2: Determine the pay-off matrix of the above set of objectives. As the matrix is unique, then go to step 3’. Step 3’: (Please, note that this is step no. 4 in general algorithm of Sumpsi et al.). Formulate and solve a weighted goal programming which will provide a set of weights that surrogate the preferences of farmers. When weights are satisfactory, then stop. Step 4’: (Step 5 in Sumpsi et al.) The initial solution (set of weights) obtained is improved by resorting to an iterative structured trial and error procedure until a satisfactory solution is obtained. In their paper Sumpsi et al. work with individual farmers, finding for each case a set of weights that are a surrogate of individual preferences. In a similar approach, Mendez-Barrios (1995) and Gomez-Limon and Berbel (1995) use the methodology for analysing a small area but on an aggregate level, finding a surrogate for the “collective decision-maker”, probably when the region is not perfectly homogeneous, the result may suffer some “aggregation bias”. The present paper will make an intermediate approach: it will analyse a small region homogeneous in technical aspects but sorting the complete set of farmers into “cluster” or homogeneous groups. Cluster techniques are therefore used as a help to avoid aggregation problems on one hand and on the other to avoid an excessive amount of data, as it will imply using individual information. Results on cluster analysis allow us to classify farmers in small and manageable relatively homogeneous groups. The descriptive analysis explained above, shows that production plans in each of both irrigation units might be classified in three clusters. Also we could see (Table 3) that decisions were more dependent on socio-economic characteristics than on other sources of variation. We will therefore try to understand weights given to different criteria by each of the decision types by using the model developed by Sumpsi et al. (1997). According to experience gained in the first stage of research, when questioning farmers directly
Research IO7 (1998) 108-118
about criteria, we propose that the following criteria be analysed: (Wi) maximisation of net income; (WJ minimisation of hired labour; (Ws) minimisation of working capital requirements; and ( W,) optimising the MAXIMIN for the period 198881992. Net income is simulated according to data gathered on yields and prices in the area, and cost of production, and complemented by direct payments due to Common Agricultural Policy (CAP) rules. Farmers try to avoid hired labour because they prefer to get as much as possible out of family labour. Cash requirements for working capital are minimised because a great need of capital implies external financing via a bank debt and, simultaneously working capital invested in a production plan is associated with risk. Risk itself was modelled with different parameters suggested in the literature but MAXIMIN was selected because of its simplicity and good results with our data set. Nine crops are included in the analysis covering 99% of production in the area of study: soft wheat; vitreous (durum) wheat; corn; potatoes; sugar beet; cotton; onion; watermelon and sunflower. The set-a-side (no cultivation) area is included in the scheme in accordance with European Common Agricultural Policy regulations. After objectives and decision variables are defined, it is necessary to explicit the acreage, soil quality, technical, irrigation water constraints and administrative and marketing quotas which define the feasible set. As we have defined three decision types for each irrigation unit we have six feasible sets, where technical coefficients are always the same but different resources availability is supposed for land, water, and labour resource level. The weighted goal programming (WGP) proposed by Sumpsi et al. (1997) aims to find weights that make the decision making plan as close as possible to the real decision plan. Applying the above mentioned algorithm to our model is solved as follows: Step 1: To formulate the four hypothesised objectives h(x), i = 1,4. Step 2: To obtain the pay-off matrix by solving the program:
J. Berhel, A. Rodriguez-Ocaria I European Journal of Operational Research 107 (1998) 108-I 18
subject to x E F.
maximise j”t(x) ,
(1)
The optimum of Eq. (1) f; = ftt is the first entry of the matrix. To obtain the other terms of the first column we only need to substitute the optimum vector of decisional variables provided by Eq. (1) in the remaining i = 2,4 objectives. By implementing the same calculation we obtain a squared matrix shown in Table 3 for County or irrigation unit number 1. Easily we find a similar matrix for area 2, but we show only the first one to illustrate the procedure. Step 3: To solve the problem: min
[
1
1 (no +pl)z+...+(ni+pi’fi
f...
