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William J. Stevenson

OPERATIONS RESEARCH. Operations Management. Enos. William J. Stevenson . 8 th edition. DUALITAS DALAM LINEAR PROGRAMING. KONSEP DUALITAS . Setiap persoalan linear programing mempunyai suatu linear program yang berkaitan, yang disebut “dual”.

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William J. Stevenson

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  1. OPERATIONSRESEARCH Operations Management Enos William J. Stevenson 8th edition

  2. DUALITAS DALAM LINEAR PROGRAMING

  3. KONSEP DUALITAS • Setiap persoalan linear programing mempunyai suatu linear program yang berkaitan, yang disebut “dual”. • Solusi dari persoalan asli LP (Primal), juga memberikan solusi pada dualnya

  4. Hubungan primal-dual

  5. Contoh : (masalah primal) Tabel primal-dual

  6. Fungsi primal-dual Tabel primal-dual Kunci 1 Batasan i Variabel i Kunci 2 Fungsi Tujuan Nilai Kanan

  7. Interpretasi Ekonomis Fungsi primal Xj = Tingkat aktivitas ke j Cj = Laba persatuan aktivitas j Z = Laba total dari seluruh aktivitas bi = Jumlah sumber i yang tersedia aij = jumlah sumber i yang “dipakai” oleh setiap satuan aktivitas j Dengan menggantikan Zj, metode simpleks dapat diartikan mencari nilai Ym Fungsi dual Yi = kontribusi persatuan sumber i terhadap laba

  8. Hasil masalah dual Y = 8(0) + 15(5/6) + 30(1/2) Y = 271/2 Analisis Simplex Y1 = 0, Y2 = 5/6, Y3 = 1/2

  9. SEKIANTERIMAKASIH

  10. End of Slide show, clik to exit

  11. Interpretasi dual yang lain : Tugas !!!! (Tidak di kumpulkan) • Marginal Value • Shadow Price • Surplus Variabel

  12. ALAT ANALISIS • QSB+ • AB:QM • AB:POM • QM (DOS/WINDOWS) • LINDO • SAS

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