SARAN - KESIMPULAN DAN SARAN - OPTIMASI WAKTU PRODUKSI DAN ANALISIS KEPERIODIKAN PADA GRAF SIST

BAB V KESIMPULAN DAN SARAN

B. SARAN

], merupakan nilai

eigen maksimum dari matriks , dan input bersesuaian dengan matriks , serta diketahui hingga merupakan unit pemrosesan yang memulai pemrosesan tanpa bergantung pada pemrosesan lainnya maka barisan input paling lambat agar barisan keadaan sistem periodik adalah [ dengan .

B. SARAN

Adapun saran-saran yang dapat penulis berikan bagi penelitian selanjutnya adalah sebagai berikut.

1. Sistem produksi yang dibahas dalam penelitian ini dibatasi pada sistem produksi pada graf ber-loop dengan satu input satu output. Penelitian selanjutnya dapat membahas tentang sistem produksi pada graf ber-loop dengan multi input multi output.

2. Penelitian ini dilakukan dengan menggunakan proses produksi kue secara manual pada beberapa unit pemrosesan sebagai contoh nyata. Hal ini menyebabkan perhitungan waktu transfer menjadi kurang akurat. Penelitian selanjutnya dapat menggunakan contoh pada suatu produksi dengan semua unit pemrosesan berupa mesin.

3. Pemodelan graf sistem produksi ber-loop pada penelitian ini dibuat dengan memodifikasi graf melalui penambahan unit pemrosesan.

Penelitian selanjutnya dapat membuat pemodelan tanpa menambahkan unit pemrosesan bayangan.

135

DAFTAR PUSTAKA

Arifin, Mustofa dan Mustofa. 2012. Aplikasi Sistem Persamaan Linear Aljabar

Max-Plus dalam Mengoptimalisasi Waktu Produksi Bakpia Pathok Jaya “25” Daerah Istimewa Yogyakarta. Skripsi diajukan kepada Fakultas

Matematika dan Ilmu Pengetahuan Alam Universitas Negeri Yogyakarta. Berlianty, Arifin. (2002). Teknik-Teknik Optimasi Heuristik. ISBN : 987-979-756-

625-8.

De Schutter, B. 1996. Max-Algebraic System Theory for Discrete Event Systems. PhD Thesis. Leuven: Department of Electrical Engineering, Katholieke Universiteit.

De Schutter, B and T. Van den Boom. 2008. Max-plus algebra and max-plus linear discrete event system : An Introduction, “Proceedings of the 9th

International Workshop on Discrete Event System”. Goteborg, Sweden.

Farlow, Kasie G. (2009). Max-Plus Algebra. Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University.

Rudhito, Andy. 2016. Aljabar Max-Plus dan Penerapannya. Yogyakarta : Program Studi Pendidikan Matematika, FKIP-Universitas Sanata Dharma, Yogyakarta.

Subiono and Nur Shofianah. 2009. Using Max-Plus Algebra in The Flow Shop

Scheduling. The Journal of Technology and Science, Vol. 20, No. 3.

Subiono. 2015. Aljabar Min-Max Plus dan Terapannya. Surabaya : Jurusan Matematika, FMIPA-ITS, Surabaya.

136

137

LAMPIRAN

1. Hasil Perhitungan MATLAB untuk Contoh 1

2. Hasil Perhitungan MATLAB untuk Contoh 2

3. Hasil Perhitungan MATLAB untuk Contoh 3

4. Foto Penelitian

138 1. Nilai Eigen dan Vektor Eigen Max-Plus Matriks Pada Contoh 1

Matriks yang dihitung A = [10 -inf 10 -inf -inf -inf;-inf 8 -inf -inf -inf -inf;22 -inf 22 -inf -inf -inf;22 19 22 15 -inf -inf;34 31 34 -inf 10 -inf;47 44 47 30 23 12]

