# Computer science | OPERATIONS RESEARCH

## Computer science OPERATIONS RESEARCH

 0512100012 DIPARTIMENTO DI INFORMATICA EQF6 COMPUTER SCIENCE 2017/2018

 OBBLIGATORIO YEAR OF COURSE 3 YEAR OF DIDACTIC SYSTEM 2015 SECONDO SEMESTRE
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/09 6 48 LESSONS SUPPLEMENTARY COMPULSORY SUBJECTS
 RAFFAELE CERULLI T FRANCESCO CARRABS
Objectives
KNOWLEDGE AND UNDERSTANDING
THE OPERATIONAL RESEARCH COURSE AIMS TO PROVIDE KNOWLEDGE NEEDED TO SOLVE DECISION PROBLEMS, FORMULATED AS CONTINUOUS LINEAR PROGRAMMING PROBLEMS. STUDENTS WILL LEARN HOW TO FORMULATE REAL PROBLEMS BY MEANS OF LINEAR PROGRAMMING. THE SIMPLEX METHOD TO SOLVE MATHEMATICAL MODELS WITH CONTINUOUS VARIABLES WILL ALSO BE TAUGHT. STUDENTS WILL ALSO ACQUIRE KNOWLEDGE FOR THE STUDY OF SENSITIVITY ANALYSIS APPLIED TO CONTINUOUS LINEAR PROGRAMMING PROBLEMS. BASIC KNOWLDGE ABOUT THE RESOLUTION OF OPTIMIZATION MODEL THROUGH THE EXCEL SPREADSHEET SOFTWARE WILL ALSO BE ACQUIRED.

APPLYING KNOWLEDGE AND UNDERSTANDING
•KNOW HOW TO MODEL REAL WORLD OPTIMIZATION PROBLEMS;
•KNOW HOW TO APPLY THE SIMPLEX METHOD TO SOLVE LINEAR PROGRAMMING PROBLEMS.
•KNOW HOW TO APPLY THE APPROPRIATE ALGORITHMS TO USE TO SOLVE GRAPH OPTIMIZATION PROBLEMS.
Prerequisites
STUDENTS SHOULD KNOW BASIC CONCEPTS OF MATHEMATICS ANALYSIS, DISCRETE MATHEMATICS.
Contents
1. LINEAR PROGRAMMING (LP):
- ELEMENTARY OPERATIONS ON MATRICES AND VECTORS; POLYHEDRA; EXTREME DIRECTIONS, VERTICES; REPRESENTATION THEOREM; TRANSFORMING A REAL PROBLEM INTO AN OPTIMIZATION PROBLEM; SIMPLEX METHOD: EXTREME POINTS, OPTIMALITY AND UNBOUNDEDNESS CONDITIONS. SIMPLEX METHOD ALGEBRA: INITIAL BASIC FEASIBLE SOLUTION, TWO-PHASES METHOD, BIG-M METHOD, SIMPLEX CONVERGENCE. USE OF THE EXCEL SOFTWARE TO SOLVE 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, OPTIMAL POINT VARIATION, OPTIMAL SOLUTION VALUE VARIATION BY CHANGING DATA.

2. NETWORK OPTIMIZATION:
- FORMULATIONS AND RESOLUTION ALGORITHMS FOR THE FOLLOWING NETWORK FLOW PROBLEMS: SHORTEST PATH, MINIMUM SPANNING TREE, MAX FLOW, TRANSPORTATION PROBLEM.
Teaching Methods
THE COURSE IS ORGANIZED IN 48 HOURS OF FRONTAL LESSONS (6 CFU), USING PROJECTED SLIDES. AT THE END OF EACH TOPIC, SOME APPLICATION EXAMPLES AND EXERCISES ARE PRESENTED.
Verification of learning
THE FINAL EXAM IS DESIGNED TO EVALUATE AS A WHOLE: THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED IN THE COURSE, AS WELL AS THE ABILITY TO APPLY SUCH KNOWLEDGE FOR THE RESOLUTION OF LINEAR ROGRAMMING 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 TOPICS OF THE COURSE. USUALLY, THE WRITTEN TEST LASTS 120 MINUTES. 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. SOME EXAMINATION SESSIONS COULD ONLY CONSIST OF A WRITTEN TEST.
Texts
- M.S. BAZARAA, J.J. JARVIS & H.D. SHERALI, LINEAR PROGRAMMING AND NETWORK FLOWS, FOURTH EDITION, JOHN WILEY, 2010.
- APPUNTI DELLE LEZIONI.

PER APPROFONDIMENTI:
HILLIER FREDERICK S., RICERCA OPERATIVA, MCGRAW-HILL EDUCATION, 2010.
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