Defining Problem for LP Properties Objective: Maximize or minimize? Objective: Maximize or minimize? Constraints Constraints Other alternative? Other alternative?

Presentasi berjudul: "Defining Problem for LP Properties Objective: Maximize or minimize? Objective: Maximize or minimize? Constraints Constraints Other alternative? Other alternative?"— Transcript presentasi:

1 Defining Problem for LP Properties Objective: Maximize or minimize? Objective: Maximize or minimize? Constraints Constraints Other alternative? Other alternative? Linear mathematical relationship Linear mathematical relationshipAssumptions Certainty Certainty Proportionality in objective and constraints Proportionality in objective and constraints Additivity, total of all activities = the sum of the individual activities Additivity, total of all activities = the sum of the individual activities Divisibility, solution not neccesarily be integer number Divisibility, solution not neccesarily be integer number Nonnegative variable, negative quantity is imposible Nonnegative variable, negative quantity is imposible

2 Formulating LP Problems Sepenuhnya memahami permasalahan manajerial yang sedang dihadapi Sepenuhnya memahami permasalahan manajerial yang sedang dihadapi Mengidentifikasi tujuan dan kendala Mengidentifikasi tujuan dan kendala Tentukan variabel keputusan (decision variable) Tentukan variabel keputusan (decision variable) Gunakan decision variable untuk memformulasikan ekspresi matematis fungsi tujuan dan kendala Gunakan decision variable untuk memformulasikan ekspresi matematis fungsi tujuan dan kendala

3 Graphical Solution C T 0 Area of positive numbers Constraint #1 Constraint #2 Objective/iso profit Maksimasi: Geserlah garis isoprofit kearah kanan atas dengan tidak mengubah gradien/slope/kemiringan garis tsb. Titik terjauh yang bisa dicapai oleh isoprofit line dalam feasible region merupakan solusi optimumnya.

4 Corner Point Solution C T 0 Area of positive numbers Constraint #1 Constraint #2 Objective/iso profit Pada masing-masing titik, cari koordinatnya, kemudian masukkan koordinat tsb kedalam fungsi tujuan!

5 Computer Solution (Algorithm/Iterations) Use QM for windows Use QM for windows POM for windows POM for windows Microsoft Excel with Solver Microsoft Excel with Solver Manual: Simplex method Manual: Simplex method

6 Special Cases: Infeasibility C T 0 Area of positive numbers Constraint #1 Constraint #2 Objective/iso profit Constraint #3 Satisfying region for respective constraints

7 Special Cases: Unboundedness C T 0 Area of positive numbers Constraint #1 Constraint #2 Objective/iso profit Constraint #3 Feasible region for maximization

8 Special Cases: Redundancy C T 0 Area of positive numbers Constraint #1 Constraint #2 Objective/iso profit Redundant Constraint #3 Satisfying region for respective constraints

9 Special Cases: Alternate Optimal Solution C T 0 Area of positive numbers Constraint #1 Constraint #2 Objective/iso profit Redundant Constraint #3 Satisfying region for respective constraints Solution lies in this line

10 Sensitivity Analysis Seberapa sensitifkah solusi optimal yang didapat terhadap perbahan profit/unit, resources, dan parameter input lainnya? Seberapa sensitifkah solusi optimal yang didapat terhadap perbahan profit/unit, resources, dan parameter input lainnya? Sensitifitas terhadap: Sensitifitas terhadap: –Perubahan constraint –Perubahan fungsi tujuan Cek kembali apa dampak perubahan di atas terhadap kemiringan garis fungsi tujuan dan fungsi kendala Cek kembali apa dampak perubahan di atas terhadap kemiringan garis fungsi tujuan dan fungsi kendala Teliti kembali akibatnya terhadap perubahan feasible region Teliti kembali akibatnya terhadap perubahan feasible region Apakah solusi optimalnya masih sama? Seberapa besar perubahan fungsi kendala dan fungsi tujuan tidak mengubah solusi optimal? Apakah solusi optimalnya masih sama? Seberapa besar perubahan fungsi kendala dan fungsi tujuan tidak mengubah solusi optimal?