HASIL PERHITUNGAN : =================== Matriks A =

10 -Inf 10 -Inf -Inf -Inf -Inf 8 -Inf -Inf -Inf -Inf 22 -Inf 22 -Inf -Inf -Inf 22 19 22 15 -Inf -Inf 34 31 34 -Inf 10 -Inf 47 44 47 30 23 12 Matriks A TIDAK IRREDUSIBEL

NILAI EIGEN max-plus maksimum matriks A = 22

VEKTOR EIGEN max-plus yang bersesuaian = -12 -Inf 0 0 12 25

139

INPUT-OUTPUT SLMI(A, B, C, x0)

Masukkan matriks A(nxn) = [10 -inf 10 -inf -inf -inf;-inf 8 -inf -inf -inf -inf;22 -inf 22 -inf -inf -inf;22 19 22 15 -inf -inf;34 31 34 -inf 10 -inf;47 44 47 30 23 12]

Masukkan matriks B(nx1) = [1;2;13;13;25;38]

Masukkan matriks C(1xn) = [-inf -inf -inf -inf -inf 12]

Masukkan kondisi awal x0(nx1) = [1;2;-inf;-inf;-inf;-inf]

Masukkan barisan input sp kej ke-k u(kx1) = [0;13;20;35;48;60]

HASIL PERHITUNGAN : =================== Matriks A =

10 -Inf 10 -Inf -Inf -Inf -Inf 8 -Inf -Inf -Inf -Inf 22 -Inf 22 -Inf -Inf -Inf 22 19 22 15 -Inf -Inf 34 31 34 -Inf 10 -Inf 47 44 47 30 23 12 Matriks B = 1 2 13 13 25 38

140

Matriks C =

-Inf -Inf -Inf -Inf -Inf 12 Kondisi awal x0 = 1 2 -Inf -Inf -Inf -Inf Barisan input u = 0 13 20 35 48 60

Barisan vektor keadaan sistem x(k) utk k = 0,1, 2, ... : 1 11 33 55 77 99 121 2 10 18 26 37 50 62 -Inf 23 45 67 89 111 133 -Inf 23 45 67 89 111 133 -Inf 35 57 79 101 123 145 -Inf 48 70 92 114 136 158 Barisan output sistem y(k) utk k = 1, 2, ... : 60 82 104 126 148 170

141

---

Masukkan matriks A = [10 -inf 10 -inf -inf -inf;-inf 8 -inf -inf -inf -inf;22 -inf 22 -inf -inf -inf;22 19 22 15 -inf -inf;34 31 34 -inf 10 -inf;47 44 47 30 23 12]

Masukkan matriks B = [1;2;13;13;25;38]

Masukkan matriks C = [-inf -inf -inf -inf -inf 12]

Masukkan kondisi awal x0 = [1;2;-inf;-inf;-inf;-inf]

Masukkan barisan output (dalam vektor kolom) y = [60;82;104;126;148;170]

HASIL PERHITUNGAN : =================== Matriks A =

10 -Inf 10 -Inf -Inf -Inf -Inf 8 -Inf -Inf -Inf -Inf 22 -Inf 22 -Inf -Inf -Inf 22 19 22 15 -Inf -Inf 34 31 34 -Inf 10 -Inf 47 44 47 30 23 12 Matriks B = 1 2 13 13 25 38

142

Matriks C =

-Inf -Inf -Inf -Inf -Inf 12 Kondisi awal x0 = 1 2 -Inf -Inf -Inf -Inf Barisan output y = 60 82 104 126 148 170

Barisan input paling lambat u_topi = 10 32 54 76 98 120 Barisan output y untuk u_topi = 60 82 104 126 148 170

