Presentasi sedang didownload. Silahkan tunggu

Presentasi sedang didownload. Silahkan tunggu

Problems in The Simplex Method Minggu 3 Part 3. Solusi yang tidak fisibel (infeasible solution) Masalah yang tidak terbatas (The unbounded linear programming)

Presentasi serupa


Presentasi berjudul: "Problems in The Simplex Method Minggu 3 Part 3. Solusi yang tidak fisibel (infeasible solution) Masalah yang tidak terbatas (The unbounded linear programming)"— Transcript presentasi:

1 Problems in The Simplex Method Minggu 3 Part 3

2 Solusi yang tidak fisibel (infeasible solution) Masalah yang tidak terbatas (The unbounded linear programming) Solusi optimal majemuk (The alternate optimal solution) Pivot row yang seri (degeneracy)

3 The infeasible linear programming problem No solution that satisfies the constraints and non-negativity conditions for the problem. Maximize Z = 2x 1 + 4x 2 subject to 2.5x 1 + 3x 2  300 5x 1 + 2x 2  400 2x 2  150 x 1  60 x 2  60 with x 1, x 2  0

4 Initial Simplex Tableau for Infeasibility Problem cjcj 240000-M 0 cbcb BASISx1x1 x2x2 S1S1 S2S2 S3S3 S4S4 A1A1 S5S5 A2A2 Solution 0 -M S1S2S3A1A2S1S2S3A1A2 2.5 5 0 1 0 3220132201 1000010000 0100001000 0010000100 0 0001000010 0000100001 300 400 150 60 ZjZj -M 000M M -120M c j - Z j 2+M4+M000-M0 0

5 Second Simplex Tableau for Infeasibility Problem cjcj 240000-M 0 cbcb BASISx1x1 x2x2 S1S1 S2S2 S3S3 S4S4 A1A1 S5S5 A2A2 Solution 0 -M 4 S1S2S3A1x2S1S2S3A1x2 2.5 5 0 1 0 0000100001 1000010000 0100001000 0010000100 0 0001000010 3 2 0 -3 -2 0 1 120 280 30 60 ZjZj -M 000M -44240-6M c j - Z j 2+MM000-M04-M-4

6 Third Simplex Tableau for Infeasibility Problem cjcj 240000-M 0 cbcb BASISx1x1 x2x2 S1S1 S2S2 S3S3 S4S4 A1A1 S5S5 A2A2 Solutio n 2 0 -M 4 x1S2S3A1x2x1S2S3A1x2 1000010000 0000100001 0.4 -2 0 -0.4 0 0100001000 0010000100 0 0001000010 1.2 -4 2 -1.2 -1.2 4 -2 1.2 1 48 40 30 12 60 ZjZj 24 (0.8 + 0.4M) 00M-M (-1.6 + 1.2M) (1.6 - 1.2M 336 - 12M c j - Z j 00 (-0.8 - 0.4M) 00-M0 (1.6 - 1.2M (-1.6 + 0.2M)

7 Final Simplex Tableau for Infeasibility Problem cjcj 240000-M 0 cbcb BASISx1x1 x2x2 S1S1 S2S2 S3S3 S4S4 A1A1 S5S5 A2A2 Solution 2 -M 0 -M 4 x1A2S3A1x2x1A2S3A1x2 1000010000 0000100001 -0.2 -0.5 1 0.2 0.5 0.3 0.25 0.5 -0.3 -0.25 0010000100 0 0 0001000010 1.2 -4 2 -1.2 -1.2 4 -2 1.2 1 120 280 30 60 ZjZj 24 (1.6 + 0.3M) (-0.4 + 0.05M) 0M-MM 320 – 10M c j - Z j 00 (-1.6 - 0.3M) (0.4 - 0.05M) 0-M0 0

8 Infeasible LP Ketidaklayakan solusi Kesalahan memformulasi program linear

9 The unbounded linear programming If the objective function can be made infinitely large without violating any of the constraints. Maximize Z = 2x 1 + 3x 2 subject to x 1 - x 2  2 -3x 1 + x 2  4 with x 1, x 2  0

10 Initial Simplex Tableau for Unbounded Illustration cjcj 2300 cbcb BASISx1x1 x2x2 S1S1 S2S2 Solution 0000 S1S2S1S2 1 -3 1 1010 0101 2424 ZjZj 00000 c j - Z j 2300

11 Second Simplex Tableau for Unbounded Illustration cjcj 3400 cbcb BASISx1x1 x2x2 S1S1 S2S2 Solution 0303 S1x2S1x2 -2 -3 0101 1010 0101 6464 ZjZj -900012 c j - Z j 1100-3

