View of The Weighted Product Method and the Multi-Objective Optimization on the Basis of Ratio Analysis Method for Determining the Best Customer

(1)

https://doi.org/10.33558/piksel.v11i1.6325

PIKSEL status is accredited by the Directorate General of Research Strengthening and

The Weighted Product Method and the Multi-Objective Optimization on the Basis of Ratio Analysis Method

for Determining the Best Customer

Mugiarso ^1,*, Rasim ¹

* Corespondence Author: e-mail: [email protected]

1 Informatics; Universitas Bhayangkara Jakarta Raya;

Jl. Raya Perjuangan No. 81 Margamulya, Bekasi Utara, Bekasi, Indonesia; telp. (021)88955882; e-mail:

[email protected], [email protected] Submitted : 08/02/2023 Revised : 22/02/2023 Accepted : 08/03/2023 Published : 31/03/2023

Abstract

The objective of this study is to compare the effectiveness of the Weighted Product (WP) and Multi- Objective Optimization on the Basis of Ratio Analysis (MOORA) methods in determining the best customers.

Onesnet, the case study service provider, provides discounts and rewards to eligible customers to support this objective. The problem addressed in this study is how to determine the most relevant method for selecting eligible customers for bonuses. To achieve this, sensitivity testing was conducted by altering the weights of each criterion in both methods and observing the percentage changes of the results. The Weighted Product method multiplies the rating of each connected attribute, which is raised to the appropriate attribute weight, to decide. Data for this study was collected through interviews and observations at Onesnet and processed using the Rank Order Centroid (ROC) method for weighting, and the WP and MOORA methods for evaluating and selecting a decision. The WP and MOORA methods produced different total values and rankings, but the modeling with either method can be used equally for selecting the best customers. While there was a 60% similarity in data between the two methods, the WP method is recommended over MOORA, as it prioritizes customers with high loyalty criteria as the best customers.

Keywords: best customer, ROC, WP, MOORA

1. Introduction

Building a positive relationship with customers is a crucial factor in developing business on a larger scale. One way to maintain a good relationship with customers is through giving rewards or recognition to loyal customers, such as discounts or other incentives (Siregar et al., 2021). Retaining customer loyalty is a benefit for companies in selling their products. Therefore, companies strive to maintain customer loyalty so that they continue to choose the products they have used before (Oktaviana & Himawan, 2015).

(2)

Onesnet is an internet service provider located at Perumahan Mustika Karangsatria Blok EA 18 Nomor 3A. Currently, Onesnet has not provided any reward or discount to its customers. Therefore, the aim of this study is to compare methods in determining the best customers, and Onesnet strives to provide discounts or rewards to support this goal after conducting observations and interviews. The decision-making method used is Weighted Product (WP) and Multi-Objective Optimization on The Basis of Ratio Analysis (MOORA) method to determine which customers are eligible for discounts or rewards. The most effective method will be chosen to make decisions based on the highest percentage value. Two methods will be evaluated, and the best one will be selected (Herlambang et al., 2022). The MOORA method has the calculation with the minimum and very simple calculation (Revi et al., 2018). The process of determining the appropriate criteria and determining eligible customers for bonuses in the assessment of the best customers. The decision-making process determines the best customers, which is supported by the weighted product method to obtain accurate results (Oktaviana & Himawan, 2015). By using the Rank Order Centroid weighting method, it is possible to make decisions for the provision of rewards (Setiawan et al., 2022).

2. Research Method

To ensure the success of the research, various data collection techniques were employed, including interviewing relevant parties to obtain information through questioning and directly observing issues at Onesnet. The author selected these techniques to gather data directly from the field and address emerging issues, while also utilizing reference materials such as books, scientific journals, and other relevant media to the writing topic.

To generate accurate decisions, the Rank Order Centroid (ROC) method requires determining the ideal weight. In a study, the ROC method was utilized to determine the weights of the criteria. Mathematical equations were employed to measure the importance level of each criterion in the research, as explained in references (Damanik & Utomo, 2020; Setiawan et al., 2022).