Barisan input minimum simpangan u_tilde = 10 32 54 76 98 120

Barisan output y untuk u_tilde = 60 82 104 126 148 170

143

>> hitung ans =

function io_SLMI = maxio

INPUT-OUTPUT SLMI(A, B, C, x0) ---

Masukkan matriks A(nxn) = [10 -inf 10 -inf -inf -inf;-inf 8 -inf -inf -inf -inf;22 -inf 22 -inf -inf -inf;22 19 22 15 -inf -inf;34 31 34 -inf 10 -inf;47 44 47 30 23 12]

Masukkan matriks B(nx1) = [1;2;13;13;25;38]

Masukkan matriks C(1xn) = [-inf -inf -inf -inf -inf 12]

Masukkan kondisi awal x0(nx1) = [1;2;-inf;-inf;-inf;-inf]

Masukkan barisan input sp kej ke-k u(kx1) = [10;32;54;76;98;120]

HASIL PERHITUNGAN : =================== Matriks A =

10 -Inf 10 -Inf -Inf -Inf -Inf 8 -Inf -Inf -Inf -Inf 22 -Inf 22 -Inf -Inf -Inf 22 19 22 15 -Inf -Inf 34 31 34 -Inf 10 -Inf 47 44 47 30 23 12

144 Matriks B = 1 2 13 13 25 38

Matriks C = -Inf -Inf -Inf -Inf -Inf 12 Kondisi awal x0 = 1 2 -Inf -Inf -Inf -Inf Barisan input u = 10 32 54 76 98 120

Barisan vektor keadaan sistem x(k) utk k = 0,1, 2, ... : 1 11 33 55 77 99 121 2 12 34 56 78 100 122 -Inf 23 45 67 89 111 133 -Inf 23 45 67 89 111 133 -Inf 35 57 79 101 123 145 -Inf 48 70 92 114 136 158 Barisan output sistem y(k) utk k = 1, 2, ... : 60 82 104 126 148 170

145 1. Nilai Eigen dan Vektor Eigen Max-Plus Matriks Pada Contoh 2

Matriks yang dihitung A = [5 -inf -inf -inf -inf -inf -inf -inf;-inf 10 -inf -inf -inf -inf -inf -inf;11 -inf 10 -inf -inf -inf 10 -inf;23 22 22 8 -inf -inf 22 -inf;23 -inf 22 -inf 10 -inf 22 -inf;38 33 37 19 25 12 37 -inf;35 -inf 34 -inf 22 -inf 34 -inf;52 47 51 33 39 26 51 10]

HASIL PERHITUNGAN : =================== Matriks A =

5 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf 10 -Inf -Inf -Inf -Inf -Inf -Inf 11 -Inf 10 -Inf -Inf -Inf 10 -Inf 23 22 22 8 -Inf -Inf 22 -Inf 23 -Inf 22 -Inf 10 -Inf 22 -Inf 38 33 37 19 25 12 37 -Inf 35 -Inf 34 -Inf 22 -Inf 34 -Inf 52 47 51 33 39 26 51 10 Matriks A TIDAK IRREDUSIBEL

NILAI EIGEN max-plus maksimum matriks A = 34

VEKTOR EIGEN max-plus yang bersesuaian = -Inf -Inf -24 -12 -12 3 0 17

146

INPUT-OUTPUT SLMI(A, B, C, x0) ---

Masukkan matriks A(nxn) = [5 -inf -inf -inf -inf -inf -inf -inf;-inf 10 -inf -inf -inf -inf -inf -inf;11 -inf 10 -inf -inf -inf 10 -inf;23 22 22 8 -inf -inf 22 -inf;23 -inf 22 -inf 10 -inf 22 -inf;38 33 37 19 25 12 37 -inf;35 -inf 34 -inf 22 -inf 34 -inf;52 47 51 33 39 26 51 10]

Masukkan matriks B(nx1) = [0;1;6;18;18;33;30;47]

Masukkan matriks C(1xn) = [-inf -inf -inf -inf -inf -inf -inf 10]

Masukkan kondisi awal x0(nx1) = [0;1;-inf;-inf;-inf;-inf;-inf;-inf]

