Francesco CARRABS | OPERATIONS RESEARCH

cod. 0512300034

OPERATIONS RESEARCH

	0512300034
	DIPARTIMENTO DI MATEMATICA
	EQF6
	MATHEMATICS
	2020/2021

PERCORSO SHARED STUDY PATHWAY

	OBBLIGATORIO
	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2018
	PRIMO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/09	7	56	LESSONS	SUPPLEMENTARY COMPULSORY SUBJECTS

PROFESSORS

	FRANCESCO CARRABS T Curriculum
	RAFFAELE CERULLI Curriculum

	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 KNOWLEDGE ABOUT THE RESOLUTION OF OPTIMIZATION MODEL THROUGH THE EXCEL SPREADSHEET SOFTWARE WILL ALSO BE ACQUIRED. APPLYING KNOWLEDGE AND UNDERSTANDING ABILITY TO: - FORMULATE A REAL-WORLD OPTIMIZATION PROBLEM AS A LINEAR PROGRAMMING MODEL (WHEN POSSIBLE); - APPLY THE SIMPLEX METHOD TO SOLVE LINEAR PROGRAMMING MODELS. - CARRY OUT THE SENSITIVE ANALYSIS OF THE OPTIMAL SOLUTIONS OF SOLVED PROBLEMS. - APPLY THE APPROPRIATE ALGORITHMS TO SOLVE GRAPH OPTIMIZATION PROBLEMS.

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 KNOWLEDGE ABOUT THE RESOLUTION OF OPTIMIZATION MODEL THROUGH THE EXCEL SPREADSHEET SOFTWARE WILL ALSO BE ACQUIRED.

APPLYING KNOWLEDGE AND UNDERSTANDING
ABILITY TO:
- FORMULATE A REAL-WORLD OPTIMIZATION PROBLEM AS A LINEAR PROGRAMMING MODEL (WHEN POSSIBLE);
- APPLY THE SIMPLEX METHOD TO SOLVE LINEAR PROGRAMMING MODELS.
- CARRY OUT THE SENSITIVE ANALYSIS OF THE OPTIMAL SOLUTIONS OF SOLVED PROBLEMS.
- APPLY THE APPROPRIATE ALGORITHMS TO SOLVE GRAPH OPTIMIZATION PROBLEMS.

	Prerequisites
	STUDENTS SHOULD KNOW BASIC CONCEPTS OF MATHEMATICS ANALYSIS AND DISCRETE MATHEMATICS.

	Contents
	1. LINEAR PROGRAMMING (LP) (LECTURES: 10H; EXERCISE 4H) - ELEMENTARY OPERATIONS ON MATRICES AND VECTORS; - TRANSFORMING A REAL PROBLEM INTO AN OPTIMIZATION PROBLEM; - POLYHEDRA; EXTREME DIRECTIONS, VERTICES; REPRESENTATION THEOREM; 2. SIMPLEX METHOD (LECTURES: 6H; EXERCISE 4H) - EXTREME POINTS, OPTIMALITY AND UNBOUNDEDNESS CONDITIONS, SIMPLEX METHOD ALGEBRA, DEGENERATE BASIC FEASIBLE SOLUTION AND CYCLING PHENOMENON, SIMPLEX CONVERGENCE; - INITIAL BASIC FEASIBLE SOLUTION, TWO-PHASES METHOD, BIG-M METHOD; 3. DUALITY (LECTURES: 6H; EXERCISE 6H) - DUAL PROBLEM FORMULATION, 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. - USE OF THE EXCEL SOFTWARE TO SOLVE LINEAR PROGRAMMING PROBLEMS. 4. NETWORK OPTIMIZATION PROBLEMS (LECTURES: 14H; EXERCISE 6H) FORMULATIONS AND RESOLUTION ALGORITHMS FOR THE FOLLOWING NETWORK FLOW PROBLEMS: - TRANSPORTATION; - MAX FLOW; - SHORTEST PATH; - MINIMUM SPANNING TREE.

Contents

1. LINEAR PROGRAMMING (LP) (LECTURES: 10H; EXERCISE 4H)
- ELEMENTARY OPERATIONS ON MATRICES AND VECTORS;
- TRANSFORMING A REAL PROBLEM INTO AN OPTIMIZATION PROBLEM;
- POLYHEDRA; EXTREME DIRECTIONS, VERTICES; REPRESENTATION THEOREM;

2. SIMPLEX METHOD (LECTURES: 6H; EXERCISE 4H)
- EXTREME POINTS, OPTIMALITY AND UNBOUNDEDNESS CONDITIONS, SIMPLEX METHOD ALGEBRA, DEGENERATE BASIC FEASIBLE SOLUTION AND CYCLING PHENOMENON, SIMPLEX CONVERGENCE;
- INITIAL BASIC FEASIBLE SOLUTION, TWO-PHASES METHOD, BIG-M METHOD;

3. DUALITY (LECTURES: 6H; EXERCISE 6H)
- DUAL PROBLEM FORMULATION, 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.
- USE OF THE EXCEL SOFTWARE TO SOLVE LINEAR PROGRAMMING PROBLEMS.

