Proceeding, National Seminar NKI-ICID, November 2013
Application of Fuzzy Multiple Attribute Decision Making to Determine Technology of Discharge Report in ProvincialAuthoriy Irrigation System Murtiningrum1, Noto2, Nur Rohmad2, Wisnu Wardana3, and Sigit Supadmo Arif3 1
Lecturer, Department of Agricultural Engineering, Universitas Gadjah Mada, Jl. Flora, Bulaksumur, Yogyakarta,
[email protected] 2
Student, Department of Agricultural Engineering, Universitas Gadjah Mada, Jl. Flora, Bulaksumur, Yogyakarta 3
Lecturer, Department of Agricultural Engineering, Universitas Gadjah Mada, Jl. Flora, Bulaksumur, Yogyakarta ABSTRACT Peraturan Pemerintah No 20/2006 tentang Irigasi menyatakan bahwa Daerah Irigasi (DI) dengan luas 1000 ha – 3000 ha dan DI lintas kabupaten/kota menjadi kewenangan pemerintah provinsi. Kebijakan tersebut mengimplikasikan bahwa pemerintah provinsi harus mempunyai cukup petugas untuk melaksanakan tugas operasi irigasi di lapangan. Saat ini operasi irigasi menggunakan blangko sebagai teknologi untuk melaporkan debit sungai maupun saluran. Keterbatasan sumberdaya manusia yang dimiliki Provinsi Daerah Istimewa Yogyakarta menjadikan pengelolaan irigasi tidak dapat mengantisipasi permintaan informasi yang semakin cepat akhir-akhir ini. Penelitian ini bertujuan untuk menentukan bentuk teknologi untuk pelaporan debit. Alternatif yang ditawarkan adalah tetap menggunakan blangko, Short Message Service (SMS), komputer dengan pengumpulan data manual, komputer dengan pengumpulan data lewat internet, dan penggunaan Automatic Water Level Recorder (AWLR) yang datanya langsung terkirim. Kriteria yang digunakan untuk memilih alternatif teknologi adalah ketrampilan petugas, kemudahan digunakan, dukungan fasilitas, dana, dan efisiensi waktu. Metode yang digunakan untuk menentukan teknologi adalah Pengambilan Keputusan Multi Kriteria (MADM) yaitu Simple Additive Weighting (SAW), Weighted Product (WP), Technique for Order Preference by Similary to Ideal Solution (TOPSIS), dan Elimination Et Choix TRaduisant la realitÉ (Electre). Semua metode menunjukkan hasil yang sama bahwa urutan teknologi yang dipilih adalah SMS, blangko, komputer dengan pengiriman data manual, computer dengan pengiriman data internet, and AWLR. Kata kunci : Fuzzy MADM, operasi irigasi, pelaporan debit, daerah irigasi
1. INTRODUCTION Irrigation is an essential input to for the agriculture production system. Therefore the development and management of irrigation plays an important role in Indonesian agriculture to support food self sufficiency. Therefore, a policy on irrigation has been launched in the form of the Government Regulation No. 20/2006 on Irrigation. The Government Regulation No. 20/2006 on Irrigation shared the authority and responsibility of irrigation management and development between the government in main system and farmers in tertiary system. In the main system, the authority and responsibility of irrigation management and development were shared among government levels. The government is responsible for irrigation systems with more than 3000-ha command area and cross-province-boundary irrigation systems. The provincial government is responsible for irrigation system with command area between 1000 ha - 3000 ha and cross-district-boundary irrigation systems. The district