Masukkan barisan input sp kej ke-k u(kx1) = [10;20;30;40;50]

HASIL PERHITUNGAN : =================== Matriks A =

147 0 1 6 18 18 33 30 47

Matriks C = -Inf -Inf -Inf -Inf -Inf -Inf -Inf 10 Kondisi awal x0 = 0 1 -Inf -Inf -Inf -Inf -Inf -Inf Barisan input u = 10 20 30 40 50

Barisan vektor keadaan sistem x(k) utk k = 0,1, 2, ... : 0 10 20 30 40 50 1 11 21 31 41 51 -Inf 16 50 84 118 152 -Inf 28 62 96 130 164 -Inf 28 62 96 130 164 -Inf 43 77 111 145 179

148

-Inf 57 91 125 159 193

Barisan output sistem y(k) utk k = 1, 2, ... : 67 101 135 169 203

OPTIMISASI INPUT-OUTPUT Sistem Linear Max-Plus Waktu-Invariant ---

Masukkan matriks A = [5 -inf -inf -inf -inf -inf -inf -inf; -inf 10 -inf -inf -inf -inf -inf -inf;

11 -inf 10 -inf -inf -inf 10 -inf; 23 22 22 8 -inf -inf 22 -inf; 23 -inf 22 -inf 10 -inf 22 -inf; 38 33 37 19 25 12 37 -inf; 35 -inf 34 -inf 22 -inf 34 -inf; 52 47 51 33 39 26 51 10]

Masukkan matriks B = [0;1;6;18;18;33;30;47]

Masukkan matriks C = [-inf -inf -inf -inf -inf -inf -inf 10]

Masukkan kondisi awal x0 = [0;1;-inf;-inf;-inf;-inf;-inf;-inf]

Masukkan barisan output (dalam vektor kolom) y = [67;101;135;169;203]

149

=================== Matriks A =

-Inf -Inf -Inf -Inf -Inf -Inf -Inf 10 Kondisi awal x0 = 0 1 -Inf -Inf -Inf

150 -Inf -Inf Barisan output y = 67 101 135 169 203

Barisan input paling lambat u_topi = 10 44 78 112 146

Barisan output y untuk u_topi = 67 101 135 169 203

Barisan input minimum simpangan u_tilde = 10 44 78 112 146

Barisan output y untuk u_tilde = 67 101 135 169 203 >>

151

---

Masukkan matriks A(nxn) = [5 -inf -inf -inf -inf -inf -inf -inf; -inf 10 -inf -inf -inf -inf -inf -inf;

11 -inf 10 -inf -inf -inf 10 -inf; 23 22 22 8 -inf -inf 22 -inf; 23 -inf 22 -inf 10 -inf 22 -inf; 38 33 37 19 25 12 37 -inf; 35 -inf 34 -inf 22 -inf 34 -inf; 52 47 51 33 39 26 51 10]

Masukkan matriks B(nx1) = [0;1;6;18;18;33;30;47]

Masukkan matriks C(1xn) = [-inf -inf -inf -inf -inf -inf -inf 10]

Masukkan kondisi awal x0(nx1) = [0;1;-inf;-inf;-inf;-inf;-inf;-inf]

Masukkan barisan input sp kej ke-k u(kx1) = [10;44;78;112;146]

HASIL PERHITUNGAN : =================== Matriks A =

152 Matriks B = 0 1 6 18 18 33 30 47 Matriks C =

-Inf -Inf -Inf -Inf -Inf -Inf -Inf 10 Kondisi awal x0 = 0 1 -Inf -Inf -Inf -Inf -Inf -Inf Barisan input u = 10 44 78 112 146

Barisan vektor keadaan sistem x(k) utk k = 0,1, 2, ... : 0 10 44 78 112 146

1 11 45 79 113 147 -Inf 16 50 84 118 152

153

-Inf 28 62 96 130 164 -Inf 43 77 111 145 179 -Inf 40 74 108 142 176 -Inf 57 91 125 159 193