Cr1≥Cr2≥Cr3≥⋯Cn (1)

(3)

The weight values are then calculated using the following equation:

(2)

To utilize the Weighted Product method (Agustian & Mujilahwati, 2020;

Oktaviana & Himawan, 2015), several calculation steps must be followed. First, the cost attribute for each alternative is transformed into the positive power of the assigned attribute weight. Next, the sum of the products of all attributes is calculated for each available alternative. The V value for each alternative is then divided by the total value of all alternatives. Using this method, the given equation can be used to determine the best alternative ranking that aligns with the preferences.

(3) where S represents the preference of the alternative, which is analogized as vector S, X represents the value of the criteria, W represents the weight of the criteria, i represents the alternative, j represents the criteria, and n represents the number of criteria.

The Weighted Product method is considered an efficient method to support decision-making as it requires a relatively short time to calculate the relative preferences of each alternative, as explained below:

(4)

The criteria can be grouped into two categories, namely benefit criteria with positive values, and cost criteria with negative values. Where V Represents the preference vector for a particular alternative, x Represents the value of each criterion, w Represents the weight of each criterion, i Represents the alternative, j Represents the criterion, and n Represents the total number of criteria evaluated.

MOORA is a system with multiple objectives, where there are two or more attributes that are conflicting. This method helps to avoid subjectivity in the evaluation process by converting it into weighted criteria with several

(4)

decision-making attributes. This is done in a simpler and more easily understandable way (Rosita et al., 2020).

The steps to calculate the MOORA method include collecting data, as explained in (Pranata et al., 2021; Revi et al., 2018) which include determining the decision matrix values using the following equation:

The next step is to normalize the matrix using the following MOORA normalization:

For j = 1, 2, …. m. Determine the weighted Normalized Matrix with the following equation:

The next step is to multiply the normalized matrix by the predetermined weights and then calculate the values of the benefit, cost, and index criteria.

Therefore, the best option will have the highest YI value, while the worst option will have the lowest YI value.

3. Results and Analysis

To determine the best customers using the WP and MOORA methods and compare them, data collection is required first due to the large number of customers. This data collection includes determining the criteria and their weights, so that calculations can be made to produce the best alternatives.

3.1. Determination of Criteria, Weight, and Alternatives

Based on this basis, the author developed the Rank Order Centroid (ROC) method for determining weights to assist decision making in determining the best customers eligible for internet subscription payment discounts and

(5)

(6)

(7)

(8)

(5)

bandwidth allocation. Several criteria used in determining the best customers include Internet Package (C1), Payment Activity (C2), Loyalty (C3), and Usage (C4). In determining the weights, the Rank Order Centroid (ROC) method is applied, as shown in Equation 2 (Khalida et al., 2021). From this formula, the following weights can be obtained.

When adding up the weights, there will be a result of 1. Therefore, Table 1 below shows the weight values for each criterion.

Table 1. Weight of Each Criterion.

Criteria Nature Weight

C1: Internet Package Benefit 0.521

C2: Payment Activity Pembayaran Cost 0.271

C3: Loyalty Benefit 0.146

C4: Usage Cost 0.063

Source: Research Result (2023)

Here is Table 2 which shows the alternative values associated with each criterion.

Table 2. Alternative Values for Each Criterion.

Alternative Criteria

C1 C2 C3 C4

A1 Moderate Good Moderate Moderate

A2 Good Good Sufficient Excellent

A3 Sufficient Good Moderate Moderate

A4 Good Excellent Moderate Moderate

A5 Moderate Sufficient Good Good

A6 Moderate Good Good Excellent

A7 Excellent Excellent Good Good

(6)

C1 C2 C3 C4

A8 Moderate Good Sufficient Good

A9 Excellent Sufficient Sufficient Sufficient

A10 Moderate Sufficient Excellent Moderate

Tables 3, 4, 5, and 6 below establish the weights for each criterion (w𝑗), where C1 and C3 are benefit criteria, while C2 and C4 are cost criteria.

