A Combined Approach of Analytic Hierarchy Process and Zero-One Goal Programming to Select CSR Program

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A Combined Approach of Analytic Hierarchy Process and Zero-One Goal Programming to Select CSR Program

Asrin Lubis¹, Herman Mawengkang²

1Department of Mathematics, University Negeri Medan, Medan, Indonesia

2 Departement of Mathematics, University of Sumatera Utara, Medan, Indonesia

Abstract. In Indonesia, Corporate Social Responsibility (CSR) is an inherent responsibility of every industrial company to create and sustain a harmonious and balanced relationship with local community. The company is expected to proactively take part in supporting the basic needs of society and simultaneously developing healthy environment. The industrial company considered in this paper is crude palm oil (CPO) industry, located in Riau province of Indonesia. A set of activities program of CSR was formulated to meet the expectations of the society toward sustainable CPO industry. We use Analytic Hierarchy Process (AHP) to find the priority of the program. The zero-one goal programming is then used to choose which program to be implemented based on the priority result. The optimal result of the combined method show that the alternatives selected is in accordance with the priority result of AHP.

Keywords: Analytic hierarchy process, Goal programming, Integer Programming, CSR, Crude palm oil, Sustainable industry.

INTRODUCTION

Corporate Social Responsibility (CSR) is a new corporate behaviour and management philosophy. This new paradigm comes up as a shift from business oriented activities to include society and environment consideration.

Surprisingly, CSR is getting more popular and has been adopted by industry companies worldwide [1], [2]. While there are variations of the CSR definition, a commonly used definition is “firm actions designed to improve social or environmental conditions” [3], [4], [5]. The long term benefit of CSR is to increase companies market size in the form of new customers [1], [6], [7], [8], [35]..

In Indonesia CSR program is still on debate whether or not CSR is mandatory, and if there are applicable sanctions for corporations that are negligent in including CSR into their business activities. Nevertheless, there are many industry companies put this program into practices in their activities. In this paper we focus on CSR program to be implemented by a crude palm oil (CPO) milling industry located in Riau Province, Indonesia. We choose this kind of industry due to the fact that crude palm oil industry has become the main sector for Indonesian economic development.

The other positive part of this industry is that it could generate employment opportunities. Unfortunately, it creates serious environmental problem in the production process [9]. Therefore, it is expected that through CSR program the CPO company could reduce the environmental impact while supporting the value of life of the society surrounding.

Beside of that CSR could increase positively and significantly influences institutional investors to invest more in socially responsible companies [10].

The management of the palm oil industry has decided to put forward a set of CSR program to be implemented. It is necessary to structure systematically the CSR program in such a way that it could give an optimal result for the company. One analytical approach often suggested to systemize an unstructured problem to become a simple hierarchy form is the Analytic Hierarchy Process (AHP), introduced firstly by [11]. The present paper utilizes the AHP approach for the CSR program in order to prioritize alternatives from a set of multiple criteria. The priority result from several alternatives obtained from AHP need to be processed to get the overall best decision. A well known optimization technique to tackle multi-criteria decision problem contained several priority objectives is Goal Programming. The

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problem to select CSR program contains both quantitative and qualitative criteria, it would be appropriate to use a combined of AHP-GP approach to get the optimal result.

A number of studies have been addressed in the literature to discuss about implementation of the combined AHP and GP approach. [12] proposed the use of AHP-GP approach to solve the facility location-allocation problem. In his paper, the AHP was used to evaluate the alternative locations with respect to several criteria. The decision of optimal location was obtained by using GP. The same author [13] used the integrated approach for quality control systems.

The implementation in selecting software architecture was proposed by [14], in designing a sustainable supply chain [15], in selecting maintenance strategies [16], in selecting risk-based maintenance policy [17], in selecting interdependent information system project [18], in land use optimization at watershed scale [19], in constructing an efficient university course planning [20], in selecting construction contracts [21]. An interesting literature review on integrated of AHP and other mathematical programming approach can be found in [22].

In Indonesia the main objective of CSR is to contribute some set of firms’ resources, such as, money, to improve social welfare for the community. Therefore our research addresses avenue of choosing the right CSR program to be implemented for social benefit, simultaneously to achieve sustainable palm oil industry. We use Analytic Hierarchy Process (AHP) to get the weight of alternative. The zero-one lexicographic GP is then used to select the appropriate CSR program. We show that the final result is in accordance with the need of the community.

