2. Professors
  3. D'AMBROSIO CIRIACO
  4. Teaching

DECISION SUPPORT SYSTEMS

CIRIACO D'AMBROSIO DECISION SUPPORT SYSTEMS

0522200049
DEPARTMENT OF MATHEMATICS
EQF7
MATHEMATICS
2024/2025

YEAR OF COURSE 2
YEAR OF DIDACTIC SYSTEM 2018
SPRING SEMESTER
CFUHOURSACTIVITY
648LESSONS
RAFFAELE CERULLI T Curriculum
CIRIACO D'AMBROSIO Curriculum
ExamDate
SISTEMI DI SUPPORTO ALLE DECISIONI15/01/2025 - 10:00
SISTEMI DI SUPPORTO ALLE DECISIONI05/02/2025 - 10:00
SISTEMI DI SUPPORTO ALLE DECISIONI19/02/2025 - 10:00
Objectives
THE DECISION SUPPORT SYSTEMS COURSE AIMS TO PROVIDE A SERIES OF TOOLS TO DEAL WITH DECISION-MAKING PROBLEMS CHARACTERIZED BY A HIGH LEVEL OF COMPLEXITY, BY SITUATIONS OF UNCERTAINTY ABOUT DATA, OR BY THE PRESENCE OF MULTIPLE AND CONFLICTING OBJECTIVES. IN ADDITION, IT INTRODUCES THE MAIN MATHEMATICAL MODEL-BASED APPROACHES FOR MACHINE LEARNING AND DATA MINING TO ADDRESS CLASSIFICATION AND IDENTIFICATION, REGRESSION, AND CLUSTERING PROBLEMS.
THE COURSE HAS A STRONG METHODOLOGICAL AND APPLICATIVE CONNOTATION. IN ADDITION TO THE NECESSARY THEORETICAL CONTENT, THE COURSE AIMS TO PROVIDE THE KNOWLEDGE FOR THE USE OF SOFTWARE TO SOLVE PRACTICAL PROBLEMS.

KNOWLEDGE AND UNDERSTANDING
AT THE END OF THE COURSE THE STUDENT:
- WILL KNOW THE BASIC CONCEPTS OF BIG DATA AND DATA MINING;
- UNDERSTAND THE MAIN DIFFERENCES BETWEEN THE CLASSICAL DEFINITION OF ALGORITHM AND MACHINE LEARNING ALGORITHM;
- UNDERSTAND THE MAIN DIFFERENCES BETWEEN SUPERVISED AND UNSUPERVISED LEARNING;
- WILL KNOW THE MAIN STEPS FOR THE REALIZATION OF A MACHINE LEARNING SYSTEM;
- WILL KNOW THE MAIN CLASSIFICATION, REGRESSION, AND CLUSTERING ALGORITHMS;
- WILL KNOW THE MAIN FUNDAMENTALS ON WHICH NEURAL NETWORKS ARE BASED.

APPLYING KNOWLEDGE AND UNDERSTANDING
AT THE END OF THE COURSE THE STUDENT WILL BE ABLE TO:
- USE IT TOOLS FOR THE CREATION OF SIMPLE DECISION-MAKING MODELS;
- DESIGN AND IMPLEMENT SIMPLE SYSTEMS BASED ON SUPERVISED LEARNING;
- DESIGN AND IMPLEMENT SIMPLE SYSTEMS BASED ON UNSUPERVISED LEARNING;
- DESIGN, IMPLEMENT AND APPLY A MACHINE LEARNING SYSTEM FOR CLASSIFICATION, REGRESSION, AND CLUSTERING IN DIFFERENT CONTEXTS;
- DESIGN, IMPLEMENT AND APPLY A MACHINE LEARNING SYSTEM BASED ON NEURAL NETWORKS.

MAKING JUDGMENTS
AT THE END OF THE COURSE THE STUDENT WILL BE ABLE TO:
- AUTONOMOUSLY AND EFFECTIVELY RECOGNIZE THE MOST SUITABLE MODELS AND MACHINE LEARNING SYSTEMS FOR SOLVING THE PROBLEM UNDER CONSIDERATION;
- CONFIGURE THE BEHAVIOR OF AN AUTOMATIC SYSTEM BASED ON THE RESULTS OBTAINED AND TO BE ABLE TO INTERPRET THE RESULTS CORRECTLY.

COMMUNICATION SKILLS
AT THE END OF THE COURSE THE STUDENT WILL HAVE ACQUIRED ADEQUATE SKILLS IN THE ANALYSIS OF DECISION-MAKING PROBLEMS. HE/SHE WILL BE ABLE TO ANALYZE AND PRESENT THE APPROACHES TO SOLVE THESE PROBLEMS USING AN APPROPRIATE NOTATION AND AN APPROPRIATE LANGUAGE THAT HIGHLIGHTS THE SKILLS OF THE THEORETICAL AND PRACTICAL METHODOLOGIES ACQUIRED. THE STUDENT WILL ALSO BE ABLE TO DESIGN A DECISION-MAKING SYSTEM AND TO CLEARLY DESCRIBE THE CONCEPTS NECESSARY FOR UNDERSTANDING THE PRINCIPLES, MODELS AND ALGORITHMS USED FOR ITS IMPLEMENTATION.