Table 3. Internet Package Criteria

Criteria Customer Criteria Description Value

Internet Package

<100.000 Sufficient 1

100.000-200.000 Moderate 2

200.001-300.000 Good 3

>300.000 Excellent 4

Table 4. Payment Activity Criteria

Payment Activity

Date 1 Excellent 4

Date l 2 Good 3

Date 3 Moderate 2

≥ Date 4 Sufficient 1

Table 5. Loyality Criteria

Loyalty

<1 Tahun Sufficient 1

1-2 Tahun Moderate 2

3-4 Tahun Good 3

>4 Tahun Excellent 4

Table 6. Usage Criteria

Usage

< 10 GB Excellent 4

10- 25,99 GB Good 3

26-50 GB Moderate 2

> 50 GB Sufficient 1

(7)

Converting raw data values into categorical data is what is referred to as Alternative Compatibility Rating (Pradana et al., 2019). If Table 2 still uses linguistic values for alternatives, Tables 3, 4, 5, and 6 are used to provide weights on a simple scale. This is intended to produce Table 7, which shows the ranking of suitability from the weighting results of the previous alternative values.

Table 7. Suitability Rating

C1 C2 C3 C4

A1 2 3 2 2

A2 3 3 1 4

A3 1 3 2 2

A4 3 4 2 2

A5 2 1 3 3

A6 2 3 3 4

A7 4 4 3 3

A8 2 3 1 3

A9 4 1 1 1

A10 2 1 4 2

3.2. Calculation of Weighted Product

To use the Weighted Product method in calculations, the first step is to make corrections to the criterion weight values. This is done by ensuring that the total weight of the criteria is one (∑ 𝑤𝑗 = 1). Previously, calculations were made using the Rank Order Centroid (ROC) method with the following results:

W1 = (1+1/2+1/3+1/4)/4=0.521 W2 = (0+1/2+1/3+1/4)/4=0.271 W3 = (0+0+1/3+1/4)/4=0.146 W4 = (0+0+0+1/4)/4=0.063

Where W1 and W3 are benefits criteria, while W2 and W4 are cost criteria.

After that, the next step is to calculate the value of Vector S. To do this, formula equation (3) is used by taking into account the value of alternative and corrected criterion weights, and multiplying them. Thus, the calculation of Vector S for customers A1:

A1 = (2^0.521)(3^-0.271)(2^0.146)(2^-0.063)

(8)

= 1.435 x 0.743 x1.106 x 0.958

= 1.129

The results for A2, A3, A4, A5, A6, A7, A8, A9, and A10 were obtained using the same method, with values of 1.207, 0.787, 1.290, 1.572, 1.147, 1.550, 0.995, 1.224, and 1.682, respectively.

The next step is to calculate the vector value Vi. After obtaining the vector value, we need to sum all the vectors S to calculate the vector V, which can be calculated as follows:

Vi= 1.129 + 1.207 + 0.787+ 1.290 + 1.572 + 1.147 + 1.550 + 0.995 + 1.224 + 1.682 Vi=12.582

The results of the vector calculation for the customer alternatives A1 is:

The results for A2, A3, A4, A5, A6, A7, A8, A9, and A10 were obtained using the same method, with values of A2, A3, A4, A5, A6, A7, A8, A9, and A10 were 0.096, 0.063, 0.096, 0.126, 0.092, 0.124, 0.080, 0.098, and 0.134, respectively.

3.3. MOORA Calculation

The MOORA method utilized in this case study employs the criteria and weights specified in Table 1. The steps involved in the MOORA calculation are as follows (Budihartanti, 2020):

The initial step is to create the Decision Matrix (X) based on the compatibility values between alternatives and criteria, as shown in the following example:

(9)

The next step is to determine the normalization value for each criterion for each alternative and convert it into a normalization matrix. The following is a detailed calculation result for the Package Internet criterion for C1.1

The results for C1.2, C1.3, C1.4, C1.5, C1.6, C1.7, C1.8, C1.9 and C1.10 were obtained using the same method, with values of C1.2, C1.3, C1.4, C1.5, C1.6, C1.7, C1.8, C1.9 and C1.10 were 0.356, 0.119, 0.356, 0.237, 0.237, 0.475, 0.237, 0.475, and 0.237, respectively.