Barisan output sistem y(k) utk k = 1, 2, ... : 67 101 135 169 203

154 1. Nilai Eigen dan Vektor Eigen Max-Plus Matriks Pada Contoh 3

NILAI EIGEN DAN VEKTOR EIGEN MAX-PLUS MATRIKS ---

Matriks yang dihitung A = [934 -inf -inf -inf 295 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf 435 -inf 435 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf -inf 934 -inf -inf 295 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf 875 -inf 875 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;1868 875 -inf 875 1229 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf 1315 1868 1315 -inf 1229 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf 875 -inf 875 -inf -inf 365 -inf 365 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf; 2176 1255 -inf 1255 1537 -inf 745 295 745 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf 1315 -inf 1315 -inf -inf 745 -inf 745 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf 1695 2176 1695 -inf 1537 1125 -inf 1125 295 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;2556 1635 -inf 1635 1917 -inf 1125 675 1125 -inf 212 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf 212 -inf -inf;2826 1905 -inf 1905 2187 -inf 1395 945 1395 -inf 482 212 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf 482 -inf -inf;3086 2165 -inf 2165 2447 -inf 1655 1205 1655 -inf 742 472 212 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf 742 -inf -inf;3339 2418 -inf 2418 2700 -inf 1908 1458 1908 -inf 995 725 465 212 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf 995 -inf -inf; 3617 2696 -inf 2696 2978 -inf 2186 1736 2186 -inf 1273 1003 743 490 212 -inf -inf -inf -inf -inf -inf -inf -inf -inf 1273 -inf -inf;3870 2949 -inf 2949 3231 -inf 2439 1989 2439 -inf 1526 1256 996 743 465 212 -inf -inf -inf -inf -inf -inf -inf -inf

155

732 479 212 -inf -inf -inf -inf -inf -inf -inf 1793 -inf -inf;4417 3496 2836 3496 3778 2197 2986 2536 2986 955 2073 1803 1543 1290 1012 759 492 212 -inf -inf -inf -inf -inf -inf 2073 -inf -inf;4695 3774 3114 3774 4056 2475 3264 2814 3264 1233 2351 2081 1821 1568 1290 1037 770 490 212 -inf -inf -inf -inf -inf 2351 -inf -inf;4975 4054 3394 4054 4336 2755 3544 3094 3544 1513 2631 2361 2101 1848 1570 1317 1050 770 492 212 -inf -inf -inf -inf 2631 -inf -inf;5267 4346 3686 4346 4628 3047 3836 3386 3836 1805 2923 2653 2393 2140 1862 1609 1342 1062 784 504 212 -inf -inf -inf 2923 -inf -inf;5551 4630 3970 4630 4912 3331 4120 3670 4120 2089 3207 2937 2677 2424 2146 1893 1626 1346 1068 788 496 212 -inf -inf 3207 -inf -inf;5849 4928 4268 4928 5210 3629 4418 3968 4418 2387 3505 3235 2975 2722 2444 2191 1924 1644 1366 1086 794 510 212 -inf 3505 -inf -inf;6148 5227 4567 5227 5509 3928 4717 4267 4717 2686 3804 3534 3274 3021 2743 2490 2223 1943 1665 1385 1093 809 511 212 3804 -inf -inf;6509 5588 4928 5588 5870 4289 5078 4628 5078 3047 4165 3895 3635 3382 3104 2851 2584 2304 2026 1746 1454 1170 872 573 4165 -inf -inf;6803 5882 5222 5882 6164 4583 5372 4922 5372 3341 4459 4189 3929 3676 3398 3145 2878 2598 2320 2040 1748 1464 1166 867 4459 2217 -inf;9176 8255 7595 8255 8537 6956 7745 7295 7745 5714 6832 6562 6302 6049 5771 5518 5251 4971 4693 4413 4121 3837 3539 3240 6832 4590 848]

