Optimization Techniques


  1. Video lectures are available on Video Lectures(UMA035)
  2. For Syllabus see,  UMA035 
  3. Course Handout 
  4. Tutorial Sheets are available on Tutorial Sheets  and for solutions click to Solutions of Tutorial Sheets 
  5. 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'
  6. For Lab work List of Experiments, Lab Manual   



Current Year  2024 Notes:  Click Here 
Reference Code for Lab 2 Evaluation:  Simplex Method Big M  LCM Steepest Descent Method 
1.   Formulation 
2.   Slack/surplus/Standard Form/Basic Solutions 3. 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: Part-1(Branch & Bound) Part-2(IPP using Addition of Gomary's Constant) 
11 Transportation Problem: Part 1 (Introduction)Part 2-Necessary & Sufficient Conditions  (Only Statments, No Proofs to be done for exam)Part 3-North West & LCM Method Part 4-Dual of Transportation  Problem Part 5-UV Method for Optimal solution of TP Part 6-Unbalanced TP Part 7-Loop in TP Part 8- Maximization TPPart 9-Alternate Optimal Solution in TP 
12. Assignment Problem: AP-Part 1 AP-part 2 13. Project Management: Part-1(Project) Part-2 (Crashing) 14. Search Techniques:  Unimodal function & Steepest Descent Method 15. Multiobjective Prog Problem: MOPP 16. NLPP: Part-1 Part-2 Part-3 





Older Notes: Standard Form & Basic Solutions-Part 2 
Part 2- Convex Sets Part 3- Convex Sets, Extreme Points/ Vertex,  & Fundamental Theorem of LPP 
Part 2- Simplex Method Part 3- Big-M Method Part 4- Two-Phase Method  Part 5- Exceptional Cases A Part 6-Interesting Example -1 Part-7 Interesting Example-2  Part-8 Construct Simplex table without row operations Part9-Solve LPP without artificial variables Part 10-Tie in Entering VariablePart11-Tie in Leaving Variable Part12-Find inverse of matrix using Simplex Method 
Part 2- Weak Duality Theorem & Finding Optimal SolutionPart 3-Application of Dual Part 4-Complementary Slackness Conditions  Part 5-Dual Simplex Method 
Post Optimality Analysis-Part 2 Post Optimality Analysis-Part 3 Post Optimality Analysis-Part 4 Post Optimality Analysis-Part 5 Post Optimality Analysis-Part 6 
IPP-Branch & Bound Techniques IPP-Gomory Constraint IPP-Examples for Gomory Constaints/Fractional Cut
Network Drawing Earliest Time, Latest Time & Critical Path Float Time in Network Crashing/Scheduling of Project 
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  
Assignment Problem-Hungarian Method-Part 2 

Non-Linear Programming Problem-Lecture 2 Non-linear Programming Problem-Lecture 3 


The follwoing topic is not a part of UMA035
Game Theory-Lecture 2 Game Theory-Lecture 3 Game Theory-Lecture 4 Game Theory-Lecture 5 
  1. Old Exam Papers: