MTM3691 – Theory of Linear Programming (Fall 2024-2025)

Instructor Information

• Instructors: Hale Gonce Köçken (Gr. 2) and Gökhan Göksu (Gr. 4)

• E-mail (HGK): hgonce [at] yildiz [dot] edu [dot] tr

• E-mail (GG): gokhan [dot] goksu [at] yildiz [dot] edu [dot] tr

• Course Web Site: gokhangoksu.github.io/MTM3691

General Information

• Schedule: Monday, 09:00-12:00

• Classroom: KMB-320

• Office Hours: Monday, 13:00-16:00

Expectations and Goals

• To gain the ability to create mathematical models to find the optimum solution in engineering problems and to give the methods required to solve the resulting model.

Course Materials

• Textbook:

  • H. A. Taha (2008). Operations Research: An Introduction, 8/e, Pearson Education.

• Optional Materials (in Turkish):

  • H. A. Taha (2000), Çeviren ve Uyarlayanlar: Ş. A. Baray, Ş. Esnaf, Yöneylem Araştırması, 6. Basımdan Çeviri, Literatür Yayınevi.

Tentative Course Schedule

• Week 1 (30.09.2024): Linear Programming (LP) Problem: Definition, Two-Variable LP Model and Model Construction
  [Slide]

• Week 2 (07.10.2024): Properties of LP Model, Graphical Solution Method (Max/Min), LP Model in Equation Form, Transition from Graphical Solution to Algebraic Solution
  [Slide]

• Week 3 (14.10.2024): No Class
  [No Class]

• Week 4 (21.10.2024): Algebraic Method, Simplex Method: Optimality and Feasibility Conditions
  [Slide]

• Week 5 (28.10.2024, Online Session): Artificial Starting Solution: M-Method
  [Slide]

• Week 6 (04.11.2024): Special Cases in the Simplex Method: Degeneration, Alternative Optima, Unbounded Solution, Infeasible Solution
  [Slide]

• Week 7 (11.11.2024): Converting an LP to Standard Form: Lower/Upper/Range Bounded Variables, Free Variables
  [Slide]

• Week 8 (22.11.2024, 11:00-12:40): Midterm I
  Midterm I will take place at KMB-212, KMB-224, KMB-320!

• Week 9 (25.11.2024): Optimality and Feasibility Conditions, Some Basic Theorems and their Proofs
  [Slide]

• Week 10 (02.12.2024): Sensitivity Analysis: Graphical and Algebraic
  [Slide]

• Week 11 (09.12.2024): Duality: Canonical Form, Primal-Dual Relations, Inverse Matrix, Optimal-Dual Solution
  [Slide]

• Week 12 (16.12.2024): Midterm II
  [Midterm II]

• Week 13 (23.12.2024): Dual Simplex Algorithm: Dual Feasibility and Optimality Conditions
  [Slide]

• Week 14 (30.12.2024): Transportation Problem (TP) and its Algorithm: Balancing the TP, Determining the Initial Solution
  [Slide]

• Week 15 (06.01.2025): Transportation Problem (TP) and its Algorithm: Determining the Initial Solution (Continued), Optimization Calculations of the TP Algorithm
  [Slide]

Course Evaluation

• Midterm I: 35 %

• Midterm II: 25 %

• Final: 40 %