CIRIACO D'AMBROSIO | Operational Research
CIRIACO D'AMBROSIO Operational Research
cod. 0612600014
OPERATIONAL RESEARCH
| 0612600014 | |
| DIPARTIMENTO DI INGEGNERIA INDUSTRIALE | |
| EQF6 | |
| INDUSTRIAL ENGINEERING AND MANAGEMENT | |
| 2018/2019 |
| OBBLIGATORIO | |
| YEAR OF COURSE 3 | |
| YEAR OF DIDACTIC SYSTEM 2016 | |
| SECONDO SEMESTRE |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/09 | 6 | 60 | LESSONS |
| Objectives | |
|---|---|
| KNOWLEDGE AND UNDERSTANDING: THE COURSE AIMS TO DEEPEN AND BROADEN THE KNOWLEDGE FOR SOLVING OF DECISIONAL PROBLEMS FORMULATED THROUGH CONTINUOUS LINEAR PROGRAMMING MODELS. KNOWING THE NECESSARY METHODOLOGY TO FORMULATE REAL PROBLEMS AS LINEAR MATHEMATICAL MODELS. KNOW THE SIMPLEX ALGORITHM FOR THE SOLUTION OF CONTINUOUS MATHEMATICAL MODELS. STUDY OF SENSITIVITY ANALYSIS APPLIED TO LINEAR PROGRAMMING MODELS. BASIC KNOWLEDGE FOR THE SOLUTION OF OPTIMIZATION MODELS USING EXCEL. APPLYING KNOWLEDGE AND UNDERSTANDING: CAPACITY TO RECOGNIZE AND ABILITY TO FORMULATE DECISIONAL PROBLEMS OF REAL INTEREST THAT ARE IN THE CLASS OF LINEAR OPTIMIZATION PROBLEMS AND NETWORKS OPTIMIZATION PROBLEMS. KNOWLEDGE OF THE MATHEMATICAL MODELS AND THEIR APPLICABILITY FOR THE SOLUTION OF REAL PROBLEMS. KNOWLEDGE OF THE SIMPLEX ALGORITHM FOR THE SOLUTION OF LINEAR PROGRAMMING MODELS. KNOWLEDGE OF THE MAIN ELEMENTS FOR RESOLVING PROBLEMS DEFINED AS MIN COST FLOW ON GRAPHS. |
| Prerequisites | |
|---|---|
| STUDENTS SHOULD KNOW BASIC CONCEPTS OF MATHEMATICS ANALYSIS, DISCRETE MATHEMATICS AND LINEAR ALGEBRA. |
| Contents | |
|---|---|
| 1. LINEAR PROGRAMMING (LP). (THEORY 20 HOURS; EXERCISES 10 HOURS): - ELEMENTARY OPERATIONS ON MATRICES AND VECTORS; POLYHEDRONS; EXTREME DIRECTIONS, VERTICES; REPRESENTATION THEOREM; FROM THE REAL PROBLEM TO THE OPTIMIZATION MODEL; SIMPLEX METHOD: ESTREME POINTS, OPTIMALITY CONDITIONS. SIMPLEX METHOD ALGEBRA: INITIAL BASIC FEASIBLE SOLUTION, TWO-PHASES METHOD, BIG-M METHOD, SIMPLEX CONVERGENCY. USING THE EXCEL PROGRAM FOR THE SOLUTION OF LINEAR PROGRAMMING PROBLEMS. 2. THEORY OF DUALITY. (THEORY 10 HOURS; EXERCISES 4 HOURS): - DUALITY: DUAL PROBLEM FORMULATION, REDUCED COSTS, THEOREM OF WEAK DUALITY, THEOREM OF STRONG DUALITY, COMPLEMENTARY SLACKNESS CONDITIONS, PRIMAL-DUAL RELATION, ECONOMIC INTERPRETATION OF DUALITY. - SENSITIVITY ANALYSIS: POST-OPTIMALITY ANALYSIS, OPTIMUM POINT VARIATION, OPTIMUM SOLUTION VALUE VARIATION. 3. NETWORK OPTIMIZATION. (THEORY 10 HOURS; EXERCISES 6 HOURS): - SHORTEST PATH PROBLEMS, MINIMUM SPANNING TREE PROBLEM, MAX FLOW PROBLEM, TRANSPORTATION PROBLEM, ASSIGNMENT PROBLEM. MATHEMATICAL MODELS AND ALGORITHMS. |
| Teaching Methods | |
|---|---|
| FRONTAL LESSONS. EACH LESSON PROVIDES, AT THE END OF THE PRESENTATION OF A TOPIC, EXAMPLES ON THIS TOPIC. |
| Verification of learning | |
|---|---|
| THE FINAL EXAM IS DESIGNED TO EVALUATE AS A WHOLE: THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED IN THE COURSE, AND THE ABILITY TO APPLY SUCH KNOWLEDGE FOR THE RESOLUTION OF LINEAR PROGRAMMING PROBLEMS. THE EXAM CONSISTS OF A WRITTEN TEST AND AN ORAL INTERVIEW. THE WRITTEN TEST CONSISTS OF SOLVING TYPICAL PROBLEMS PRESENTED IN THE COURSE AND ANSWERING QUESTIONS RELATED TO ARGUMENTS OF THE COURSE. THE ORAL EXAMINATION WILL COVER ALL THE TOPICS OF THE COURSE AND ASSESSMENT WILL TAKE INTO ACCOUNT THE KNOWLEDGE DEMONSTRATED BY THE STUDENT IN THE MODELING AND RESOLUTION OF LINEAR PROGRAMMING PROBLEMS. THE EVALUATION OF THE WRITTEN TEST AND OF THE ORAL EXAMINATION IS EXPRESSED IN THIRTIES. IT IS NECESSARY TO GAIN AT LEAST 18/30 IN BOTH TESTS TO PASS THE EXAM. |
| Texts | |
|---|---|
| - M.S. BAZARAA, J.J JARVIS & H.D. SHERALI LINEAR PROGRAMMING AND NETWORK FLOWS, FOURTH EDITION, JOHN WILEY, 2010. - LECTURE SLIDES TO LEARN MORE: HILLIER FREDERICK S., RICERCA OPERATIVA, MCGRAW-HILL EDUCATION, 2010. |
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