This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
and Graphical Solutionand Graphical Solution Scoring ModelsScoring Models Analytic Hierarchy Process (AHP)Analytic Hierarchy Process (AHP) Establishing Priorities Using AHPEstablishing Priorities Using AHP Using AHP to Develop an Overall Priority Using AHP to Develop an Overall Priority
Analytic Hierarchy ProcessAnalytic Hierarchy Process
Analytic Hierarchy Process (AHP)Analytic Hierarchy Process (AHP), Adalah , Adalah prosedur yang dirancang untuk meng-angkakan prosedur yang dirancang untuk meng-angkakan pertimbangan manajerial kepentingan relatif dari pertimbangan manajerial kepentingan relatif dari setiap kriteria-kriteria yang memiliki arah dan setiap kriteria-kriteria yang memiliki arah dan kegunaan berbeda dalam pengambilan kegunaan berbeda dalam pengambilan keputusan. keputusan.
Tetapkan nilai tingkat kepentingan relatif Tetapkan nilai tingkat kepentingan relatif antara setiap pasangan dari alternatif keputusan. antara setiap pasangan dari alternatif keputusan. The matrix lists the alternatives horizontally and The matrix lists the alternatives horizontally and vertically and has the numerical ratings comparing vertically and has the numerical ratings comparing the horizontal (first) alternative with the vertical the horizontal (first) alternative with the vertical (second) alternative.(second) alternative.
nilai tingkat adalah sbb:nilai tingkat adalah sbb:
. . . continued. . . continued
------- For each criterion, perform steps 2 through 5 -------------- For each criterion, perform steps 2 through 5 -------------- For each criterion, perform steps 2 through 5 -------------- For each criterion, perform steps 2 through 5 -------
Compared to the secondCompared to the secondalternative, the first alternative isalternative, the first alternative is: : Numerical Numerical ratingrating
Dipilih ekstrem Dipilih ekstrem 99
Dipilih secara sangat kuat 7Dipilih secara sangat kuat 7
Nilai tingkat angka antara yaitu 8, 6, 4, 2 Nilai tingkat angka antara yaitu 8, 6, 4, 2 dapat di ikutkan. A reciprocal rating (i.e. 1/9, dapat di ikutkan. A reciprocal rating (i.e. 1/9, 1/8, etc.) is assigned when the second 1/8, etc.) is assigned when the second alternative is preferred to the first. The value of alternative is preferred to the first. The value of 1 is always assigned when comparing an 1 is always assigned when comparing an alternative with itself. alternative with itself.
Analytic Hierarchy ProcessAnalytic Hierarchy Process
Step 3: Develop a Normalized MatrixStep 3: Develop a Normalized Matrix
bagilah setiap angka di dalam sebuah bagilah setiap angka di dalam sebuah kolom dari matrix perbandingan pairwise kolom dari matrix perbandingan pairwise (berpasangan) dengan jumlah kolomnya.(berpasangan) dengan jumlah kolomnya.
Step 4: Develop the Priority VectorStep 4: Develop the Priority Vector
Rata ratakan setiap baris dalam Rata ratakan setiap baris dalam normalized matrix. Hal ini membentuk vector normalized matrix. Hal ini membentuk vector prioritas dari pilihan alternatif dikaitkan prioritas dari pilihan alternatif dikaitkan dengan kriteria tertentu, jumlah vector adalah dengan kriteria tertentu, jumlah vector adalah 1. 1.
Analytic Hierarchy ProcessAnalytic Hierarchy Process
Step 5: Calculate a Consistency RatioStep 5: Calculate a Consistency RatioKonsistensi masukan subyektif dalam Konsistensi masukan subyektif dalam
pairwise matrix dapat diukur dengan pairwise matrix dapat diukur dengan menghitung ratio konsistensi. A consistency menghitung ratio konsistensi. A consistency ratio of less than .1 is good. Untuk rasio yang ratio of less than .1 is good. Untuk rasio yang lebih dari 0.1 maka harus di evaluasi kembali.lebih dari 0.1 maka harus di evaluasi kembali.
Step 6: Develop a Priority MatrixStep 6: Develop a Priority MatrixSetelah steps 2 through 5 telah Setelah steps 2 through 5 telah
dikerjakan untuk semua kriteria, hasil dari step dikerjakan untuk semua kriteria, hasil dari step 4 dijumlahkan dalam sebuah matrix priority 4 dijumlahkan dalam sebuah matrix priority dengan mendaftarkan pilihan keputusan dengan mendaftarkan pilihan keputusan (alternatif keputusan) secara horisontal dan (alternatif keputusan) secara horisontal dan kriteria secara vertikal. Masukan dalam kolom kriteria secara vertikal. Masukan dalam kolom adalah vektor vektor prioritas dari setiap adalah vektor vektor prioritas dari setiap kriteria. kriteria.