By using the same normalization method for the Internet Package (C1), Payment Activity (C2), Loyalty (C3), and Usage (C4) criteria, the normalization calculation was obtained, resulting in a normalization matrix, as follows:

After obtaining the normalized values, the next step is to calculate the optimization value, which refers to the weight of each criterion. The optimization value is calculated for each given alternative. The value is the sum of the multiplication between the weight of the criterion and the normalized value. The following are the results of the optimization value calculation for each Internet Package criterion:

(10)

Using the same method to calculate the optimization value for Internet Package Criteria (C1), Payment Activity (C2), Loyalty (C3), and Usage (C4), the optimization value is obtained as follows:

Table 8. Calculation Results of Yi Value Normalization * Weight

Optimization Result

Criteria C1 C2 C3 C4

Type benefit cost benefit cost

Weight 0.52 0.27 0.15 0.06

A1 0.124 -0.091 0.038 -0.014 0.057

A2 0.185 -0.091 0.019 -0.029 0.085

A3 0.062 -0.091 0.038 -0.014 -0.005

A4 0.185 -0.121 0.038 -0.014 0.088

A5 0.124 -0.030 0.057 -0.022 0.129

A6 0.124 -0.091 0.057 -0.029 0.062

A7 0.247 -0.121 0.057 -0.022 0.162

A8 0.124 -0.091 0.019 -0.022 0.030

A9 0.247 -0.030 0.019 -0.007 0.229

A10 0.124 -0.030 0.077 -0.014 0.156

The next step is to determine the ranking. From the optimization value calculation results, the results can be sorted from the largest to the smallest, where the largest optimization value is the best alternative. The order of the optimization value results can be seen in Table 9.

(11)

PIKSEL status is accredited by the Directorate General of Research Strengthening and Table 9. Ranking Results of MOORA Method

No. Alternative YI Rangking

1 A1 0.057 8

2 A2 0.085 6

3 A3 -0.005 10

4 A4 0.088 5

5 A5 0.129 4

6 A6 0.062 7

7 A7 0.162 2

8 A8 0.030 9

9 A9 0.229 1

10 A10 0.156 3

3.4. Comparison between WP and MOORA

The study revealed differences between the WP and MOORA methods, as the results obtained were not the same. Alternative A10 ranked first using the WP method, representing a customer with high or very good loyalty, a medium internet package, sufficient payment activity, and medium internet usage.

However, alternative A9 ranked first using the MOORA method, representing a customer with a high or very good monthly rate, sufficient loyalty, payment activity, and internet usage. Table 10 presents a comparison between the results obtained by the WP and MOORA methods.

Table 10. Comparison of SAW and MOORA Results Alternative WP Rangking MOORA Rangking

A1 0.090 8 0.057 8

A2 0.096 6 0.085 6

A3 0.063 10 -0.005 10

A4 0.097 5 0.088 5

A5 0.126 2 0.129 4

A6 0.092 7 0.062 7

A7 0.124 3 0.162 2

A8 0.080 9 0.03 9

A9 0.098 4 0.229 1

A10 0.134 1 0.156 3

(12)

Based on the results in Table 10, there are 6 data that have the same value out of a total of 10 data, or in other words, there is a 60% similarity in the data of the two methods. The alternatives that occupy the same position are A1, A2, A3, A4, A6, and A8. The WP and MOORA methods produce different total values and rankings. Therefore, both WP and MOORA models can be used for selecting the best customer.

4. Conclusion

Based on the results and discussion of the study, it can be concluded that there are differences in the results of selecting the best customer using the WP and MOORA methods. The results obtained in selecting alternative A10 ranked first using the WP method, which is the customer with the highest loyalty, while alternative A9 ranked first using the MOORA method, which is the customer with the highest internet package. There are similarities in rankings for some alternatives based on the calculation results. Using the WP method instead of MOORA is recommended because customers with high loyalty are selected as the best customer.

Acknowledgements

The authors would like to express their gratitude to the reviewers who have helped to improve the manuscript.

Author Contributions

Mugiarso proposed the topic; Mugiarso and Rasim conceived the implementation; Mugiarso and Rasim analysed the result.

Conflicts of Interest

The author declare no conflict of interest.