+Pq$ 1
h
+
(2)
115
pay-off matrix (J ,fn), these values depend upon what farmers are doing in the real world. A theoretical problem of this methodology maybe the possibility of some objectives closely correlated in the sense that maximising one objective implies the simultaneous achievement of the rest. An advice may be to be very selective in the number of objectives, avoiding those closely related, (e.g. in agricultural production, sales are closely related to gross margin). Pay-off matrix shows the degree of conflict among criteria, and in the hypothetical case that all objectives are closely related (maximisation of an objective implies almost optima for the rest), we conclude that there is not a Multicriteria problem. Nevertheless real decision system almost always shows conflict between decision criteria.
4
s.t.
Wjfil + “6,
+n1
Wlfj] .fiq
”
+
W]f,l
’ +
-PI
+
.
ni
-
wj
+
Wi
”
fii
+
”
’ +
’ ‘.
+
6. Empirical findings
Wq
Wq
Pl = fi
(3)
+“.+Wi
+
+
=f1
fqi+‘..+Wq
fqq+nq-pq WI
f,i
=fq +
Wi
+
”
+
Wq
=
1
(4)
Step 4: The initial solution (set of weights) obtained is improved by resorting to an iterative trial and error procedure as Sumpsi et al.
Results are shown in Section 6. We should comment that pay-off matrix results from technical characteristics of the system, and the observed behaviour may be seen in the added column to the
Table 4 Pay-off matrix,
County
The result of the descriptive analysis by cluster techniques was the definition for each of the irrigation units analysed three crops orientations, which is to say, three farm enterprises decision groups (Variable D, Tables 2 and 4). According to MCDM theory each of these three groups selected according to crop plan should have similar ‘values orientation’ and consequently similar objective weights. As we mentioned before it was not possible to find a relationship between decisions and elicited criteria, because we suppose that there are some linguistic and psychological problems that we have not solved yet. Therefore, we shall seek the objective weights with the help of the weighted goal programming (WGP) methodology explained above. The final output of Sumpsi et al. algorithm gives the objective weights shown in Table 5 for
1
Objective
Zl
22
23
24
Zl: 22: 23: 24:
345.590 46.064 332.009 9.083
68.589 10.605 63.699 7.090
335.636 37.919 336.799 27.066
74.013 11.503 70.183 0
Max income Min hired labor Maxmin Min working capital
J. Berbel, A. Rodriguez-OcaCa I European Journal of Operational Research IO7 (1998) 108-118
116
farmer groups D1, D2 and Dj. When applying the WGP to the three cluster distributions we found that group D1 of irrigation unit 1 seems to take into account three criteria in decision making: maximising income (56%) minimising working capital (35%) and minimising hired labour (g%). Group D2 is quite different as the main criteria is minimising labour (60%) minimising risk (31%) and thirdly maximising profit (6%). Finally group 03 seems to seek a risk minimisation (64%) and, secondly, minimising hired labour (35%). We can draw the conclusion that the study area is quite heterogeneous in production plans as a consequence of variations in socio-economic and technical characteristics of farm enterprises. Three orientations may explain the production plans: D1 instrumental values orientation (maximising income, expanding business); 02 and 03 seems to be expressive or intrinsic orientation, with different degrees of risk aversion. Results for irrigation unit 2 are similar when we proceed to apply the methodology, and differences may be explained by different technical characteristics (soil quality, water supply, climate) and socio-economic characteristics. Nevertheless, as the counties are quite close to each other (25 km) we expected to have similar results as could be seen in Table 5. Relative weights given to decision criteria in clusters Dl-D3 are remarkably similar in both irrigation units, showing that the WGP method when applied to a region where a previous sorting in of
Table 5 Objective
weights
by type of decision
cluster
farm operators is made, may be an appropriate methodology for analysing real decision making. Table 6 shows for irrigation unit #l the result of applied weights to objectives and projected real area of crops. It can be seen that crop distribution is fairly heterogeneous according to farm-type. On the other hand, results are remarkably close to real crop plans, but it should be noted as model approximates behaviour in the objectives space and not in decision space and there is not perfect correlation between both spaces.
