Optimization Techniques

Current Year 2025 Lecture Notes:
Unit-1 Unit-2 Unit-3
Unit-4 & IPP-Gomory Constraint IPP-Examples for Gomory Constaints/Fractional Cut
Unit-5: Transportation Problem: TP-Part 1-Introduction TP-Part 2-Necessary & Sufficient Conditions (Only Statements, No Proofs to be done for exam)TP Part 3-North West & LCM Method TP-Part 4-VAM Method (Not to be asked in exam)TP-Part 5-Dual of Transportation Problem TP-Part 6-UV Method for Optimal solution of TP TP-Part 7-Unbalanced TP TP-Part 8-Loop in TP TP-Part 9- Maximization TPTP-Part 10-Alternate Optimal Solution in TP TP-Part 11-Restricted Transportation Problem
Assignment Problem: AP-Part 1 AP-part 2
Project Management: Part-1-Introduction to Project mangement Part -2-Network Drawing Part -3-Earliest Time, Latest Time & Critical Path Part-4-Float Time in Network Part -5-Crashing/Scheduling of Project
Search Techniques: Unimodal function & Steepest Descent Method
Multi-objective Prog Problem: MOPP (Only Graphical method)
NLPP: Part-1 Part-2 Part-3 Part-4(KKT) KKT Examples

For Syllabus see, UMA035
Course Handout
Tutorial Sheets are available on Tutorial Sheets and for solutions click to Solutions of Tutorial Sheets
More Practice Problems from book H A Taha-Operation Research: Practice Set 1 , also refer exercise problem of from Book: Suresh Chandra et al. 'Numerical Optimization with Applications'
For Lab work List of Experiments, Lab Manual ,

Reference Code for Lab Work: Graphical Method Basic Solutions Simplex Method Big M Dual Simplex Method LCM Steepest Descent Method

Video lectures are available on Video Lectures(UMA035)
Old Exam Papers:

Last semester Handwritten notes:
1 Introduction & Formulations , Graphical Method
2. Slack/surplus/Standard Form/Basic Solutions Part 1-Hyperplane, Half Spaces, Polyheron, convex sets, Fundamental Theorem of LPP Part 2- Convex Sets Part 3- Convex Sets, Extreme Points/ Vertex, & Fundamental Theorem of LPP
4. Simplex Method-Introduction & Algorithm 5. Big-M Method for LPP 6. Two-Phase Method for LPP 7. Exceptional Cases (Unbounded/Infeasible/Infinite Solutions/Some other related examples
8 Duality : PART-1 PART-2 PART-3
9. Sensitivity Analysis/Post Optimality Analysis Part-1(cost Change) Part-2 (Resource/Availability Change) Part-3 (Change in Coefficient matrix) Part-4 (Addition of Variable) Part-5 (Addition of Constraint)
10 IPP: Integer Programming Problem-Introduction IPP-Branch & Bound Techniques IPP-Gomory Constraint IPP-Examples for Gomory Constaints/Fractional Cut

11 Transportation Problem: TP-Part 1-Introduction TP-Part 2-Necessary & Sufficient Conditions TP Part 3-North West & LCM Method TP-Part 4-VAM Method TP-Part 5-Dual of Transportation Problem TP-Part 6-UV Method for Optimal solution of TP TP-Part 7-Unbalanced TP TP-Part 8-Loop in TP TP-Part 9- Maximization TPTP-Part 10-Alternate Optimal Solution in TP TP-Part 11-Restricted Transportation Problem
12. Assignment Problem: AP-Part 1 AP-part 2

13. Project Management: Part-1-Introduction to Project mangement Part -2-Network Drawing Part -3-Earliest Time, Latest Time & Critical Path Part-4-Float Time in Network Part -5-Crashing/Scheduling of Project

14. Search Techniques: Unimodal function & Steepest Descent Method
15. Multiobjective Prog Problem: MOPP
16. NLPP: Part-1 Part-2 Part-3 Part-4(KKT) KKT Examples

14. Game Theory : (Not in syllabus of UMA035)Game Theory-Lecture 1 Game Theory-Lecture 2 Game Theory-Lecture 3 Game Theory-Lecture 4 Game Theory-Lecture 5
15. Goal Programming: Notes (Not in syllabus of UMA035)16. Queueing Theory: Notes (Not in syllabus of UMA035)

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