References

Agustian, M. A., & Mujilahwati, S. (2020). Pelanggan Terbaik pada Toko Fanny Cosmetic. Seminar Nasional Illmu Terapan (STINER), 4(1), 1–8.

(13)

https://ojs.widyakartika.ac.id/index.php/sniter/article/view/189/179

Budihartanti, C. (2020). Komparasi Metode SAW dan Moora pada SMAN 15 Jakarta dalam Pemilihan Siswa Berprestasi. PROSISKO: Jurnal Pengembangan Riset dan Observasi Sistem Komputer, 7(2), 124–131.

https://doi.org/10.30656/prosisko.v7i2.2474

Damanik, S., & Utomo, D. P. (2020). Implementasi Metode ROC (Rank Order Centroid) dan Waspas Dalam Sistem Pendukung Keputusan Pemilihan Kerjasama Vendor. KOMIK (Konferensi Nasional Teknologi Informasi dan Komputer), 4, 242–248. https://doi.org/10.30865/komik.v4i1.2690

Herlambang, I. M., Abdi, P. K., & Filda, F. (2022). Analisis Perbandingan Metode SAW dengan WP dalam Mendukung Keputusan Calon Karyawan Hyfresh Blitar. JATI (Jurnal Mahasiswa Teknik Informatika), 6(2), 920–925.

https://doi.org/10.36040/jati.v6i2.5788

Khalida, R., Bangun, B., Mesran, M., & Oktari, N. (2021). Penerapan Metode ROC dan Weighted Aggregated Sum Product Assesment (WASPAS) dalam Penerimaan Asisten Perkebunan. Jurnal Media Informatika Budidarma, 5(3), 937. https://doi.org/10.30865/mib.v5i3.3092

Oktaviana, R., & Himawan, H. (2015). Pelanggan Terbaik pada Tb . Bangun Jaya. Universitas Dian Nuswantoro, 1–9.

Pradana, M. G., Kusrini, K., & Luthfi, E. T. (2019). Perbandingan Metode Weighted Product dan Simple Additive Weighting dalam Seleksi Pengurus Forum Asisten (Studi Kasus Universitas AMIKOM Yogyakarta). Informasi

Interaktif, 4(2). http://e-

journal.janabadra.ac.id/index.php/informasiinteraktif/article/view/868

Pranata, A. S., Rosiani, U. D., & Mentari, M. (2021). Sistem Pengambil Keputusan Rekomendasi Lokasi Wisata Malang Raya dengan Metode MOORA. POSITIF : Jurnal Sistem dan Teknologi Informasi, 7(1), 10–16.

https://doi.org/10.31961/positif.v7i1.1091

Revi, A., Parlina, I., & Wardani, S. (2018). Analisis Perhitungan Metode MOORA dalam Pemilihan Supplier Bahan Bangunan di Toko Megah Gracindo Jaya. InfoTekJar (Jurnal Nasional Informatika Dan Teknologi Jaringan), 3(1), 95–99. https://doi.org/10.30743/infotekjar.v3i1.524

(14)

Rosita, I., Gunawan, & Apriani, D. (2020). Penerapan Metode Moora pada Sistem Pendukung Keputusan Pemilihan Media Promosi Sekolah (Studi Kasus: SMK Airlangga Balikpapan). Metik Jurnal, 4(2), 55–61.

https://doi.org/10.47002/metik.v4i2.191

Setiawan, F., Lusiyanti, L., & Setiawan, D. (2022). Implementasi Metode Weighted Product dan Pembobotan Rank Order Centroid Dalam Pemberian Penghargaan Predikat Kader Terbaik. JURNAL MEDIA

INFORMATIKA BUDIDARMA, 6(1), 215.

https://doi.org/10.30865/mib.v6i1.3375

Siregar, V. M. M., Sonang, S., & Damanik, E. (2021). Sistem Pendukung Keputusan Penentuan Pelanggan Terbaik Menggunakan Metode Weighted Product. Jurnal Teknik Informasi dan Komputer (Tekinkom), 4(2), 239.

https://doi.org/10.37600/tekinkom.v4i2.392