LEARNING SKILLS
THE STUDENT WILL BE ABLE TO:
- USE THE DOCUMENTATION OF IT TOOLS FOR THE IMPLEMENTATION OF A MACHINE LEARNING SYSTEM;
- USE SOFTWARE LIBRARIES AND CONTINUOUSLY UPDATE THEIR KNOWLEDGE, USING THE LITERATURE AND TECHNICAL DOCUMENTATION OF THE ALGORITHMS AND TOOLS PRESENTED IN THE COURSE;
- APPLY THE ACQUIRED KNOWLEDGE TO CONTEXTS DIFFERENT FROM THOSE PRESENTED DURING THE COURSE;
- DELVE DEEPER INTO THE TOPICS COVERED USING TEACHING OR SCIENTIFIC MATERIALS DIFFERENT FROM THE ONES USED DURING THE COURSE.
Prerequisites
THE COURSE REQUIRES A KNOWLEDGE OF THE BASIC NOTIONS OF LINEAR ALGEBRA AND ANALYTICAL GEOMETRY AND THE CAPACITY OF SOLVING SYSTEMS OF LINEAR EQUATIONS AND PERFORMING OPERATIONS ON VECTORS AND MATRICES.
Contents
1. LINEAR PROGRAMMING (PL) (LECTURES: 12H; EXERCISE 4H)
- BASIC OPERATIONS ON MATRICES AND VECTORS, SYSTEM OF LINEAR EQUATIONS.
- FORMULATION OF REAL PROBLEMS. PL PROBLEMS IN STANDARD AND CANONICAL FORM. TRANSFORMATION RULES BETWEEN STANDARD AND CANONICAL FORM.
- GRAPHICAL RESOLUTION OF PL PROBLEMS. DEFINITION OF HYPERPLANES, HALF-SPACES, POLYHEDRAL, CONVEX FUNCTION AND CONVEX SET. CORRESPONDENCE BETWEEN THE LOCAL AND GLOBAL OPTIMUM FOR THE PL PROBLEMS (THEOREM AND PROOF).
- FINDING THE EXTREME DIRECTIONS OF A POLYHEDRON, REPRESENTATION THEOREM. RESOLUTION OF PL PROBLEMS BY REPRESENTATION THEOREM.