156

=================== Matriks A =

Columns 1 through 16

934 -Inf -Inf -Inf 295 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf 435 -Inf 435 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf 934 -Inf -Inf 295 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf 875 -Inf 875 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf 1868 875 -Inf 875 1229 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf 1315 1868 1315 -Inf 1229 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf 875 -Inf 875 -Inf -Inf 365 -Inf 365 -Inf -Inf -Inf -Inf -Inf -Inf -Inf 2176 1255 -Inf 1255 1537 -Inf 745 295 745 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf 1315 -Inf 1315 -Inf -Inf 745 -Inf 745 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf 1695 2176 1695 -Inf 1537 1125 -Inf 1125 295 -Inf -Inf -Inf -Inf -Inf -Inf 2556 1635 -Inf 1635 1917 -Inf 1125 675 1125 -Inf 212 -Inf -Inf -Inf -Inf -Inf 2826 1905 -Inf 1905 2187 -Inf 1395 945 1395 -Inf 482 212 -Inf -Inf -Inf -Inf 3086 2165 -Inf 2165 2447 -Inf 1655 1205 1655 -Inf 742 472 212 -Inf -Inf -Inf 3339 2418 -Inf 2418 2700 -Inf 1908 1458 1908 -Inf 995 725 465 212 -Inf -Inf 3617 2696 -Inf 2696 2978 -Inf 2186 1736 2186 -Inf 1273 1003 743 490 212 -Inf 3870 2949 -Inf 2949 3231 -Inf 2439 1989 2439 -Inf 1526 1256 996 743 465 212 4137 3216 2556 3216 3498 1917 2706 2256 2706 675 1793 1523 1263 1010 732 479 4417 3496 2836 3496 3778 2197 2986 2536 2986 955 2073 1803 1543 1290 1012 759 4695 3774 3114 3774 4056 2475 3264 2814 3264 1233 2351 2081 1821 1568 1290 1037 4975 4054 3394 4054 4336 2755 3544 3094 3544 1513 2631 2361 2101 1848 1570 1317 5267 4346 3686 4346 4628 3047 3836 3386 3836 1805 2923 2653 2393 2140 1862 1609 5551 4630 3970 4630 4912 3331 4120 3670 4120 2089 3207 2937 2677 2424 2146 1893 5849 4928 4268 4928 5210 3629 4418 3968 4418 2387 3505 3235 2975 2722 2444 2191 6148 5227 4567 5227 5509 3928 4717 4267 4717 2686 3804 3534 3274 3021 2743 2490 6509 5588 4928 5588 5870 4289 5078 4628 5078 3047 4165 3895 3635 3382 3104 2851 6803 5882 5222 5882 6164 4583 5372 4922 5372 3341 4459 4189 3929 3676 3398 3145 9176 8255 7595 8255 8537 6956 7745 7295 7745 5714 6832 6562 6302 6049 5771 5518

157

Matriks A TIDAK IRREDUSIBEL

-Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf 212 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf 482 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf 742 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf 995 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf 1273 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf 1526 -Inf -Inf 212 -Inf -Inf -Inf -Inf -Inf -Inf -Inf 1793 -Inf -Inf 492 212 -Inf -Inf -Inf -Inf -Inf -Inf 2073 -Inf -Inf 770 490 212 -Inf -Inf -Inf -Inf -Inf 2351 -Inf -Inf 1050 770 492 212 -Inf -Inf -Inf -Inf 2631 -Inf -Inf 1342 1062 784 504 212 -Inf -Inf -Inf 2923 -Inf -Inf 1626 1346 1068 788 496 212 -Inf -Inf 3207 -Inf -Inf 1924 1644 1366 1086 794 510 212 -Inf 3505 -Inf -Inf 2223 1943 1665 1385 1093 809 511 212 3804 -Inf -Inf 2584 2304 2026 1746 1454 1170 872 573 4165 -Inf -Inf 2878 2598 2320 2040 1748 1464 1166 867 4459 2217 -Inf 5251 4971 4693 4413 4121 3837 3539 3240 6832 4590 848