ANALYTIC HIERARCHY PROCESS (AHP)

AHP proposed by [23] and [24] is a widely used technique for multi-criteria decision making to determine the relative importance of a set of alternatives. The AHP which combines two fundamental approaches in problem solving, i.e., deductive approach and inductive approach, is designed to tackle situations in which subjective judgments belongs to the important part of the decision process. The basic idea of the AHP is to breakdown the unstructured decision problem into a hierarchical level of decision. Then it is necessary to assign numerical values to the defined subjective judgment based on the relative importance of each level. The assigning process is based upon pairwise comparison of subjective judgment of a level. These numerical values are then used to complete a matrix. The eigenvalue for each element is then utilized to assess the contribution of that element to the overall component. This is to determine which element have the highest priority. The general methodology of AHP can be found in [11].

Assume that there are n elements, then we require (n(n-1))/2 pairwise judgments to complete the matrix, where each judgment reflects the perception of the ratio of the relative contributions of elements i and j to the overall component be assessed, so a_ij =(w w_i/ _j), subject to the following constraints; a_ij 0,a_ij =1, and a_ij =(1 /a_ji) . [11] argues that the technique can only be effectively used where the elements are homogeneous, that is within the same order of magnitude, hence [11] proposed the ratios are in the range from 1 to 9. If two alternatives are of equal importance, a value of 1 is given in the comparison, while a 9 indicates the absolute importance of one alternative over the other [24].

In group decision making, several axiomatic conditions such as separability, unanimity, homogeneity and power conditions have to be satisfied in order to aggregate individual judgements [23], [25] proved that the geometric mean is consistent and upholds the above mentioned axiomatic conditions. Following the notation of [26] for p individuals, the geometric mean of composite judgement of their amn values (amn values are quantitative measures of each respondent's judgement concerning the relative degree of importance of alternative m over alternative n), is defined as:

^*

1 p

k p

mn k mn

a a

= = (1) Using geometrically averaged a_mn^* values, a set of numerical weights w1, w2,…, wi can be computed to represent the relative degree of importance among the decision alternatives and a set of numerical weights v1, …, v2,…, vp to represent the relative importance of p individual's (or group's) judgements. Both of these numerical weights sum to one.

One problem that can occur, especially since the judgements are subjective, is that values assigned are inconsistent.

For example, one would expect to observe transitivity. Consistency can be measured as the deviation of the principal eigenvalue of the matrix from the order of the matrix.

The consistency index, CI, is calculated as follows:

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𝐶𝐼 = (𝜆

^𝑚𝑎𝑥

− 𝑛)

(𝑛 − 1)

⁄

(2) where



_max is the maximum principal eigenvalue of the judgments matrix. The nearer CI is to zero the more consistent the judgements. The CI can be compared with the consistency index of a random matrix (RI). The ratio (CI/RI) is known as the consistency ratio (CR). [11] suggests CR should be less than 0.1.

AHP APPROACH FOR CSR PROGRAM

This research was conducted at several villages in Riau Province of Indonesia. There are several palm oil industries in the area. As for AHP, the decision problem is structured in a hierarchy manner. The hierarchy structure of AHP is formulated as shown in Figure 1

FIGURE 1. Hierarchy structure for the CSR Program [27]

From Fig. 1, the top level of decision is to choose CSR program in the area in a way to achieve a sustainable palm oil industry. The next level is the criteria needed in order to fulfill the goal. There are three criteria to be satisfied, i.e., developing social aspects, developing community economic aspects, and maintaining clean surrounding environment.

There are eight alternatives to meet these criteria.

The following notations are used for alternatives.

A1 Education aid

A2 Fund for starting business A3 Healthcare aid

A4 Skill training

Developing CSR Program to Achieve

Sustainable Palm Oil Industry

Developing Social Aspect

Developing Community Economic Aspect

Maintaining Clean Environment

Aspects

Educati on Aid

Fund Starting Business

Healthca re aid

Skill Training

Partnership with Farmers

Repairing Facilities

Worship Place

Processing Liquid Waste

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A5 Partnership with farmers A6 Repairing facilities A7 Worship place

A8 Processing liquid waste

THE RESULTING MATRICS

We distributed the questionnaire regarding to those criteria and alternatives as mentioned in Fig. 1. The respondents were people from the villages where this research was conducted and after some explanation it was considered that they fully understood for each item. The objective from these questionnaire is to get a pairwise comparison matrix.

The eigenvector method is applied to each of the matrices along with geometric mean (Eq. 1) and then in turn using Expert Choice version 11 software [28]. The result of this application is the relative priority of each alternative decision based on each criterion. The computed result is shown in Table 1.

