Multi Criteria Governmental Crop Planning Problem: an Analytic Hierarchy Approach

The goal of this study is to rank crops to cultivate in the governmental agricultural lands in Gaza St rip using AHP methodology as a Multi Criteria Decision Making (MCDM) tool. Th is study is applied under the normal condition, from the governmental point of view. Seven main criteria were first identified consisting of economical, financial, market ing, environmental, technical, political, and social criteria, while thirty one sub-criteria were then identified. Crops were divided into eight types that include vegetables, fruits, citrus, olives, palms, export crops, field crops and medical and aromat ic crops. The results indicate that the economic criteria are the most important criteria as they represent 0.33 of the total weight, while the technical criteria are the least important criteria as they represent 0.07 of the total weight. Sub-criteria weights indicate that the contribution to GDP sub-criterion is the most important one with respect to the goal as it has 0.103 of the total weight. Cropping pattern is skewed towards export crops, citrus and vegetables.


Introduction
Crop planning plays a vital role in agricultural sector. Many problems associated with agriculture such as soil fertility, seasonality, productivity fluctuations can be controlled by successful crop planning. The Min istry Of Agricultural (MOA) in Ga za Strip attempts to develop a crop plan as an effect ive agricultural strategy to deal with agricultural problems. Th is study aims to help MOA make a strategic decision of selecting the most proper crops to cultivate.
As opposed to the resistant economy condition which is mainly characterized by the siege imposed on Ga za Strip after 2006 [1], this paper focuses on treating the crop planning problem in Ga za St rip under the normal economy condition which prevailed Ga za Strip before 2006. Normal economy is characterised by the following: • Imports and exports are allo wed.
• Production inputs are available.
• There are surpluses in some crops and shortages in others.
• MOA focused on cultivating crops that greatly contribute to Gross Domestic Product (GDP) and can face co mpetition between local and foreign crops due to its high quality characteristics.
The process of developing a suitable and effective crop plan is a co mple x decision making problem involving mu ltip le ob jectives. The purpose of this paper is to ran k the crops according to the certain criteria, using Analytic Hierarchy Process (AHP).
The selection of AHP in this study is due to its ability to structure a problem hierarchically, thus; it provides users with a better focus on specific criteria and sub-criteria when allocating the weights. Furthermore, qualitative and quantitative criteria can be evaluated on the sa me preference scale of nine levels [2]. This study is motivated by the following: • The previous studies [3][4][5][6][7][8][9][10][11][12][13][14] focused on resources consumption criteria such as land, water, fertilizers, labor…..etc., while this study considers many other criteria to develop effective long term crop plan, such as self sufficiency, food security, intercropping, organic agricu lture, postharvest storage and many other criteria as will be illustrated through this study.
• More criteria are considered in this study.
• The agricultural sector in Ga za Strip has many problems that are not typical in related literature.
In this paper, sections are organized as follows: section two reviews the literature on crop planning, followed by AHP methodology in section three, section four presents crop planning in Gaza Strip fo llo wed by the model application in section five. Results and analysis are given in section six fo llowed by conclusions in section seven.
Cropping decisions mainly involve determining the crops to be cultivated and the area to be planted for each crop. The crop planning issue is usually formu lated as a single objective linear programming model. Ho wever, at a regional level and in term of sustainable agricultural development, crop planning pursues multiple object ives where each objective has to be monitored and measured using the appropriate criteria. Many papers have been written on this subject. [3,4] suggest the methods of mu lti-objective programming for land use in reg ional level. [5] considers a nation-wide crop-planning problem, formulates the problem as a goal program and discusses the importance of three different goals for a case problem. [1] uses an integrated AHP-PROM ETHEE approach to solve the crop planning problem under t wo conditions: the norma l economy condition and the resistant economy condition. [6] builds a model including mu ltip le crops, ma rket and nonmarket crop uses, and seasonality in production, consumption, and labor supply. [7] uses a mu lti-objective programming approach to examine the possibilit ies of simultaneously achieving environ mental goals such as the reduction of agrochemical and irrigation water use as well as acceptable farm inco mes. [8] uses mu lti-objective programming modeling and solved crop planning problems for optimal production of several seasonal crops in a planning year. [9] develops a model that focused on attaining three objectives simultaneously, namely, profit maximization, emp loyment maximization and erosion min imization. Results of the model indicated that, when compared with the current cropping structure, the implementation of the optimal cropping pattern could increase profit and employ ment and decrease soil erosion significantly. [10] p roposes a mathemat ical model for optimal cropping patterns under water deficits in dry regions. They identified both the total area and the irrigation level allocated to a given selected crop taking into accounts the possible successors and predecessors of this crop. Both annual and seasonal crops were examined in the sa me study. [11,12] present how fu zzy goal programming can be efficiently used for modeling and solving land-use planning problems in agricultural systems for optimal production. [13] develops a fu zzy mu lti-object ive linear programming model for solving the mu lti-lever and mu lti species production of edible fungus circular economy system decision problem in a fu zzy environment. [14] develops Linear programming and fuzzy optimizat ion models for p lanning and management of available land-water-crop system of Mahanadi-Kathajodi delta in eastern India. The models were used to optimize the economic return, production and labor utilization, and to search the related cropping patterns and intensities with specified land, water, fertilizer and labor availability, and water use pattern constraints.

Analytic Hierarchy Process
Analytic Hierarchy Process (AHP) is one of mult i criteria decision-making methods; it was originally developed by Thomas L. Saaty in the mid 1970s. It co mb ines tangible and intangible aspects to obtain the priorities associated with the alternatives of the problem. A HP is a structural framework that allows decision-make rs to model a co mp lex problem in a hierarch ical structure by breaking it down into smaller parts, then calling for a simple co mparison with respect to pairs of judg ments to develop priorit ies within each level of hierarchy. Finally, results are synthesized to obtain overall weights of the alternatives. The input can be obtained from actual measurement such as price, weight etc., or fro m subjective opinion. AHP has been applied in many and diverse areas of decision-support. These applications involve: Selection [15]; allocation [16]; evaluation and benchmarking [17]; ran king and prioritization [18][19][20]. The AHP methodology is explained in the following steps.

Hierarchical Structuring of the Problem
The first step of AHP is to develop the hierarch ical structure representing the problem at hand. A general form of AHP structure is presented in Figure 1. In the simp lest case, the hierarchy has three levels. The first level represents the goal of the decision problem and is analyzed as resulting from the aggregation of evaluation criteria represented by the second level; the last level of the hierarchy involves the alternatives to be evaluated. In mo re complex cases, there may be mo re levels, corresponding to splitting criteria into sub-criteria.

Performi ng Pairwise Comparisons
Once the hierarchy of the problem is defined, the decision-ma ker performs a series of pairwise comparisons within the same hierarchical level and then between sections at a higher level in the hierarchy structure to have n*(n-1)/2 co mparisons if there are n criteria. In co mparisons, a ratio scale of 1-9 is used to compare any two elements. Table 1 shows the measurement scale defined by Saaty [21].
The pairwise comparisons of various criteria are organized into a square matrix A(a ij ) where a ij = w i /w j and i, j =1,2...,n. The d iagonal elements of the matrix are 1. The criterion in the i th row is better than criterion in the j th colu mn if the value of element (i, j) is more than 1; otherwise the criterion in the j th co lu mn is better than that in the i th row. The (j, i) element of the matrix is the reciprocal of the (i, j) element.

Synthesis
Once judg ments have been entered for each part of the model, the rating of alternative is mult iplied by the weights of the sub-criteria and aggregated to get local ratings with respect to each criterion. The local ratings are then mu ltip lied by the weights of the criteria and aggregated to get global ratings. The AHP produces weight values for each alternative based on the judged importance of one alternative over another with respect to a co mmon criterion. The results are then synthesized to obtain rank of the alternatives in relation to the overall goal. Co mparisons made are subjective and AHP tolerates inconsistency through the amount of redundancy in the approach. This consistency measure is called the Consistency Index (CI) wh ich is calculated as shown in equation (1):

Consistency Eval uation
CI= (λ max -n)/ (n-1) (1) Where λ max is the ma ximu m eigen value of the judgment matrix. Th is CI can be co mpared with that of Random Consistency Index, RI. Values of RI are shown in table 2. The ratio derived, CI/ RI, is termed the Consistency Ratio, CR. Saaty suggests the value of CR should be less than 0.1, otherwise, the level of inconsistency is considered unacceptable. In this situation, the evaluation procedure has to be repeated to improve consistency. The detailed AHP process is shown in Figure 2.