government is responsible for the irrigation systems with less-than-1000-ha command area. Due to regional autonomy in Indonesia, this regulation urged the provincial government to provide field level irrigation managament. The appropriate field level irrigation management required competent field officers, such as sub-system level officers, gate guards, and weir guards. These field officers were recently unavailable because in the centralistic era in the past they were organized as subordinate of the district level government but recently the specific regulation on it was absent. For those reason, the Government of Yogyakarta Special Region (Daerah Istimewa Yogyakarta, DIY) recruited some non-permanent employees as irrigation field officers. The irrigation operation procedure based on Regulation of Ministry of Public Work No. 32/PRT/M/2007 on Guideline on Irrigation Operation and Maintenance used form as information system. The use of form as information system in irrigation operation has many weaknesses. This method involved many paper work and needed bulky paper archives. It also required many staffs to operate the form and transportation of the form from field office to provincial office. To resolve the weaknesses another method of irrigation operation should be employed. This paper aimed to determine the most appropriate irrigation operation method in current condition using the fuzzy multiple attribute decision making (fuzzy MADM). Decision means choice, a choice between two or among many posibilities. Decision making is generally defined as choice amone some alternatives. Decision making is more than a matter of right or wrong, but also a choice of some possible alternatives affected by unique, uncertain, and complex condition. Decision making involved some phases namely inventory of alternatives and selection of alternatives as problem resolution (Kamaluddin, 2003). Every human being always deals with decision making in their life including in irrigation management. The characteristics of irrigation management, which consisted of various aspects and were affected by various factors, resulted in the complexity in making decision. The decision making in irrigation management became complex because of multiple attribute to be fulfilled. The Multiple Criteria Decision Making (MADM) is a decision making method to choos among alternatives based on several criterias. Criterias are usually measures, rules, or standards used in decision making. The MADM can be classified based on types of data used or the number of decision maker. Data type of MADM could be deterministic, stochatic, or fuzzy. In this paper the data to make decision was fuzzy. General definition of MADM (Kusumadewi, et.al, 2006): Let 𝐴 = 𝑎𝑖 𝑖 = 1,2, … , 𝑛 is a set of decision alternatives and 𝐶 = 𝑐𝑗 𝑗 = 1,2, … , 𝑚 is a set of objectives, then it will be decided alternative x0 with highest confidence to relevant objective cj. Decision matrix for every alternative to each atribute X 𝑥11 𝑥21 𝑋= ⋮ 𝑥𝑚1
𝑥12 𝑥22 ⋮ 𝑥𝑚2
… … …
𝑥1𝑛 𝑥2𝑛 ⋮ 𝑥𝑚𝑛
Where xij is the i-th alternative performance rating for the j-th attribute. Weighted value to show relative interest of each atribute W
(1)
𝑊 = 𝑤1
𝑤2
… 𝑤𝑛
(2)
Performance rating X and weighted factor W are the main value represent the absolute preference of the decision maker. The MADM problems ends with rank process to obtain the best alternative based on the available overall preference. Five alternatives were offered in this study. The alternatives were the usage of form, Short Message Service (SMS), computer with manually data submission, computer with internet data submission, and automatic water level recorder (AWLR) with directly data transmission. This become matrix A = (ai). To get the most appropriate decision, fuzzy logic was employed to solve the matrix to obtain the rank of the alternatives. In this paper, method employed to solve matrix A were Simple Additive Weighting (SAW), Weighted Product (WP), Technique for Order Preference by Similary to Ideal Solution (TOPSIS), and Elimination Et Choix TRaduisant la realitÉ (Electre).