4. NETWORK OPTIMIZATION PROBLEMS (LECTURES: 14H; EXERCISE 6H)
FORMULATIONS AND RESOLUTION ALGORITHMS FOR THE FOLLOWING NETWORK FLOW PROBLEMS:
- TRANSPORTATION;
- MAX FLOW;
- SHORTEST PATH;
- MINIMUM SPANNING TREE.

	Teaching Methods
	THE COURSE IS ORGANIZED IN 48 HOURS OF FRONTAL LESSONS (6 CFU), USING PROJECTED SLIDES. AT THE END OF EACH TOPIC, SOME EXAMPLES AND CLASSROOM EXERCISES ARE PRESENTED. IN CLASS EXERCISES, AN EXERCISE, CONCERNING THE TECHNIQUES PRESENTED IN THE LECTURES, IS ASSIGNED TO THE STUDENTS. THE SOLUTION OF THE EXERCISE, WHICH IS CARRIED OUT UNDER THE SUPERVISION OF THE TEACHER, SEEKS TO DEVELOP AND STRENGTHEN THE STUDENT CAPACITY OF IDENTIFYING THE MOST APPROPRIATE TECHNIQUES TO SOLVE IT. METHODS TO PRODUCE A CLEAR AND ACCURATE PRESENTATION OF THE ACHIEVED RESULTS ARE ALSO PROPOSED.

Teaching Methods

THE COURSE IS ORGANIZED IN 48 HOURS OF FRONTAL LESSONS (6 CFU), USING PROJECTED SLIDES. AT THE END OF EACH TOPIC, SOME EXAMPLES AND CLASSROOM EXERCISES ARE PRESENTED. IN CLASS EXERCISES, AN EXERCISE, CONCERNING THE TECHNIQUES PRESENTED IN THE LECTURES, IS ASSIGNED TO THE STUDENTS. THE SOLUTION OF THE EXERCISE, WHICH IS CARRIED OUT UNDER THE SUPERVISION OF THE TEACHER, SEEKS TO DEVELOP AND STRENGTHEN THE STUDENT CAPACITY OF IDENTIFYING THE MOST APPROPRIATE TECHNIQUES TO SOLVE IT. METHODS TO PRODUCE A CLEAR AND ACCURATE PRESENTATION OF THE ACHIEVED RESULTS ARE ALSO PROPOSED.

	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 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 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. TO STIMULATE THE ATTENDANCE OF THE COURSE, IT IS GIVEN TO THE STUDENT THE CHANCE TO CONFIRM THE WRITTEN EXAMINATION SCORE IN THE FIRST EXAMINATION SESSION AFTER THE COURSE. IN THE EVENT THAT THE EXAM SHOULD TAKE PLACE REMOTELY DUE TO THE COVID-19 EMERGENCY, THE TEACHER CAN DECIDE (BY PROMPTLY INFORMING THE STUDENTS), TO ABOLISH THE WRITTEN TEST. IN THIS CASE, DURING THE ORAL EXAM STUDENTS WILL ALSO BE ASKED TO SOLVE ONE OR MORE EXERCISES OF THE TYPE PROPOSED IN THE WRITTEN TEST.

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 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 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. TO STIMULATE THE ATTENDANCE OF THE COURSE, IT IS GIVEN TO THE STUDENT THE CHANCE TO CONFIRM THE WRITTEN EXAMINATION SCORE IN THE FIRST EXAMINATION SESSION AFTER THE COURSE.

IN THE EVENT THAT THE EXAM SHOULD TAKE PLACE REMOTELY DUE TO THE COVID-19 EMERGENCY, THE TEACHER CAN DECIDE (BY PROMPTLY INFORMING THE STUDENTS), TO ABOLISH THE WRITTEN TEST. IN THIS CASE, DURING THE ORAL EXAM STUDENTS WILL ALSO BE ASKED TO SOLVE ONE OR MORE EXERCISES OF THE TYPE PROPOSED IN THE WRITTEN TEST.

	Texts
	- M.S. BAZARAA, J.J. JARVIS & H.D. SHERALI, LINEAR PROGRAMMING AND NETWORK FLOWS, FOURTH EDITION, JOHN WILEY, 2010. - SLIDES AVAILABLE HERE: HTTPS://DOCENTI.UNISA.IT/020511/RISORSE OTHER RESOURSE: HILLIER FREDERICK S., RICERCA OPERATIVA, MCGRAW-HILL EDUCATION, 2010.

	More Information
	- THE COURSE LANGUAGE IS ITALIAN. - THE ATTENDANCE OF THE LESSONS IS HIGHLY RECOMMENDED. - OTHER SUPPORTING MATERIAL, PROVIDED BY THE TEACHER, IS AVAILABLE ON THE WEBSITE: HTTPS://DOCENTI.UNISA.IT/001227/RISORSE - OFFICE HOURS FOR STUDENTS ARE AVAILABLE HERE: HTTPS://DOCENTI.UNISA.IT/001227/HOME HTTPS://DOCENTI.UNISA.IT/020511/HOME

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Francesco CARRABS | OPERATIONS RESEARCH