In the manufacturing industry and services, decision makers are often faced with a complex problem. One of the problems is the problem of determining the choice of candidates or just some sort of priority of several candidates. The examples in the manufacturing industry including supplier selection, the choice of purchasing machinery, plant site selection, and others. While the examples in service industries such as logistics vehicle selection, the selection of consultant work, route selection services, and so on.
1: equally important (equal)
3: The more important bit (slightly)
5: strongly more important (strongly)
7: The more important is very strong (very strong)
9: more important in the extreme (extreme) If all pairwise comparisons matrix was collected, we can produce the final priority weights of candidate selection. The first step is any matrix of paired comparisons necessary to find the absolute weight of each item. After that, the final priority weights obtained by multiplying the absolute weight alternative to the weights of criteria and sub-criteria on it. Then, the final priority weights can be used as a reference sequence of interest or candidate election candidate of choice.
In this paper, I will share an excel template that can be used to generate the absolute weight of a matrix of pairwise comparisons. For example, we have a matrix of pairwise comparisons with the five items as follows:
Matriks perbandingan tersebut dapat dihitung dengan template berikut (sila unduh):
AHP
Sebagai tambahan, indeks consistency ratio menunjukkan rasio kekonsistenan matriks perbandingan berpasangan tersebut. Suatu matriks perbandingan berpasangan dianggap tidak konsisten (tidak dibuat dengan baik) apabilai nilai indeks rasio tersebut lebih dari 0.1. Selain itu, sebaiknya kita tidak membandingkan lebih dari tujuh item sekaligus dalam sebuah matriks perbandingan berpasangan. Hal ini dikarenakan nilai consistency ratio tidak cukup menggambarkan tingkat kekonsistenan matriks tersebut ketika jumlah item lebih dari tujuh.
Berikut adalah tampilan dari template tersebut.
Kemudian dengan meng-klik tombol yang tersedia, kita akan mendapatkan consistency ratio maupun bobot masing-masing item seperti tampilan di bawah.
Cara perhitungan yang saya gunakan dalam template excel tersebut adalah menggunakan iterasi rataan geometri (geomean approach). Sebenarnya metode eksak untuk menghitung bobot AHP didasarkan dengan perhitungan nilai Eigen dari matriks. Akan tetapi, perhitungan nilai Eigen akan menghasilkan programa nonlinear yang cukup kompleks (untuk jumlah item lebih dari dua). Sementara itu, berdasarkan teorema, perhitungan iterasi rataan geometri ini akan secara konvergen menuju hasil yang didapatkan dengan metode nilai Eigen. Adapun metode perhitungan consistency ratio di template excel berdasarkan buku Hamdy A Taha.
Problems of decision making can be complex because of the involvement of multiple objectives and criteria. One tool (a tool), suitable for the selection of candidates or sequencing priority is the Analytic Hierarchy Process (AHP) developed by Thomas L. Saaty. Specifically, the AHP is used to permasalahaan selection of suitable candidates or sequencing of priorities which has properties as follows:
- Involve qualitative criteria that are difficult dikuantitatifkan exactly.
- Each criterion can have sub-sub criteria that can be constructed as a hierarchy
- Assessment can be done by one or several decision makers are well
- Candidate selection is specific and limited in number
In the above model, it appears there are several levels / lines that form a hierarchy. Upper level is to represent the goal. Two levels below the level of criteria and sub-criteria. While the lowest level shows the candidates will be considered for selection.
The basic concept is the use of the AHP pairwise comparison matrix (matrix of pairwise comparisons) to generate the relative weights between criteria and alternatives. A criterion will be compared with other criteria in terms of how important to the achievement of goals on it. For example, the specification criteria and cost criteria will be compared in terms of choosing how important transportation fleet. So also for alternatives. Vehicle A, B, and C are compared in pairs (and will be formed matrix) in terms of sub-criteria such as maintenance expenses.