2. METHODS 1. Sample This study was conducted from December 2012 to January 2013. Primary data were collected from 17 respondents consisted of 11 operation field staffs, 3 administrative field staffs, 1 lower management, 1 data management, and 1 top management. All of the respondents were responsible to the operation and maintenance of ProvincialAuthority Irrigation Systems. 2. Data Collection Respondents were provided with information of possible alternatives of discharge report as well as related explanation. The alternatives were: A1 = form A2 = short message service (SMS) A3 = computer with manually data submission A4 = computer with internet data transmission A5 = automatic water level recorder (AWLR) Each respondent filled a questioner to express their opinion on the alternatives of discharge report technology provided. The score ranged from 1 (most unfeasible) to 5 (most feasible). The criterias employed to score the alternatives were: C1 = knowledge on the respected technology C2 = ease of use of the operation of the technology C3 = time efficiency in using the technology C4 = availability of supporting technology in the nearby area C5 = investment and operation cost of the technology Respondents were also asked to determine weighting factor of each criteria. 3. Data analysis Simple Additive Weighting Method (SAW) SAW method is started by normalizing the decision matrix X to scale related to all alternative rates based on equation (3)
𝑥 𝑖𝑗
𝑟𝑖𝑗 =
𝑀𝑎𝑥 𝑖 𝑥 𝑖𝑗
𝑖𝑓 𝑗 is an 𝑎𝑡𝑟𝑖𝑏𝑢𝑡𝑒 𝑡𝑜 𝑏𝑒 𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒𝑑
𝑀𝑖𝑛 𝑖 𝑥 𝑖𝑗
𝑖𝑓 𝑗 is an 𝑎𝑡𝑟𝑖𝑏𝑢𝑡𝑒 𝑡𝑜 𝑏𝑒 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒𝑑
𝑥 𝑖𝑗
(3)
Preference of each alternative is determined using equation (4). The alternative with highest preference is the chosen as the decision. 𝑉𝑖 = 𝑛𝑗=1 𝑤𝑗 𝑟𝑖𝑗 (4) Where : rij = normalized rating of alternative Ai on atribute Cj; Vi = value of preference; i = 1, 2, ... m and j = 1, 2, ... n. Weighted Product (WP) WP method is said as modified SAW. WP method uses multiplication to relate along attribute rating. WP method uses equation (5) to normalize attribute rating. Preference is determined using equation (6) and equation (7). 𝑤𝑗 = 𝑆𝑖 = 𝑉𝑖 =
𝑤𝑗 𝑤𝑗 𝑤𝑗 𝑛 𝑗 =1 𝑥𝑖𝑗
𝑤𝑗 𝑛 𝑗 =1 𝑥 𝑖𝑗 𝑤𝑗 𝑛 ∗ 𝑗 =1 𝑥 𝑗
(5) with 𝑖 = 1, 2, … , 𝑚
(6)
with 𝑖 = 1, 2, … , 𝑚
(7)
Where : wj = weighted factor of criteria Cj; Si = preference of i-th alternative; Vi = relative preference of i-th alternative. Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) First step of TOPSIS method is develop normalized matrix R with elements as shown in equation (8). Normalized matrix R is then converted into weighted normalized matrix with elements as shown in equation (9). 𝑟𝑖𝑗 =
