2. Fuzzy Linear Programming Pertemuan 8 (GSLC)
Matakuliah : K0414 / Riset Operasi Bisnis dan Industri
Tahun : 2008 / 2009
Fuzzy Linear Programming Pertemuan 8 (GSLC)

3. Learning Outcomes
Mahasiswa dapat menyelesaiakan masalah Fuzzy Linear Programming untuk berbagai masalah.
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4. Outline Materi: Pengertian Fuzzy LP Kasus Maksimalisasi
Kasus Minimalisasi
Contoh pemakaian
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5. Fuzzy Sets
If X is a collection of objects denoted generically by x, then a fuzzy set à in X is a set of ordered pairs: Ã=
A fuzzy set is represented solely by stating its membership function.
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6. Linear Programming Min z=c’x St. Ax<=b, x>=0,
Linear Programming can be solved efficiently by simplex method and interior point method. In case of special structures, more efficiently methods can be applied.
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7. Fuzzy Linear Programming
There are many ways to modify a LP into a fuzzy LP.
The objective function maybe fuzzy
The constraints maybe fuzzy
The relationship between objective function and constraints maybe fuzzy.
……..
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8. Our model for fuzzy LP Ĉ~fuzzy constraints {c,Uc}
Ĝ~fuzzy goal (objective function) {g,Ug}
Ď= Ĉ and Ĝ{d,Ud}
Note: Here our decision Ď is fuzzy. If you want a crisp decision, we can define:
λ=max Ud to be the optimal decision
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9. Our model for fuzzy LP Cont’d
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10. Our model for fuzzy LP Cont’d
Maximize λ
St. λpi+Bix<=di+pi i= 1,2,….M+1
x>=0
It’s a regular LP with one more constraint and can be solved efficiently.
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11. Example A
Crisp LP
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12. Example A cont’d Fuzzy Objective function ( keep constraints crisp)
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13. Example A cont’d
Example A cont’d
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14. Example B
Crisp LP
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15. Example B cont’d Fuzzy Objective function Fuzzy Constraints Maximize λ
St. λpi+Bix<=di+pi i= 1,2,….M+1
x>=0
Apply this to both of the objective function and constraints.
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16. Example B cont’d Now d=(3700000,170,1300,6) P=(500000,10,100,6)
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17. Conclusion
Here we showed two cases of fuzzy LP. Depends on the models used, fuzzy LP can be very differently. ( The choosing of models depends on the cases, no general law exits.)
In general, the solution of a fuzzy LP is efficient and give us some advantages to be more practical.
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18. Conclusion Cont’d Advantages of our models:
1. Can be calculated efficiently.
2. Symmetrical and easy to understand.
3. Allow the decision maker to give a fuzzy description of his objectives and constraints.
4. Constraints are given different weights.
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19. Terima kasih
Semoga berhasil
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