158

4165

VEKTOR EIGEN max-plus yang bersesuaian = -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -3953 -3683 -3423 -3170 -2892 -2639 -2372 -2092 -1814 -1534 -1242 -958 -660 -361 0 294 2667

159

>> hitung ans =

function io_SLMI = maxio

INPUT-OUTPUT SLMI(A, B, C, x0) ---

Masukkan matriks A(nxn) = [934 -inf -inf -inf 295 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf 435 -inf 435 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf -inf 934 -inf -inf 295 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf 875 -inf 875 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;1868 875 -inf 875 1229 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf 1315 1868 1315 -inf 1229 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf 875 -inf 875 -inf -inf 365 -inf 365 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf; 2176 1255 -inf 1255 1537 -inf 745 295 745 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf 1315 -inf 1315 -inf -inf 745 -inf 745 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf 1695 2176 1695 -inf 1537 1125 -inf 1125 295 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;2556 1635 -inf 1635 1917 -inf 1125 675 1125 -inf 212 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf 212 -inf -inf;2826 1905 -inf 1905 2187 -inf 1395 945 1395 -inf 482 212 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf 482 -inf -inf;3086 2165 -inf

160

-inf -inf -inf -inf 742 -inf -inf;3339 2418 -inf 2418 2700 -inf 1908 1458 1908 -inf 995 725 465 212 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf 995 -inf -inf; 3617 2696 -inf 2696 2978 -inf 2186 1736 2186 -inf 1273 1003 743 490 212 -inf -inf -inf -inf -inf -inf -inf -inf -inf 1273 -inf -inf;3870 2949 -inf 2949 3231 -inf 2439 1989 2439 -inf 1526 1256 996 743 465 212 -inf -inf -inf -inf -inf -inf -inf -inf 1526 -inf -inf;4137 3216 2556 3216 3498 1917 2706 2256 2706 675 1793 1523 1263 1010 732 479 212 -inf -inf -inf -inf -inf -inf -inf 1793 -inf -inf;4417 3496 2836 3496 3778 2197 2986 2536 2986 955 2073 1803 1543 1290 1012 759 492 212 -inf -inf -inf -inf -inf -inf 2073 -inf -inf;4695 3774 3114 3774 4056 2475 3264 2814 3264 1233 2351 2081 1821 1568 1290 1037 770 490 212 -inf -inf -inf -inf -inf 2351 -inf -inf;4975 4054 3394 4054 4336 2755 3544 3094 3544 1513 2631 2361 2101 1848 1570 1317 1050 770 492 212 -inf -inf -inf -inf 2631 -inf -inf;5267 4346 3686 4346 4628 3047 3836 3386 3836 1805 2923 2653 2393 2140 1862 1609 1342 1062 784 504 212 -inf -inf -inf 2923 -inf -inf;5551 4630 3970 4630 4912 3331 4120 3670 4120 2089 3207 2937 2677 2424 2146 1893 1626 1346 1068 788 496 212 -inf -inf 3207 -inf -inf;5849 4928 4268 4928 5210 3629 4418 3968 4418 2387 3505 3235 2975 2722 2444 2191 1924 1644 1366 1086 794 510 212 -inf 3505 -inf -inf;6148 5227 4567 5227 5509 3928 4717 4267 4717 2686 3804 3534 3274 3021 2743 2490 2223 1943 1665 1385 1093 809 511 212 3804 -inf -inf;6509 5588 4928 5588 5870 4289 5078 4628 5078 3047 4165 3895 3635 3382 3104 2851 2584 2304 2026 1746 1454 1170 872 573 4165 -inf -inf;6803 5882 5222 5882 6164 4583 5372 4922 5372 3341 4459 4189 3929 3676 3398 3145 2878 2598 2320 2040 1748 1464 1166 867 4459 2217 -inf;9176 8255 7595 8255 8537 6956 7745 7295 7745 5714 6832 6562 6302 6049 5771 5518 5251 4971 4693 4413 4121 3837 3539 3240 6832 4590 848]