𝑥 𝑖𝑗 𝑚 𝑥2 𝑖=1 𝑖𝑗
𝑦𝑖𝑗 = 𝑤𝑖𝑗 𝑟𝑖𝑗 𝑤𝑖𝑡 𝑖 = 1, 2, … , 𝑚 𝑎𝑛𝑑 𝑗 = 1, 2, … 𝑛
(8) (9)
The next step is to develop positive ideal solution matrix A+ and negative ideal solution matrix A- as shown in equation (10). Elements of matrix A+ and matrix A- is determined using equation (11). 𝐴+ = 𝑦1+, 𝑦2+, … , 𝑦𝑛+ 𝐴− = 𝑦1−, 𝑦2−, … , 𝑦𝑛− 𝑚𝑎𝑥𝑖 𝑦𝑖𝑗 𝑖𝑓 𝑗 𝑖𝑠 𝑎𝑡𝑟𝑖𝑏𝑢𝑡𝑒 𝑜𝑓 𝑏𝑒𝑛𝑒𝑓𝑖𝑡 𝑚𝑖𝑛𝑖 𝑦𝑖𝑗 𝑖𝑓 𝑗 𝑖𝑠 𝑎𝑡𝑟𝑖𝑏𝑢𝑡𝑒 𝑜𝑓 𝑐𝑜𝑠𝑡 𝑚𝑖𝑛𝑖 𝑦𝑖𝑗 𝑖𝑓 𝑗 𝑖𝑠 𝑎𝑡𝑟𝑖𝑏𝑢𝑡𝑒 𝑜𝑓 𝑏𝑒𝑛𝑒𝑓𝑖𝑡 𝑦𝑗− = 𝑚𝑎𝑥𝑖 𝑦𝑖𝑗 𝑖𝑓 𝑗 𝑖𝑠 𝑎𝑡𝑟𝑖𝑏𝑢𝑡𝑒 𝑜𝑓 𝑐𝑜𝑠𝑡
(10)
𝑦𝑗+ =
(11)
Distance of each alternative to positive ideal solution matrix D+ and that to negative ideal solution matrix D- is computed using equation (12). 𝐷𝑖+ =
𝑛 𝑗 =1
𝑦𝑖+−𝑦𝑖𝑗
2
𝐷𝑖− =
𝑛 𝑗 =1
𝑦𝑖𝑗 −𝑦𝑖−
2
𝑖 = 1, 2, … , 𝑚 𝑖 = 1, 2, … , 𝑚
Preference of i-th alternative is determined using equation (13). 𝐷𝑖− 𝑉𝑖 = 𝐷 −+𝐷 + 𝑖
(12)
(13)
𝑖
Elimination Et Choix TRaduisant la realitÉ (ELECTRE) The ELECTRE method begins with the development of pairwise comparison of each alternative on each criterion (xij). Normalized matrix R is then developed using equation (8). Matrix of preferences is formed using equation (14). 𝑉𝑖𝑗 = 𝑤𝑗 𝑥𝑖𝑗
(14)
The formation of concordance index and discordance index for every alternative pairwise. For every alternative pairwise Ak and Al (k, l = 1, 2, …, m; and k1l). Decision matix j consists of concordance index set {ckl} and discordance index set {dkl}, which are defined by equation (15) and equation (16). 𝐶𝑘𝑙 = 𝑗 𝑣𝑘𝑙 ≥ 𝑣𝑙𝑗 ; for j = 1, 2, … n 𝐷𝑘𝑙 = 𝑗 𝑣𝑘𝑙 < 𝑣𝑙𝑗 ; for j = 1, 2, … n
(15) (16)
Element of concordance matrix C is defined by equation (17) while equation (18) shows the elements of discordance matrix D. 𝑐𝑘𝑙 = 𝑑𝑘𝑙 =
𝑗 ∈𝑐 𝑘𝑙 𝑤𝑗 𝑚𝑎𝑥 𝑣𝑘𝑗 −𝑣𝑘𝑙
(17) 𝑗 ∈𝐷 𝑘𝑙
𝑚𝑎𝑥 𝑣𝑘𝑗 −𝑣𝑘𝑙 ∀𝑗
(18)
The development of the matrices above uses a threshold c, which is defined by equation (19). 𝑐=
𝑚 𝑘 =1
𝑚 𝑙=1 𝑐 𝑘𝑙
𝑚 𝑚 −1
(19)
Alternative Ak dominate Al if concordance index ckl is more than threshhold c. Similarly for discordance matrix D, the threshold d is defined by equation (20). 𝑑=
𝑚 𝑘 =1
𝑚 𝑙=1 𝑑 𝑘𝑙
𝑚 𝑚 −1
(20)
The next step is to develop matrix F and matrix G with elements as shown in equation (21) for matrix F and equation (22) for matrix G.
1, if 𝑐𝑘𝑙 ≥ 𝑐 0, if 𝑐𝑘𝑙 < 𝑐 1, if 𝑑𝑘𝑙 ≥ 𝑑 𝑔𝑘𝑙 = 0, if 𝑑𝑘𝑙 < 𝑑 𝑓𝑘𝑙 =
(21) (22)
Preference rank of alternatives is then determined by dominant agregate matrix E. Elements of matix E is shown in equation (23). 𝑒𝑘𝑙 = 𝑓𝑘𝑙 × 𝑔𝑘𝑙
(23)
Ekl = 1 indicates that Ak is prefered to Al.