TABLE 1. Result of pair-wise comparison of alternatives regarding to each criterion

Decision Alternatives Developing Social Aspects

Developing Community Economics Aspects

₈ 0.125 0.113 0.458

Total 1.000 1.000 1.000

Inconsistency Ratio 0.060 0.100 0.060

At the bottom row of Table1 1 we can find the Inconsistency Ratio values for each criterion obtained from Eq. (2).

All of these values are



0.10.

Next we calculate the relative priority for each criterion using the same method as for Table1. The result of the calculation can be found in Table 2.

TABLE 2. Resulting Priority Values for Each Criterian Criterian Decision Priority

Developing Social Aspects 0.360

Developing Community Economics

Aspects 0.358

Maintaining Clean Environment Aspects 0.282

Total 1.000

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As seen in Table 2 that, in terms of criteria, the first priority is Developing Social Aspects (0.360). In order to get the overall prioritization of the decision alternative matrix obtained from Table 1 is pre-multiplied with matrix obtained from Table 2. The result is given in Table 3.

0.214

Total 1.000

This is the overall rankings (in terms of weights) for the eight alternatives

GOAL PROGRAMMING

Nowadays it is quite often in the realm of decision making one encounters with problems which contain more than one objectives. These objectives in particular are independent and may have conflicts to one and another. In terms of mathematical programming, this type of problem belongs to an approach which is called multi-objective decision making (MODM). Practically, goal programming (GP) is the most popular among all MODM techniques [29]. An interesting characteristic of GP is that a decision maker is allowed to consider the environmental, organizational, and managerial situation into the model via goal levels and priorities. Due to its ability GP is widely used in the real world problems. A survey of its applications and algorithms can be found in [30], [31], [32].

The objective of GP is to measure the minimization of unwanted deviations from goals. Considering the way of objective functions and priorities are determined GP is divided into two variants [16], [33], [34]. First, weighted goal programming is an approach where weights (or priorities) are assigned to the goals that measure their relative importance and then finds a solution which attempts to minimize the total weighted sum of the deviations from all goals. The second approach is called preemptive GP (or Lexicographic GP) in which it is necessary to rank the goals in order of importance.

In this research, we use the second approach, lexicographic GP. The rational reason for choosing this approach is that the GP is used after the overall priority of alternatives have been obtained from AHP method. In the lexicographic approach, the decision maker must define the priority level, P_j , of his or her goals. It starts from the most important goal, P₁ , to the least important, P_m . Therefore in the objective function, these different priority levels are arranged in decreasing order. The solution process starts firstly to solve the highest priority and the constraints involved, and then the next priority up till the least priority. It should be noted that the solution process would achieve the overall results as long as the achievement of the lower priorities do not degrade the achievement of their higher priorities.

Mathematically, the lexicographic GP are expressed as follows. As the model is intended for solving the CSR program, the alternatives (A_j) would be treated as decision variables.

The objective is to minimize deviation from the desired goals which is consistent with the AHP ranking of the alternatives.

1

P ( )

m

i i i

i

Minimize z d⁺ d⁻

=



+ (3) Subject to

399

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Goal constraints:

1

, 1,...,

n

ij j i i i

j

a A d⁺ d⁻ b for i m

=

− + = =



(4) System constraints :

1

, 1,...,

n

ij j i

j

a A b for i m m k

=

= = + +



(5) with

d

_i⁺

, d

_i⁻

, A

_j

 0, for i = 1,..., ; m j = 1,... n

(6)

It can be seen that there are m goals, k system constraints and n decision variables. Where di+

is a deviational variable of overachievement of goal i, and di- is a deviational variable of underachievement of goal i.

The CSR problem is to select the alternative of the CSR program. It is then necessary to insert logical constraint in the model.

1

n j j

A

=



= (7) A_j =0or1, j (8) Now the model can be called zero-one GP problem.

THE M

ATHEMATICAL MODEL FOR THE CSR PROGRAM

The model formulated for CSR program is a combination from the result of AHP as shown in Section 4 and zero- one GP approach. The constraints for selecting the CSR program are formulated as follows. As mentioned before (in Section 1) that most of CSR program in Indonesia is to spend money. The management of the palm oil company has allocated funds to be spent for each criteria. The constraints (9) to (11) are then to present the spending formulation for each alternative considering fund allocations of each criteria. The data for these constraints are from Table 4.

TABLE 4. Characteristic data on alternative of CSR Program (in Million Rp.)

Criterion Alternatives

₈

Developing Social Aspects 700 650 750 600 500 700 650 750 700

Developing Community

Economic Aspects 400 700 600 500 600 500 450 600 600

+ − + =

(11)

400

(7)

It should be noted that the results obtained from AHP are originally from questionnaire data which was distributed among the people surrounding. Therefore, the management of the palm oil industry wanted that the selection of alternatives should be in accordance with the expectation of the community. In order to meet the management’s demand the next constraint (Eq. 12) is then expressed to assure that the alternative with the highest priorities would be selected. The data for this constraint are from Table 3.