161 5; 10; 445; 944; 944; 445; 1252; 885; 1265; 1632; 1902; 2162; 2415; 2693; 2946; 3213; 3493; 3771; 4051; 4343; 4627; 4925; 5224; 5585; 5879; 8252]

Masukkan matriks C(1xn) = [-inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf 848]

162 5; 10; -inf; -inf; -inf; -inf; -inf; -inf; -inf; -inf; -inf; -inf; -inf; -inf; -inf; -inf; -inf; -inf; -inf; -inf; -inf; -inf; -inf; -inf; -inf; -inf]

Masukkan barisan input sp kej ke-k u(kx1) = [0;600;1800;2400;3000;3600]

163

=================== Matriks A =

Columns 1 through 16

164

165 10 5 10 445 944 944 445 1252 885 1265 1632 1902 2162 2415 2693 2946 3213 3493 3771 4051 4343 4627 4925 5224 5585 5879 8252

-Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf 848 Kondisi awal x0 = 10 5 10 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf

167

Barisan input u = 0 600 1800 2400 3000 3600 Barisan vektor keadaan sistem x(k) utk k = 0,1, 2, ... :

10 5 10 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf 944 2173 3402 4631 5860 7089 440 1315 2190 3065 3940 4815 944 2173 3402 4631 5860 7089 880 1755 2630 3505 4380 5255 1878 3107 4336 5565 6794 8023 1878 3107 4336 5565 6794 8023 880 1755 2630 3505 4380 5255 2186 3415 4644 5873 7102 8331 1320 2195 3070 3945 4820 5695 2186 3415 4644 5873 7102 8331 2566 6731 10896 15061 19226 23391 2836 7001 11166 15331 19496 23661 3096 7261 11426 15591 19756 23921 3349 7514 11679 15844 20009 24174 3627 7792 11957 16122 20287 24452 3880 8045 12210 16375 20540 24705 4147 8312 12477 16642 20807 24972 4427 8592 12757 16922 21087 25252 4705 8870 13035 17200 21365 25530 4985 9150 13315 17480 21645 25810 5277 9442 13607 17772 21937 26102 5561 9726 13891 18056 22221 26386 5859 10024 14189 18354 22519 26684 6158 10323 14488 18653 22818 26983 6519 10684 14849 19014 23179 27344 6813 10978 15143 19308 23473 27638 9186 13351 17516 21681 25846 30011

168

Barisan output sistem y(k) utk k = 1, 2, ... :

10034 14199 18364 22529 26694 30859 >> optio

OPTIMISASI INPUT-OUTPUT Sistem Linear Max-Plus Waktu-Invariant ---

Masukkan matriks A [934 -inf -inf -inf 295 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf 435 -inf 435 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf -inf 934 -inf -inf 295 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf 875 -inf 875 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;1868 875 -inf 875 1229 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf 1315 1868 1315 -inf 1229 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf 875 -inf 875 -inf -inf 365 -inf 365 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf; 2176 1255 -inf 1255 1537 -inf 745 295 745 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf;-inf 1315 -inf 1315 -inf -inf 745 -inf 745 -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf

Dalam dokumen OPTIMASI WAKTU PRODUKSI DAN ANALISIS KEPERIODIKAN PADA GRAF SISTEM PRODUKSI BER-LOOP DENGAN MENGGUNAKAN SISTEM PERSAMAAN LINEAR ALJABAR MAX-PLUS (Halaman 150-200)