Selesaikan kasus berikut ini menggunakan metode TOPSIS

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Soal: Menggunakan Metode TOPSIS

Sebuah PTS di Kota Medan, akan memberikan beasiswa kepada 5 orang mahasiswanya. Adapun syarat pemberian beasiswa tersebut, yaitu harus memenuhi ketentuan berikut ini :

Syarat :
C1: Semester Aktif Perkuliahan (Attribut Keuntungan)
C2: IPK  (Attribut Keuntungan)
C3: Penghasilan Orang Tua  (Attribut Biaya)
C4: Aktif Berorganisasi (Attribut Keuntungan)

Untuk bobot W=[4,4,5,3]

Adapun mahasiswa yang menjadi alternatif dalam pemberian beasiswa yaitu :

No	Nama	C1	C2	C3	C4
1	Joko	VI	3.7	1.850.000	Aktif
2	Widodo	VI	3.5	1.500.000	Aktif
3	Simamora	IV	3.8	1.350.000	Tidak Aktif
4	Susilawati	II	3.9	1.650.000	Tidak Aktif
5	Dian	II	3.6	2.300.000	Aktif
6	Roma	IV	3.3	2.250.000	Aktif
7	Hendro	VIII	3.4	1.950.000	Aktif

Untuk pembobotan yang digunakan bisa mengacu pada bobot di bawah ini :

C1:Semester Aktif Perkuliahan
Semester II --> 1
Semester IV --> 2
Semester VI -->  3
Semester VIII -->  4

C2: IPK
IPK  3.00 - 3.249 --> 1
IPK  3.25 - 3.499 --> 2
IPK  3.50 - 3.749 --> 3
IPK  3.75 - 3.999 --> 4
IPK  4.00 --> 5
 
C3: Penghasilan Orang Tua 
1.000.000 --> 1
1.400.000 --> 2
1.800.000 --> 3
2.200.000 --> 4
2.600.000 --> 5

C4: Aktif Berorganisasi
Aktif --> 2
Tidak Aktif --> 1

Penyelesaian:
- X₁ =   =   = 6,633

R₁₁ =                                              R₅₁ =

R₂₁ =                                           R₆₁ =

R₃₁ =                                           R₇₁ =

R₄₁ =

- X₂ =   =   = 8,185

R₁₂ =                                              R₅₂ =            

R₂₂ =                                           R₆₂ =  

R₃₂ =                                           R₇₂ =

R₄₂ =

- X₃ =   =   = 7,681

R₁₃ =                                              R₅₃ =

R₂₃ =                                           R₆₃ =

R₃₃ =                                           R₇₃ =                                             

R₄₃ =

- X₄ =   =   = 4,690

R₁₄ =                                              R₅₄ =  

R₂₄ =                                           R₆₄ =  

R₃₄ =                                           R₇₄ =                                              

R₄₄ =

 

0,4522             0,3665             0,3905             0,4264

0,4522             0,3665             0,2603             0,4264

0,3015             0,4886             0,1301             0,2132

R =        0,1507                        0,4886             0,2603             0,2132

0,1507             0,3665             0,5207             0,4264

0,3015             0,2443             0,5207             0,4264

0,6030             0,2443             0,3905             0,4264

y_ij = w_ij r_ij    w = [4,4,5,3]

y₁₁ = 4(0,4522) = 1,8090                     y₁₃ = 5(0,3905) = 1,9528        

y₂₁ = 4(0,4522) = 1,8090                     y₂₃ = 5(0,2603) = 1,3018

y₃₁ = 4(0,3015) = 1,2060                     y₃₃ = 5(0,1301) = 0,6509

y₄₁ = 4(0,1507) = 0,6030                     y₄₃ = 5(0,2603) = 1,3018

y₅₁ = 4(0,1507) = 0,6030                     y₅₃ = 5(0,5207) = 2,6037

y₆₁ = 4(0,3015) = 1,2060                     y₆₃ = 5(0,5207) = 2,6037

y₇₁ = 4(0,6030) = 2,4120                     y₇₃ = 5(0,3905) = 1,9528

           

y₁₂ = 4(0,3665) = 1,4660                     y₁₄ = 3(0,4264) = 1,2792        

y₂₂ = 4(0,3665) = 1,4660                     y₂₄ = 3(0,4264) = 1,2792

y₃₂ = 4(0,4886) = 1,9547                     y₃₄ = 3(0,2132) = 0,6396

y₄₂ = 4(0,4886) = 1,9547                     y₄₄ = 3(0,2132) = 0,6396

y₅₂ = 4(0,3665) = 1,4660                     y₅₄ = 3(0,4264) = 1,2792

y₆₂ = 4(0,2443) = 0,9773                     y₆₄ = 3(0,4264) = 1,2792

y₇₂ = 4(0,2443) = 0,9773                     y₇₄ = 3(0,4264) = 1,2792

 

1,8090             1,4660             1,9528             1,2792

1,8090             1,4660             1,3018             1,2792

1,2060             1,9547             0,6509             0,6396

R =        0,6030                        1,9547             1,3018             0,6396

0,6030             1,4660             2,6037             1,2792

1,2060             0,9773             2,6037             1,2792

2,4120             0,9773             1,9528             1,2792

A⁺                                                                                                                 A^-

Y₁⁺ = max 2,4120                                 Y₁^- = min 0,6030

Y₂⁺ = max 1,9547                                 Y₂^- = min 0,9773

Y₃⁺ = min 0,6509                                  Y₃^- = max 2,6037

Y₄⁺ = max 1,2792                                 Y₄^- = min 0,6396

D₁^-=

                       

D₁^-=

=  = 1,5893

D₂^-=

=  = 1,9486

D₃^-=

=  = 2,2654

D₄^-=

=  = 1,6279

D₅^-=

=  = 0,8049

D₆^-=

=  = 0,8790

D₇^-=

= = 2,0262

D₁⁺ =

                       

D₁⁺=

=  = 1,5157

D₂⁺=

=  = 1,0130

D₃⁺=

=  = 1,3651

D₄⁺=

=  = 2,0262

D₅⁺=

=  = 2,7064

D₆⁺=

=  = 2,4946

D₇⁺=

=  = 1,6279

V_i =

V₁ =

V₂ =

V₃ =

V₄ =

V₅ =

V₆ =

V₇ =

            Berarti yang berhak mendapatkan Beasiswa yaitu V_1, V_2, V_3, V_4, dan  V₇