3. RESULT AND DISCUSSION 1. Result of Questioner and Matrix Development Respondents’ were tend to believe that knowledge on respected technology is the most important criteria to choose a technology because the implementation of the technology is always related to the human resource who operate it. However respondents were tend to think that knowledge on respected technology, ease of use, time efficiency, as well as supporting facilities had almost similar weighting factor in choosing technology. The investment and operation cost was consider as least important factor to determine technology because the government will provide fund to apply it. The weighting factors of the criterias according to respondents opinion were then organized into matrix W. W=
4.426
4.311
4.226
4.241
3.530
Respondents also provided with their opinion on the alternative technologies based on each criterias. Table 1 shows the compilation of respondents’ opinion on the alternative technologies proposed. The score ranged from 1 (most unfeasible) to 5 (most feasible). Table 1. Respondent Rating of Alternative Technology on Each Criteria Criterias C1 4.241 4.185 3.537 3.444 3.167
Alternatives C2 C3 C4 C5 A1 4.185 3.111 4.556 3.981 A2 3.556 4.519 4.556 3.926 A3 3.167 3.185 3.074 3.241 A4 3.019 3.852 2.704 2.389 A5 3.000 3.481 2.593 2.296 Notes: A1 = form; A2 = SMS; A3 = computer with manually data submission; A4 = computer with internet data submission; A5 = AWLR C1 = knowledge; C2 = ease of use; C3 = time efficiency in using the technology; C4 = availability of supporting technology; C5 = investment and operation cost
From Table 1, the decision matrix was developed for matrix X.
4.241 4.185 3.537 3.444 3.167
X=
4.185 3.556 3.167 3.019 3.000
3.111 4.519 3.185 3.852 3.481
4.556 4.556 3.074 2.704 2.593
3.981 3.926 3.241 2.389 2.296
Matrix X and matrix W was then solved to obtain priorities of the alternatives using four fuzzy MADM method. 2. SAW Method Normalized matrix R was developed from matrix X with the elements rij were determined by equation (3). 1.000 0.987 0.834 0.812 0.747
R=
1.000 0.850 0.757 0.721 0.717
0.689 1.000 0.705 0.852 0.770
1.000 1.000 0.675 0.593 0.569
1.000 0.986 0.814 0.600 0.577
The preference of each alternative was determined using equation (4) and the result were form (V1) = 19.417; SMS (V2) = 19.978; computer with manually data submission (V3) = 15.667; computer with internet data submission (V4) = 14.941; AWLR (V5) = 14.100. 3. WP Method Respondent rating as shown in Table 1 was also used in this method. Weighting factor was then normalized using equation (5) and resulted in the following matrix W. W=
0.213
0.208
0.204
0.205
0.170
Preference of alternatives (Si) was calculated using equation (6) and relative preference (Vi) was calculated using equation (7). Results of the calculation were S1 = 3.986 V1 = 0.230 S2 = 4.136 V2 = 0.238 S3 = 3.239 V3 = 0.186 S4 = 3.066 V4 = 0.176 S5 = 2.901 V5 = 0.167 4. TOPSIS Method TOPSIS method used respondent rating in Table 1 and it was normalized using equation (8). The normalized matrix was
R=
0.507 0.501 0.423 0.412 0.379
0.548 0.466 0.415 0.395 0.393
0.380 0.551 0.389 0.470 0.425
0.565 0.565 0.381 0.355 0.322
0.548 0.541 0.446 0.329 0.316
The normalized matrix R was then shifted to weighted normalized decision matrix Y with elements determined using equation (9)
2.245 2.216 1.872 1.823 1.676
Y=
2.363 2.008 1.788 1.704 1.694
1.604 2.329 1.642 1.986 1.795
2.396 2.396 1.617 1.422 1.364
1.935 1.908 1.575 1.161 1.116
The next step was to developed positive ideal solution matrix A+ and negative ideal solution matrix A-. Elements of the matrices were determined using equation (10) and equation (11). Matrix A+ described the best possible solution while matrix A- showed the worst possible solution. A+ =
2.245
2.363
2.396
1.935
2.329
A- =
1.676
1.694
1.364
1.116
1.604
The distance from every alternative to ideal matrix was then calculated using equation (12). The best solution matrix is the closest to positive ideal matrix A+ and the farthest from negative ideal matrix A-. Total preference of each alternative was determined using equation (13). The results were D1+ = 0.726 D1- = 1.584 V1 = 0,686 D2+ = 0.358 D2- = 1.615 V2 = 0,819 D3+ = 1.296 D3- = 0.596 V3 = 0,305 D4+ = 1.509 D4- = 0.416 V4 = 0,216 D5+ = 1.672 D5- = 0.191 V5 = 0,103 5. ELECTRE Method The normalized matrix R was then converted to normalized weighted matrix V using equation (14).