7. Concluding remarks The analysis of the decision-making process in agricultural enterprises is approached in this paper with the development of a methodology based upon a combination of techniques that allow a deep understanding of the influence of socio-economic and technical heterogeneity on production decisions. A major advantage of the proposed method is that it is composed of two stages, in the first of which we enlarge our knowledge of the system under study by cluster analysis of the farm enterprises. Once the farms are classified according to productive behaviour, we may also reach a deeper understanding of the agricultural system analysed. The result of this stage is to classify farms according to crop pattern, which is the basis for the second stage. WGP is selected as the methodology
and County
D1 (“/I
D2
County 1 Campiiia Baja W, (MAX income) w2 (MIN hired labour) w3 (MAXIMIN) w4 (MIN working capital)
56.5 8.1 0.0 35.4
6.0 60.7 31.1 2.2
35.4 64.6 0.0
County 2 Las Colonias W, (MAX income) ~2 (MIN hired labour) w3 (MAXIMIN) w4 (MIN working capital)
51.7 6.1 0.0 42.1
5.0 59.5 33.0 2.4
0.0 36.6 63.4 0.0
(“/I
D3
(“4
0.0
J. Berbel, A. Rodriguez-Ocaria I European Journal of Operational Research IO7 (1998)
Table 6 Projected
values for crop areas by farm cluster Simulated
Income Hired labor Maximin Working capital Soft wheat Durum wheat Corn Potatoes Sugar beet Cotton Onion Watermelon Sunflower Set-a-side
and irrigation
117
108-118
area 1 vs. real
crop plan
Actual
crop plan
Dl
D2
D3
Dl
D2
D3
273.079 42.349 271.363 0
196.697 23.860 197.432 0
317.722 3 1.204 323.366 49.550
254.007 54.786 238.530 0
234.107 40.861 216.508 15.992
314.337 37.012 316.539 46.490
0
33.2% 1.4% 0 0 1.8% 48.6% 0 0 7.6% 7.4%
6.9% 5.4% 2.7% 4.7% 6.0% 5 1.3% 3.2% 4.1% 11.2% 4.6%
0 1.4% 41.2% 0.5% 1.8% 44.3% 1.2% 1.6% 0.5% 7.6%
5.4% 6.2% 7.1% 6.0% 59.3% 0 0.3% 11.6% 4.1%
that approaches the weights given by different farmers to the objectives of the decision process. As we applied this methodology to two different irrigation units, we found that there was an important degree of heterogeneity in production plans, and that the variation of crop plans could be explained by differences in objective weights caused by differences in the farmers’ value orientation. Also, we should point out that it was not possible to directly link value orientation to criteria by direct questioning, and this opens up an interesting field of research. This framework combined with empirical models can be a useful tool for the analysis of policies such as stabilisation programs, water management schemes, direct or indirect regulations or agricultural support programs. Also, it shows that human capital (experience, education, and age) is at least as important to explain agricultural output as technical and natural capital availability. Finally, we hope that this paper has contributed to extend the field of applications of MCDM techniques, as well as to have enlarged our knowledge of a real decision making process and decision-maker’ objectives, especially in the field of agricultural enterprises.
0 0 0
0 0 100.0 0 0 0 0
0 0
0 0 0
98.4% 1.6% 0 0 0
There are some interesting avenues of research, as to study the evolution of weights in a period of time. In the specific case of irrigated agriculture, it may be applied to analyse the projected demand on natural resources (i.e. water, fertiliser) using the weighted goal programming approach instead of the classical profit-maximising hypothesis. Also for the MCDM community, some discussion on the meaning of weights and uses of weights for economic and management models is convenient. Acknowledgements
Comments and suggestions of Dr. Pedro RuizAviles, Dr. Carlos Romero and anonymous referees is acknowledged. The authors have received the financial support of Spanish CICYT project HID96-1294. References Barnett, D., 1979. Farmer’s goals and constraints: Their effects on the cultivation of crops in sine saloum, Senegal. Unpublished M.S. Thesis, Purdue University.
118
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I European Journal of Operational
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