MTM3691 – Theory of Linear Programming (Fall 2023-2024)

Instructor Information

• Instructors: Hale Gonce Köçken (Gr. 1) and Gökhan Göksu (Gr. 2)

• 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/MTM3502

General Information

• Schedule: Thursday, 13:00-16:00

• Classroom: KMB-212

• Office Hours: Friday, 14:00-17:00 (and/or by appointment)

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.

Course Schedule

• Week 1 (05.10.2023): Linear Programming (LP) Problem: Definition, Two-Variable LP Model and Model Construction
  [Slide]

• Week 2 (12.10.2023): Properties of LP Model, Graphical Solution Method (Max/Min)
  [Slide]

• "Week 4" (19.10.2023): Simplex Method: Optimality and Feasibility Conditions
  [Slide]

• "Week 3" (26.10.2023): LP Model in Equation Form, Transition from Graphical Solution to Algebraic Solution, Algebraic Method
  [Slide]

• Week 5 (02.11.2023): Artificial Starting Solution: M-Method
  [Slide]

• Week 6 (09.11.2023): Special Cases in the Simplex Method: Degeneration, Alternative Optima, Unbounded Solution, Infeasible Solution
  [Slide]

• Week 7 (16.11.2023): Converting an LP to Standard Form: Lower/Upper/Range Bounded Variables, Free Variables
  [Slide]

• Week 8 (23.11.2023): Midterm Exam
  Results are announced in obs.yildiz.edu.tr!

• Week 9 (30.11.2023): Optimality and Feasibility Conditions, Some Basic Theorems and their Proofs
  [Slide]

• Week 10 (07.12.2023): Sensitivity Analysis: Graphical and Algebraic
  [Slide]

• Week 11 (14.12.2023): Duality: Canonical Form, Primal-Dual Relations, Inverse Matrix, Optimal-Dual Solution
  [Slide]

• Week 12 (21.12.2023): Quiz
  Results are announced in obs.yildiz.edu.tr!

• Week 13 (28.12.2023): Dual Simplex Algorithm: Dual Feasibility and Optimality Conditions
  [Slide]

• Week 14 (04.01.2024): Transportation Problem (TP) and its Algorithm: Balancing the TP, Determining the Initial Solution, Optimization Calculations of the TP Algorithm
  [Slide]

Course Evaluation

• Midterm: 35 %

• Quiz: 25 %

• Final: 40 %