¹ ² ³ ⁴ ⁵ ⁶

7 8 4 4

0.103 0.081 0.133 0.048 0.132 0.189

0.10 0.214 1

A A A A A A

A A d

⁺

d

⁻

+ + + + + +

+ + + + + +

+ − + =

(15)

There are only three alternatives of CSR program to be implemented by the palm oil company. Eq. (16) serving as logical constraint is formulated in order to force the result to choose only three variables (alternatives).

A¹+A²+A³+A⁴+A⁵+A⁶+A⁷+A⁸ =3 (16) Expressions (17) and (18) present the nature of variables used.

A_i =0or1,i=1, 2,...,8 (17)

d d

_j⁺

,

⁻_j

 0, j = 1, 2,...,7

(18) The objective function is to minimize the overall deviations which appear in each goal constraints. The management of the palm oil company has decided that the first priority is to minimize the over target spending in each criterion.

Avoiding the underachievement in selecting the community expectations would be the second priority. The third priority is to minimize the under fulfillment of each criterion.

1( 1 2 3) 2( 4) 3(0.360 5 0.358 6 0.282 7)

Minimize z=P d⁺+d⁺+d⁺ +P d⁻ +P d⁻+ d⁻+ d⁻ (19)

RESULT OF THE CSR PROGRAM COMBINED MODEL

We use software LINDO Release 6.1 Demo Version to solve the model. Table 5 shows the optimal result for the value of decision variables.

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TABLE 5. The values of decision variables

Decision variables Meaning

A3 (alternative 3) = 1.0 Healthcare aid

A6 (alternative 6) = 1.0 Repairing facilities

A8 (alternative 8) = 1.0 Processing liquid waste

A1 (alternative 1) = 0.0 Education aid

A2 (alternative 2) = 0.0 Fund for starting business

A4 (alternative 4) = 0.0 Skill training

A5 (alternative 5) = 0.0 Partnership with farmers

A7 (alternative 7) = 0.0 Worship place

As seen in Table 5, alternatives to provide fund in healthcare aid, repairing facilities, and processing liquid waste have been selected for implementation of CSR program. The result obtained from the combined method is in accordance with the result of AHP.

The resulting usage and left over of fund for each criterion is given in Table 6. From Table 6, we can observe that the allocation of fund provided by the management of palm oil company would be more than enough to be spent for all three alternatives selected. The main focus for CSR program of the palm oil company, and other industrial companies in Indonesia, is to provide fund for the welfare of the community. The optimal result obtained has made it clear that the allocation of money from the company is enough to support the social community in terms of supporting their health, repairing roads and other facilities, and to conserve healthy environment.

TABLE 6. Fund usage and left over (in Million Rp.)

Criterion Fund available Usage Left over (

d

_j⁺ ) Developing Social

Aspects

2500 2100 400

Developing Community Economics Aspects

2000 1700 300

Maintaining Clean Environment Aspects

3000 2400 600

The fulfillment of each criterion to meet the aim of the company as a sustainable industry based on individual weight of alternative is not fully met. As can be seen from Table 7 there are slight underacheivements in each criterion.

TABLE 7. Fulfillment of each criterion

Criterion Goal Optimal result Underachievement

Developing Social Aspects

0.592 0.558 0.034

Developing Community

Economics Aspects 0.550 0.432 0.118

Maintaining Clean Environment Aspects

0.72

0.643

0.077

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This paper presents a combined AHP-GP approach to select the appropriate of activities of a CSR program offered by a palm oil company to meet the basic needs of the surrounding community. The AHP method is first used to structure the CSR planning problem systematically. Hierarchically, the structure starts with the main goal to be achieved, then the criteria needed, and lastly the alternatives or activities which are necessary to fulfill the main goal. Later these activities would be implemented by the company for the society. Through pair-wise comparison from the AHP method we obtain the weight priority of each alternative regarding to the criteria.

The results obtained from AHP method are then used in the GP model, as there are multiple criteria and priorities.

After solving the GP model, we obtain the selected alternatives or activities which can be implemented by the management due to the allocated fund is more than enough.

Through AHP method, we can only get the order of priority of alternatives. However, the CSR program can be said successful if some funds from the company is very much involved. Using the combined AHP-GP method we would be able to find out whether the allocation funds from the company is suitable to implement the alternatives selected.

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