Analytic Hierarchy ProcessAnalytic Hierarchy Process
Step 7: Develop a Criteria Pairwise Development Step 7: Develop a Criteria Pairwise Development Matrix Matrix
Sama dengan bagian awal saja. This is Sama dengan bagian awal saja. This is done in the same manner as that used to done in the same manner as that used to construct alternative pairwise comparison construct alternative pairwise comparison matrices by using subjective ratings (step 2). matrices by using subjective ratings (step 2). Similarly, normalize the matrix (step 3) and Similarly, normalize the matrix (step 3) and develop a criteria priority vector (step 4). develop a criteria priority vector (step 4).
Step 8: Develop an Overall Priority VectorStep 8: Develop an Overall Priority Vector
Multiply the criteria priority vector (from Multiply the criteria priority vector (from step 7) by the priority matrix (from step 6).step 7) by the priority matrix (from step 6).
Determining the Consistency RatioDetermining the Consistency Ratio
Step 1:Step 1: For each row of the pairwise comparison For each row of the pairwise comparison
matrix, determine a weighted sum by summing matrix, determine a weighted sum by summing the multiples of the entries by the priority of its the multiples of the entries by the priority of its corresponding (column) alternative.corresponding (column) alternative.
Step 2:Step 2: For each row, divide its weighted sum by For each row, divide its weighted sum by
the priority of its corresponding (row) alternative.the priority of its corresponding (row) alternative. Step 3:Step 3:
Determine the average, Determine the average, maxmax, of the results , of the results of step 2.of step 2.
Determining the Consistency RatioDetermining the Consistency Ratio
Step 4:Step 4:
Compute the consistency index, CI, of the Compute the consistency index, CI, of the nn alternatives by: CI = (alternatives by: CI = (maxmax - - nn)/()/(nn - 1). - 1).
Step 5:Step 5:
Determine the random index, RI, as follows:Determine the random index, RI, as follows:
Number of RandomNumber of Random Number of RandomNumber of Random Alternative (Alternative (nn)) Index (RI)Index (RI) Alternative (Alternative (nn)) Index (RI)Index (RI)
Designer Gill Glass must decide which of Designer Gill Glass must decide which of three manufacturers will develop his three manufacturers will develop his "signature" toothbrushes. Three factors seem "signature" toothbrushes. Three factors seem important to Gill: (1) his costs; (2) reliability of important to Gill: (1) his costs; (2) reliability of the product; and, (3) delivery time of the the product; and, (3) delivery time of the orders.orders.
The three manufacturers are Cornell The three manufacturers are Cornell Industries, Brush Pik, and Picobuy. Cornell Industries, Brush Pik, and Picobuy. Cornell Industries will sell toothbrushes to Gill Glass for Industries will sell toothbrushes to Gill Glass for $100 per gross, Brush Pik for $80 per gross, and $100 per gross, Brush Pik for $80 per gross, and Picobuy for $144 per gross. Gill has decided Picobuy for $144 per gross. Gill has decided that in terms of price, Brush Pik is moderately that in terms of price, Brush Pik is moderately preferred to Cornell and very strongly preferred preferred to Cornell and very strongly preferred to Picobuy. In turn Cornell is strongly to very to Picobuy. In turn Cornell is strongly to very strongly preferred to Picobuy.strongly preferred to Picobuy.
Hierarchy for the Manufacturer Selection Hierarchy for the Manufacturer Selection ProblemProblem
Select the Best Toothbrush ManufacturerSelect the Best Toothbrush ManufacturerSelect the Best Toothbrush ManufacturerSelect the Best Toothbrush Manufacturer
CostCost CostCost ReliabilityReliabilityReliabilityReliability Delivery TimeDelivery TimeDelivery TimeDelivery Time
Forming the Pairwise Comparison Matrix For CostForming the Pairwise Comparison Matrix For Cost
•Since Brush Pik is moderately preferred to Since Brush Pik is moderately preferred to Cornell, Cornell's entry in the Brush Pik row is Cornell, Cornell's entry in the Brush Pik row is 3 and Brush Pik's entry in the Cornell row is 3 and Brush Pik's entry in the Cornell row is 1/3.1/3.