12 Suatu masalah yang tidak terbatas diidentifikasikan dalam simplex pada saat pemilihan pivot row tidak mungkin dilakukan  saat nilai pivot row negatif atau tak terhingga

13 The alternate optimal solution If two or more solutions yield the optimal objective value. Maximize Z = 10/3x 1 + 4x 2 subject to 2.5x 1 + 3x 2  300 5x 1 + 2x 2  400 2x 2  150 with x 1, x 2  0

14 Initial Simplex Tableau for Alternate Optimal Solution cjcj 10/34000 cbcb BASISx1x1 x2x2 S1S1 S2S2 S3S3 Solution 000000 S1S2S3S1S2S3 2.5 5 0 322322 100100 010010 001001 300 400 150 ZjZj 000000 c j - Z j 10/34000 Second Simplex Tableau for Alternate Optimal Solution cjcj 10/34000 cbcb BASISx1x1 x2x2 S1S1 S2S2 S3S3 Solution 004004 S1S2x2S1S2x2 2.5 5 0 001001 100100 010010 -1.5 0.5 75 250 75 ZjZj 040020 c j - Z j 10/3000-2

15 Fourth Simplex Tableau for Alternate Optimal Solution cjcj 10/34000 cbcb BASISx1x1 x2x2 S1S1 S2S2 S3S3 Solution 10/3 0 4 x1S3x2x1S3x2 100100 001001 -0.2 0.5 0.3 0.5 -0.25 010010 60 50 ZjZj 10/344/300400 c j - Z j 00-4/300 Third Simplex Tableau for Alternate Optimal Solution cjcj 10/34000 cbcb BASISx1x1 x2x2 S1S1 S2S2 S3S3 Solution 10/3 0 4 x1S2x2x1S2x2 100100 001001 0.4 -2 0 010010 -0.6 2 0.5 30 100 75 ZjZj 10/344/300400 c j - Z j 00-4/300

16 Jika melakukan iterasi lanjut pada tabel simplex yang sudah memenuhi syarat optimal Diindikasikan oleh nilai 0 pada baris c j -z j untuk variabel bukan dasar Memberi keleluasaan pada perusahaan untuk memilih kombinasi produk

17 The concept of degeneracy in linear programming If one or more of the basic variables has a value of zero. Occurs whenever two rows satisfy the criterion of selection as pivot row. Maximize Z = 4x 1 + 3x 2 subject to x 1 - x 2  2 2x 1 + x 3  4 x 1 + x 2 + x 3  3 with x 1, x 2, x 3  0

18 Initial Simplex Tableau for Degeneracy Illustration cjcj 403000 cbcb BASISx1x1 x2x2 x3x3 S1S1 S2S2 S3S3 Solution Ratio 000000 S1S2S3S1S2S3 121121 0 1 011011 100100 010010 001001 243243 2/1 = 2 4/2 = 2 3/1 = 3 ZjZj 0000000 c j - Z j 403000 Second Simplex Tableau for Degeneracy Illustration cjcj 403000 cbcb BASISx1x1 x2x2 x3x3 S1S1 S2S2 S3S3 Solution Ratio 400400 x1S2S3x1S2S3 100100 2 011011 1 -2 010010 001001 201201 - 0/2 1/2 ZjZj 4-404008 c j - Z j 043-400

19 Third Simplex Tableau for Degeneracy Illustration cjcj 403000 cbcb BASISx1x1 x2x2 x3x3 S1S1 S2S2 S3S3 Solution Ratio 400400 x1x2S3x1x2S3 100100 010010 0.5 0 1 0.5 001001 201201 2/0.5 0/0.5 - ZjZj 4020208 c j - Z j 0010-20 Fourth Simplex Tableau for Degeneracy Illustration cjcj 403000 cbcb BASISx1x1 x2x2 x3x3 S1S1 S2S2 S3S3 Solution Ratio 430430 x1x3S3x1x3S3 100100 2 0 010010 1 -2 1 0 1 001001 201201 2/1 - 1/1 ZjZj 423-2308 c j - Z j 0-202-30

20 Fifth Simplex Tableau for Degeneracy Illustration cjcj 403000 cbcb BASISx1x1 x2x2 x3x3 S1S1 S2S2 S3S3 Solution Ratio 430430 x1x3S1x1x3S1 100100 2 0 010010 001001 1 2 1 121121 ZjZj 42301210 c j - Z j 0-200-2

21 Degenerasi muncul ketika terdapat pivot row yang seri Pilih salah satu pivot row secara acak dan lakukan iterasi lanjut secara normal


Download ppt "Problems in The Simplex Method Minggu 3 Part 3. Solusi yang tidak fisibel (infeasible solution) Masalah yang tidak terbatas (The unbounded linear programming)"

Presentasi serupa


Iklan oleh Google