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Understanding Duality in Linear Programming: Concepts and Applications

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This presentation explores the concept of duality in linear programming as introduced in William J. Stevenson's textbook on operations management. Every linear programming problem has an associated "dual" problem, and solutions from the primal problem also aid in solving the dual. The relationship between primal and dual problems, along with key aspects such as shadow prices, marginal values, and surplus variables, are discussed. Analytical tools and methods like the Simplex method and software applications for optimization are highlighted for practical understanding.

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Understanding Duality in Linear Programming: Concepts and Applications

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  1. Operations Management OPERATIONSRESEARCH William J. Stevenson 8th edition DUALITAS Rosihan Asmara http://lecture.brawijaya.ac.id/rosihanhttp://rosihan.web.id

  2. DUALITAS DALAM LINEAR PROGRAMING rosihan asmara

  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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