•Since Brush Pik is very strongly preferred to Since Brush Pik is very strongly preferred to Picobuy, Picobuy's entry in the Brush Pik row Picobuy, Picobuy's entry in the Brush Pik row is 7 and Brush Pik's entry in the Picobuy row is is 7 and Brush Pik's entry in the Picobuy row is 1/7.1/7.
•Since Cornell is strongly to very strongly Since Cornell is strongly to very strongly preferred to Picobuy, Picobuy's entry in the preferred to Picobuy, Picobuy's entry in the Cornell row is 6 and Cornell's entry in the Cornell row is 6 and Cornell's entry in the Picobuy row is 1/6.Picobuy row is 1/6.
Normalized Matrix for CostNormalized Matrix for Cost
Bagi setiap masukan dalam pairwise Bagi setiap masukan dalam pairwise comparison matrix dengan jumlah kolom yang comparison matrix dengan jumlah kolom yang terkait. For example, for Cornell the column sum terkait. For example, for Cornell the column sum = 1 + 3 + 1/6 = 25/6. This gives:= 1 + 3 + 1/6 = 25/6. This gives:
The priority vector is determined by The priority vector is determined by averaging the row entries in the normalized averaging the row entries in the normalized matrix. Converting to decimals we get:matrix. Converting to decimals we get:
Gill Glass has determined that for Gill Glass has determined that for reliabilityreliability, Cornell is very strongly preferable to , Cornell is very strongly preferable to Brush Pik and equally preferable to Picobuy. Brush Pik and equally preferable to Picobuy. Also, Picobuy is strongly preferable to Brush Pik.Also, Picobuy is strongly preferable to Brush Pik.
Normalized Matrix for ReliabilityNormalized Matrix for Reliability
Divide each entry in the pairwise Divide each entry in the pairwise comparison matrix by its corresponding column comparison matrix by its corresponding column sum. For example, for Cornell the column sum = sum. For example, for Cornell the column sum = 1 + 1/7 + 1/2 = 23/14. This gives:1 + 1/7 + 1/2 = 23/14. This gives:
Priority Vector For ReliabilityPriority Vector For Reliability
The priority vector is determined by The priority vector is determined by averaging the row entries in the normalized matrix. averaging the row entries in the normalized matrix. Converting to decimals we get: Converting to decimals we get:
Gill Glass’ responses to reliability could be Gill Glass’ responses to reliability could be checked for consistency in the same manner as checked for consistency in the same manner as was cost.was cost.
Gill Glass has determined that for Gill Glass has determined that for delivery delivery timetime, Cornell is equally preferable to Picobuy. , Cornell is equally preferable to Picobuy. Both Cornell and Picobuy are very strongly to Both Cornell and Picobuy are very strongly to extremely preferable to Brush Pik.extremely preferable to Brush Pik.
Normalized Matrix for Delivery TimeNormalized Matrix for Delivery Time
Divide each entry in the pairwise Divide each entry in the pairwise comparison matrix by its corresponding column comparison matrix by its corresponding column sum. sum.
Priority Vector For Delivery TimePriority Vector For Delivery Time
The priority vector is determined by The priority vector is determined by averaging the row entries in the normalized averaging the row entries in the normalized matrix. Converting to decimals we get:matrix. Converting to decimals we get:
Gill Glass’ responses to delivery time could Gill Glass’ responses to delivery time could be checked for consistency in the same manner be checked for consistency in the same manner as was cost.as was cost.
The accounting department has The accounting department has determined that in terms of determined that in terms of criteriacriteria, cost is , cost is extremely preferable to delivery time and very extremely preferable to delivery time and very strongly preferable to reliability, and that strongly preferable to reliability, and that reliability is very strongly preferable to delivery reliability is very strongly preferable to delivery time.time.
Normalized Matrix for CriteriaNormalized Matrix for Criteria
Divide each entry in the pairwise Divide each entry in the pairwise comparison matrix by its corresponding column comparison matrix by its corresponding column sum.sum.
Priority Vector For CriteriaPriority Vector For Criteria
The priority vector is determined by The priority vector is determined by averaging the row entries in the normalized averaging the row entries in the normalized matrix. Converting to decimals we get:matrix. Converting to decimals we get:
The overall priorities are determined by The overall priorities are determined by multiplying the priority vector of the criteria by multiplying the priority vector of the criteria by the priorities for each decision alternative for the priorities for each decision alternative for each objective.each objective.