2. THE SIMPLEX METHOD (LECTURES: 8H; EXERCISE 4H)
- EXTREME POINTS OF A POLYHEDRON AND BASIC FEASIBLE SOLUTIONS. CORRESPONDENCE BETWEEN BASIC FEASIBLE SOLUTIONS AND EXTREME POINTS (THEOREM AND PROOF). OPTIMALITY AND UNBOUNDEDNESS CONDITIONS, SIMPLEX METHOD ALGEBRA, DEGENERATE BASIC FEASIBLE SOLUTION AND CYCLING PHENOMENON, SIMPLEX CONVERGENCE.
- STARTING BASIC FEASIBLE SOLUTION: TWO-PHASES METHOD AND BIG-M METHOD.
3. THE DUALITY THEORY (LECTURES: 8H; EXERCISE 4H)
- DUAL PROBLEM FORMULATION, THEOREM OF WEAK DUALITY, THEOREM OF STRONG DUALITY, COMPLEMENTARY SLACKNESS THEOREM, COMPUTATION OF THE DUAL OPTIMAL SOLUTION BY USING THE COMPLEMENTARY SLACKNESS CONDITIONS, PROPERTIES OBTAINED BY THE ORTHOGONALITY CONDITIONS OF THE COMPLEMENTARY SLACKNESS THEOREM, PRIMAL-DUAL RELATION;
- ECONOMIC INTERPRETATION OF DUAL VARIABLES;
- 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: 12H; EXERCISE 4H)
FORMULATIONS AND ALGORITHMS FOR THE FOLLOWING NETWORK OPTIMIZATION PROBLEMS:
- MINIMUM COST FLOW;
- TRANSPORTATION;
- MAX FLOW;
- SHORTEST PATH;
- MINIMUM SPANNING TREE.
TOTALLY UNIMODULAR MATRICES AND THEIR IMPACT ON THE COMPLEXITY OF SOME OPTIMIZATION PROBLEMS ON GRAPHS.
Teaching Methods
THE COURSE IS ORGANIZED IN 56 HOURS OF FRONTAL LESSONS (7 CFU), USING PROJECTED SLIDES. AT THE END OF EACH TOPIC, SOME EXAMPLES AND CLASSROOM EXERCISES ARE PRESENTED. DURING THE CLASSROOM EXERCISES, THE STUDENTS FACE SOME EXERCISES TO SOLVE BY USING THE TECHNIQUES PRESENTED IN THE THEORETICAL LECTURES. THE RESOLUTION OF THE EXERCISES, WHICH IS CARRIED OUT UNDER THE SUPERVISION OF THE TEACHER, SEEKS TO DEVELOP AND STRENGTHEN THE STUDENT’S CAPACITY OF IDENTIFYING THE MOST APPROPRIATE TECHNIQUES TO SOLVE THEM. METHODS TO PRODUCE A CLEAR AND ACCURATE PRESENTATION OF THE ACHIEVED RESULTS ARE ALSO PROPOSED.
Verification of learning
THERE ARE NOT MIDTERM EXAMINATIONS FOR THIS COURSE.
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 IS DESIGNED TO ASSESS THE ABILITY TO SOLVE OPTIMIZATION PROBLEMS AND NORMALLY LASTS 120 MINUTES. IT CONSISTS OF 4 OR 5 EXERCISES, AND POSSIBLY OPEN-ENDED QUESTIONS, WHICH ARE GIVEN A SCORE. THE SUM OF THESE SCORES IS 30. TYPICAL TOPICS OF THE EXERCISES CONCERN: THE GRAPHICAL RESOLUTION OF PL PROBLEMS AND THE COMPUTATION OF THE EXTREME DIRECTIONS OF THE POLYHEDRON, THE FORMULATION OF OPTIMIZATION PROBLEMS, THE RESOLUTION OF A PL PROBLEM BY USING THE SIMPLEX METHOD, THE CONSTRUCTION OF THE DUAL PROBLEM, THE SENSITIVITY ANALYSIS AND THE RESOLUTION OF GRAPH PROBLEMS PRESENTED IN THE COURSE. THE SCORE OF THE WRITTEN EXAM IS EQUAL TO THE SUM OF THE SCORES ASSIGNED BY THE TEACHER TO THE EXERCISES SOLVED BY THE STUDENT. IS ADMITTED TO THE ORAL EXAMINATION THE STUDENT THAT GAINS A SCORE OF AT LEAST 18/30.
- WITH THE ORAL INTERVIEW, ARE EVALUATED THE KNOWLEDGE ABOUT THE MODELLING AND SOLVING OF LINEAR PROGRAMMING PROBLEMS. THE INTERVIEW INCLUDES THE PRELIMINARY DISCUSSION OF THE WRITTEN TEST AND VARIOUS QUESTIONS REGARDING THE TOPICS OF THE COURSE PROGRAM. THE MINIMUM ASSESSMENT LEVEL (18) IS AWARDED WHEN THE STUDENT SHOWS A FRAGMENTARY KNOWLEDGE OF THEORETICAL CONTENTS AND A LIMITED ABILITY TO FORMULATE OPTIMIZATION PROBLEMS AND TO APPLY ALGORITHMS TO SOLVE THEM. THE MAXIMUM ASSESSMENT LEVEL (30) IS ATTRIBUTED WHEN THE STUDENT SHOWS A COMPLETE AND IN-DEPTH KNOWLEDGE OF THE COURSE TOPICS AND A REMARKABLE ABILITY TO IDENTIFY THE MOST APPROPRIATE METHODS TO SOLVE THE OPTIMIZATION PROBLEMS FACED.
THE FINAL GRADE IS DEFINED BY THE TEACHER ACCORDING TO THE RESULTS OF THE TWO TESTS. IN ANY CASE, THE FINAL GRADE CANNOT EXCEED THE WRITTEN TEST GRADE BY MORE THAN 6 POINTS.

THE ORAL INTERVIEW IS USUALLY SCHEDULED WITHIN ONE WEEK OF THE WRITTEN EXAM AND IT IS COMMUNICATED TOGETHER WITH THE PUBLICATION OF THE RESULTS OF THE WRITTEN TEST ON THE TEACHER'S WEBSITE.
TO PROVIDE MORE TIME FOR THE PREPARATION OF THE ORAL INTERVIEW, IT IS ALLOWED FOR THE STUDENT TO TAKE THE ORAL INTERVIEW IN ANY CALL OF THE SAME EXAM SESSION. THE STUDENT WHO WANTS TO TAKE ADVANTAGE OF THIS POSSIBILITY MUST NOTIFY THE TEACHER BY EMAIL IMMEDIATELY AFTER THE PUBLICATION OF THE RESULTS OF 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 RESOURCES:
HILLIER FREDERICK S., RICERCA OPERATIVA, MCGRAW-HILL EDUCATION, 2010.
More Information
- EMAIL: RAFFAELE@UNISA.IT
- THE COURSE LANGUAGE IS ITALIAN.
- THE ATTENDANCE OF THE LESSONS IS HIGHLY RECOMMENDED.
- OTHER SUPPORTING MATERIAL IS AVAILABLE ON THE WEBPAGE: HTTPS://DOCENTI.UNISA.IT/001227/RISORSE
- OFFICE HOURS FOR STUDENTS ARE AVAILABLE ON THE WEBPAGE: HTTPS://DOCENTI.UNISA.IT/001227/HOME
Lessons Timetable

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