Optimization Techniques
- Video lectures are available on Video Lectures(UMA035)
- 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
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:
- Introduction to OT & Formulation of LPP
- General Mathematical Programming Problem
- Graphical Method
- Standard Form & Basic Solutions-Part 1
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
- Old Exam Papers:
- EST-Set A (2017-18) Solutions
- EST-Set B (2017-18) Solutions
- MST (2018-19) Solutions
- EST (2018-19) Solutions
- Sessional Quiz (2021-22)
- MST Solution (2021-22) Even Semester
- EST Solution (2021-22) Even Semester
- MST (2022-23) MST Solutions
- EST (2022-23) Even Semester
- MST (2023-24) Solutions