Crop Planning in Gaza Strip
The MOA divided agricu ltural h istory in Ga za Strip into four stages according to major political events that occurred in the reg ion [22]. Every political stage has a very clear impact on agriculture. The four stages are: • Period between 1948-1967: In this period, Palestinian agriculture focused on citrus which was the first strategic crop, where production was for local and external ma rket. The problem was the citrus consumes large amounts of water which led to a sever shortage of the aquifer water. Furthermore it consumes nutrients fro m soil.
• Period between 1967-1994: In this period, the Israeli citrus competed against Palestinian citrus, wh ich required raising the quality standards for Palestinian exported citrus; therefore, farmers tended to farm larger areas of vegetables instead of citrus. At the end of 1970s, vegetables became the first strategic crop. Vegetables consume more water than citrus, which aggravated the problem of water shortage.
• Period between 1994-2006: The agricu ltural policies were the sa me as the period fro m 1967-1994. The Palestinian agricultural econo my was adversely affected by Paris Econo mic Agreement, through imposing restrictions on exports and imports. This period is characterized by greater consumption of water through focusing on the cultivation of export crops (strawberry, carnation flo wers, pimento .....) wh ich increase the water shortage problem.
• Period between 2006-until now: In this period, M OA re-read the agricultural policies. The agricultural resistant economy concept was coined, where the attention began to turn to crops that can face the existing problems including water shortage, lack of production inputs and the Figure 3 shows the road map that the researchers followed to reach the research goal. Start ing with goal definit ion, then data collection, in wh ich, criteria and alternatives are identified, ending with AHP model application and verification.

Application
The first step in mu lt i-criteria decision making, regardless of the selected method, is the identification of the alternatives and the relevant criteria. The considered alternatives and criteria were identified through: 1. Literature review.
2. The policies of MOA in Ga za Strip. 3. Interviews with e xperts and agricultural engineers fro m the MOA and some associations such as the society of agricultural relief and the institute of environmental research.

Criteria, Sub-Criteri a and Alternati ves Identi ficati on
For the crop planning problem under study, there are seven main criteria that include: economic, financial, market ing, environmental, technical, political and social criteria. These criteria are split into thirty one sub-criteria. Final criteria were adopted after presenting them to e xperts and engineers from the MOA and some agricultural societies. This was done using a questionnaire, where e xperts were asked to add, delete or combine some criteria, sub-criteria and alternatives.
Nationwide, there are many classifications of crops (alternatives). In this study, crops are classified in such a way that enable e xperts to compare between them according to the considered criteria. Therefo re, crops with similar characteristics are grouped in one alternative. Final types of crops were adopted after presenting them to e xperts using the questionnaire used to define criteria. Experts were asked to give their opinion about the classificat ion of crops, and most of them agreed with the researchers' classification. It is noted that, somewhat, this classification of crops is often used by the MOA. After identifying criteria, sub-criteria and alternatives, a hierarchy of four levels, was constructed as shown in Figure 4.  Since crops are d ivided into groups rather than into individuals, the selected criteria used to compare them cannot be quantitative. This is due to the fact that it is difficult to generalize the performance of each alternative using single score in the comparison matrix for each criteria, as each alternative contains many crops that vary in their performance. To illustrate this, let us consider the water consumption sub-criterion, as an examp le. We can define the amount of water which is consumed by one dunum of tomatoes, onions or cucumbers, but how much water is consumed by one dunum of vegetables is very difficult to quantify. So it is more accurate to use such sub-criteria as a qualitative one to compare the selected crops.

Establishing the Pairwise Comparison Matrix
To conduct the pairwise co mparison, a questionnaire was designed and distributed among nine agricultural experts. In this questionnaire, the e xperts were asked to assign a score fro m one to nine for each pairwise comparison. The questionnaire was designed in a way to help experts to fill it easily. This was made using a simple example given in the cover page of the questionnaire. Since A HP is not a statistical tool; there is no rule that defines the number of e xperts to fill the questionnaire.
After receiv ing the questionnaires fro m e xperts, the CR of each questionnaire was calculated. It was observed that some of the pairwise co mparisons have CR values larger than 0.1, which meant that they are inconsistent. Therefore, e xperts were asked to refill questionnaire again after they were told about the inconsistencies.

Obtaini ng Final Weights
Once the judg ments of each of the nine experts were obtained and tested for the consistency, the average for each comparison was computed to get the final co mparison matrices. The average scores were entered to Expert Choice 11 (E.C 11.5) [23]. The criteria and sub-criteria weights are shown in Table 3. Figure 5 shows the weights of the seven main criteria with respect to the goal. The results indicate that economic criterion is the most important one as it represents 0.33 of the total weight. Environ mental criterion comes second represents 0.15 of the total weight, whereas technical criterion ran ks the lo west among these criteria as it scored 0.07 o f the total weight. Marketing and financial criteria equally contribute to the goal for a weight of 0.13. The fact that economic criterion has the highest weight reflects the tendency of the MOA to cultivate the crops that greatly contribute to the GDP to increase the contribution of the agricultural sector to GDP.  Table 3. The weights indicate that the contribution to GDP criterion is the most important sub-criterion with respect to the goal. The focusing of MOA on GDP makes the agricultural sector the largest sector that contributes to GDP in Ga za Strip.

Criteria Results
Three sub-criteria under the technical criterion have the lowest global weight, these criteria are: t ime to harvest, number of harvest times and intercropping criterion. For financial criteria, the annual return per dunum criterion is the most important one as it has a weight mo re than 0.50 of the total weight. This result reflects the nature of crop planning problem in the study period, which gives profitability the first priority among other. Export market share criterion represents 0.65 of the total weight. This result is consistent with the nature of normal condition which pro motes exporting for many strategic and political advantages.

Fi nal Crop Weight
The rank of crops, according to AHP method, is shown in Figure 6. Export crops have the highest relative weight (0.18). Vegetables and citrus have the second priority, followed by olives then fruits and field crops with the same priority, then palms and medical crops come in the last.

Sensitivity Analysis
The sensitivity analysis of the performance of alternatives with respect to each main criterion is shown in Figure 7. Fro m this graph, it is noted that export crops have the highest performance score with respect to all criteria, except the environmental criterion, it has the lowest performance score with respect to this criterion. While vegetables have the second top performance score with respect to all criteria excluding the environmental criterion, and it has better performance score on environ mental criterion than the export crops. The performance of the other crops swings among the ma in criteria. Fru its appear to have moderate performance on all criteria.
To have mo re insights into the performance of the different alternatives with respect to criteria, the original evaluation matrix 'X8×7' was submitted to co-plot software. Co-plot is used to locate each alternative in a two-dimensional space in which the location of each action is determined by all criteria simu ltaneously. The input for this software is the evaluation matrix (alternatives versus ma in criteria). The co-plot method produces three results: 1. similarity among actions by the composite of all criteria involved. 2. the structure of correlations among the criteria. 3. the mutual relationship between the actions and the criteria [24].  Figure 8 shows the eight crops (alternatives) located in a two-dimensional space, where the alternatives are represented by circles, and criteria by axes. The coefficient of alienation for th is plot is 0.011 which is acceptable and indicates that there is a small variation between variables [25]. Figure 8 shows that the two most dissimilar alternatives are palms and export crops wh ich are the farthest apart. It is clear that palms perfo rm very well with respect to environmental criteria (located in environmental criteria direction), while, export crops perform well with respect to technical and financial criteria. The d ispersion of the arrows in opposite directions indicates the presence of conflicting criteria; for instance, technical and financial criteria versus environmental criterion. The criteria which have similar preferences are oriented in the same d irection. In Figure 8, economic, social, marketing, political and technical criteria have the same preferences.

Conclusions
Crop planning model in this study is constructed as a MCDM prob lem in order to compare eight types of crops using AHP methodology. There are many factors that affect the selection of crops. The study considered seven ma in criteria and thirty one sub criteria, which could help in developing better decisions. The results show that The economic criteria are the most important criteria as they represent 0.33 of the total weight, while the technical criteria are the lowest important criteria as they represent 0.07 of the total weight. The final A HP rank of crops shows the most important crops are export crops, citrus and vegetables, which means that cropping pattern is skewed towards these crops.
Based on the results of this study, some points are recommended for future studies: • Since goal programming (GP) provides better insights to the problem, our immediate p lan is to build a GP model to determine the area of each crop to be cultivated.
• Dealing with crops as groups forced the researchers to approximate data. To have more accurate results, it is recommended for future work to apply this study taking crops as individuals.
• Since each element in the AHP hierarchy must be independent, other MCDM method as Analytic Net work Process (ANP) can be used to deal with the dependency that could be found between some criteria.
This study is performed on the governmental agricu ltural lands in Ga za St rip fro m the govern mental v iew, the agricultural p rivate sector is not included so, the farmers view is not considered. It is recommended to consider the farmers view in other future studies.