Francesco CARRABS | OPERATIONS RESEARCH
Francesco CARRABS OPERATIONS RESEARCH
cod. 0512100012
OPERATIONS RESEARCH
| 0512100012 | |
| DIPARTIMENTO DI INFORMATICA | |
| EQF6 | |
| COMPUTER SCIENCE | |
| 2016/2017 |
| OBBLIGATORIO | |
| YEAR OF COURSE 2 | |
| YEAR OF DIDACTIC SYSTEM 2015 | |
| SECONDO SEMESTRE |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/09 | 6 | 48 | LESSONS |
| Objectives | |
|---|---|
| KNOWLEDGE AND UNDERSTANDING. STUDENT WILL HAVE KNOWLEDGE: OF THE BASIC CONCEPTS OF MATHEMATICAL MODELING OF GENERAL DECISION PROBLEMS. OF THE BASIC METHODOLOGIES TO BUILD A LINEAR MATHEMATICAL MODEL. OF THE BASIC TOOLS FOR SOLVING LINEAR OPTIMIZATION PROBLEMS WITH CONTINUOUS VARIABLES. KNOWLEDGE OF THE BASIC CONCEPTS OF NETWORK THEORY AND GRAPH THEORY AND OF THE ELEMENTARY ALGORITHMS FOR SOLVING NETWORK OPTIMIZATION PROBLEMS. OF THE MAIN TOOLS TO SOLVE LINEAR OPTIMIZATION PROBLEMS. APPLYING KNOWLEDGE AND UNDERSTANDING. STUDENT MUST BE ABLE TO: REPRESENT A SIMPLE OPTIMIZATION PROBLEM OF PROCESS OR DECISION USING A LINEAR MATHEMATICAL MODEL WITH CONTINUOUS VARIABLES. TO SOLVE LINEAR MATHEMATICAL PROGRAMMING PROBLEMS. TO MODEL SIMPLE PROBLEMS USING GRAPHS AND FLOW NETWORKS. TO SOLVE SIMPLE NETWORK OPTIMIZATION PROBLEMS. TO SOLVE, THROUGH THE USE OF COMPUTER TOOLS, SIMPLE PROBLEMS ON NETWORK OPTIMIZATION. |
| Prerequisites | |
|---|---|
| STUDENTS SHOULD KNOW BASIC CONCEPTS OF MATHEMATICS ANALYSIS, DISCRETE MATHEMATICS AND LINEAR ALGEBRA. |
| Contents | |
|---|---|
| 1. LINEAR PROGRAMMING (LP): - ELEMENTAR 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. - 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. 2. NETWORK OPTIMIZATION: - 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 | |
|---|---|
| WRITTEN AND ORAL EXAMINATION. IN THE WRITTEN TEST WILL BE CHECKED THE ABILITY TO APPLY THE KNOWLEDGE GAINED. IN THE ORAL EXAMINATION WILL BE VERIFIED THE CORRECT UNDERSTANDING OF THE TOPICS COVERED. |
| Texts | |
|---|---|
| - M.S. BAZARAA, J.J JARVIS & H.D. SHERALI LINEAR PROGRAMMING AND NETWORK FLOWS, SECOND EDITION, JOHN WILEY, 1990. - LECTURE SLIDES TO LEARN MORE: - HILLIER FREDERICK S., RICERCA OPERATIVA, MCGRAW-HILL EDUCATION, 2010. |
| More Information | |
|---|---|
| EMAIL ADDRESS FOR ANY QUESTIONS: RAFFAELE@UNISA.IT |
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