These values are recommended to create a matrix of pairwise comparisons are as follows:
The basic concept is the use of the AHP pairwise comparison matrix (matrix of pairwise comparisons) to generate the relative weights between criteria and alternatives. A criterion will be compared with other criteria in terms of how important to the achievement of goals on it. For example, the specification criteria and cost criteria will be compared in terms of choosing how important transportation fleet. So also for alternatives. Vehicle A, B, and C are compared in pairs (and will be formed matrix) in terms of sub-criteria such as maintenance expenses.
These values are recommended to create a matrix of pairwise comparisons are as follows:
3: The more important bit (slightly)
5: strongly more important (strongly)
7: The more important is very strong (very strong)
9: more important in the extreme (extreme)
In addition to the above values, the values of which can also be used, namely, 2, 4, 6, and 8. These values describe the relationship between interest in odd values mentioned above. Meanwhile, if his interests turned upside down, then we can use numbers reprisokal of the values above. For example, pairwise comparisons between criteria 1 and 3 is 1 / 5, meaning that three criteria strongly more important than criterion 1.
Matrix of pairwise comparisons should be made of each level that have the same hierarchical superiors. For example in the previous hierarchy, we must make a paired comparison matrix for sub-criteria of carrying capacity and sub-criteria of availability of spare parts to the criteria of the specification, the matrix of pairwise comparisons between sub-criteria purchase costs, maintenance costs and the cost of mileage perton against criteria of cost, and so on.
In making matrix pairs, we only need to specify an upper triangular matrix only because of a lower triangular matrix is simply the value of upper triangular reprisokal. In addition, the diagonal values in paired comparison matrix is one (because each item is compared with itself). Thus, if we want to create a matrix of pairwise comparisons with a number of n items, then we only need to make a comparison of a number n (n-1) / 2.
Matrix of pairwise comparisons should be made of each level that have the same hierarchical superiors. For example in the previous hierarchy, we must make a paired comparison matrix for sub-criteria of carrying capacity and sub-criteria of availability of spare parts to the criteria of the specification, the matrix of pairwise comparisons between sub-criteria purchase costs, maintenance costs and the cost of mileage perton against criteria of cost, and so on.
In making matrix pairs, we only need to specify an upper triangular matrix only because of a lower triangular matrix is simply the value of upper triangular reprisokal. In addition, the diagonal values in paired comparison matrix is one (because each item is compared with itself). Thus, if we want to create a matrix of pairwise comparisons with a number of n items, then we only need to make a comparison of a number n (n-1) / 2.
In this paper, I will share an excel template that can be used to generate the absolute weight of a matrix of pairwise comparisons. For example, we have a matrix of pairwise comparisons with the five items as follows:
Matriks perbandingan tersebut dapat dihitung dengan template berikut (sila unduh):
AHP
Sebagai tambahan, indeks consistency ratio menunjukkan rasio kekonsistenan matriks perbandingan berpasangan tersebut. Suatu matriks perbandingan berpasangan dianggap tidak konsisten (tidak dibuat dengan baik) apabilai nilai indeks rasio tersebut lebih dari 0.1. Selain itu, sebaiknya kita tidak membandingkan lebih dari tujuh item sekaligus dalam sebuah matriks perbandingan berpasangan. Hal ini dikarenakan nilai consistency ratio tidak cukup menggambarkan tingkat kekonsistenan matriks tersebut ketika jumlah item lebih dari tujuh.
Berikut adalah tampilan dari template tersebut.
Kemudian dengan meng-klik tombol yang tersedia, kita akan mendapatkan consistency ratio maupun bobot masing-masing item seperti tampilan di bawah.
Cara perhitungan yang saya gunakan dalam template excel tersebut adalah menggunakan iterasi rataan geometri (geomean approach). Sebenarnya metode eksak untuk menghitung bobot AHP didasarkan dengan perhitungan nilai Eigen dari matriks. Akan tetapi, perhitungan nilai Eigen akan menghasilkan programa nonlinear yang cukup kompleks (untuk jumlah item lebih dari dua). Sementara itu, berdasarkan teorema, perhitungan iterasi rataan geometri ini akan secara konvergen menuju hasil yang didapatkan dengan metode nilai Eigen. Adapun metode perhitungan consistency ratio di template excel berdasarkan buku Hamdy A Taha.
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