V=
2.245 2.216 1.872 1.823 1.676
2.426 2.061 1.836 1.750 1.739
1.680 2.440 1.720 2.080 1.880
2.501 2.501 1.688 1.484 1.423
1.426 2.392 1.75 1.456 1.399
Concordance matrix C and discordance matrix D were then developed using equation (17) and equation (18) to determine their elements.
C=
D=
7.770 4.421 4.241 4.241
16.493 0 0 0
16.493 20.773 4.241 4.241
16.493 20.773 16.493 0
16.493 20.773 16.493 16.493 -
1 0.049
0.480 0
1 1 -
1 1 1
1 1 1
0.393 0.186
0 0
0.693 0.278
0
1 -
The value of threshold c and d as computed by equation (19) and equation (20) were 10.543 and 0.604. Comparing concordance matrix C to threshold c and discordance matrix D to threshold d using equation (21) and equation (22) resulted in dominant concordace matrix F and discordance dominant matrix G.
F=
0 0 0 0
1 0 0 0
1 1 0 0
1 1 1 0
1 1 1 1 -
G=
1 0 0 0
0 0 0 0
1 1 1 0
1 1 1 0
1 1 1 1 -
The multiplication of matrix F and matrix G as shown in equation (22) was resulted in dominant agregate matrix E
E=
0 0 0 0
0 0 0 0
1 1 1 0
1 1 1 0
1 1 1 1 -
From the dominant agregate matrix E, it can be concluded that alternatives A1 (form) and A2 (SMS) were dominant compare to other three alternatives. However, the relationship between A1 and A2 cannot be concluded from the matrix. Therefore, to determine the most dominant alternative priority values for A1 and A2, which calculated from total value of each alternative from matrix V divided by number of alternatives. The priority value of A1 (form) and A2 (SMS) were 2.256 and 2.322 respectively. This means SMS was considered as the most dominant alternative. 5. Preference of Alternatives Based on the four methods above, it could be summarized that all method resulted in identical preference of alternatives. The most preferable alternative for discharge report was SMS. The following ranks of alternatives were form, computer with manually data submission, computer with internet data transmission, and AWLR. The use of SMS to report discharge in irrigation operation was considered as the closest to the ideal technology. The celular technology was relatively cheap and easy to use. The use of SMS for field staffs to report discharge might result in efficient time use for field staffs so that they could do another tasks. This was important because of limited field staffs availability. The use SMS required a server and a computer program established in water resource management office to transferred SMS data into information for further irrigation operation.
4. CONCLUSION The criterias used to determined the most appropriate technology for discharge report were knowledge on the respected technology, ease of use, time efficiency, availability of supporting technology, as well as investment and operation cost. Based on the criterias, SMS had the highest rank of preference. The second to fifth preference were form, computer with manually data submission, computer with internet data transmission, and AWLR, respectively 5. ACKNOWLEDGEMENT Appreciation is addressed to Water Resource Management Office (BPSDA) of the Yogyakarta Special Region for data and staffs as respondents in this study. Gratitute is also delivered to the Faculty of Agricultural Technology, Universitas Gadjah Mada for providing research fund. 6. REFERENCES 1. Kamaludin (2003), Pengambilan Keputusan Manajemen, Pendekatan Teori dan Studi Kasus, Penerbit Dioma, Malang. 2. Marimin, 2004, Teknik dan Aplikasi Pengambilan Keputusan Kriteria Majemuk, Gramedia Widiasarana Indonesia, Jakarta. 3. Kusumadewi, Sri Sri Hartati, Agus Harjoko, and Retantyo Wardoyo and (2006), Fuzzy Multi-Attribute Decision Making (Fuzzy MADM), Penerbit Graha Ilmu, Yogyakarta. 4. Morgan, R dan Cerullo., M. (1984). Decision Making Management Science Techniques and The Corporate Controller, Managerial Planinng, volume 32
