Ingegneria Gestionale | Operational Research

cod. 0612600014

OPERATIONAL RESEARCH

	0612600014
	DIPARTIMENTO DI INGEGNERIA INDUSTRIALE

	INDUSTRIAL ENGINEERING AND MANAGEMENT
	2014/2015

PERCORSO COMUNE

	OBBLIGATORIO
	YEAR OF COURSE 3
	YEAR OF DIDACTIC SYSTEM 2012
	PRIMO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/09	6	60	LESSONS	BASIC COMPULSORY SUBJECTS

	Objectives
	THE COURSE AIMS AT THE ACQUISITION OF THE BASIC ELEMENTS OF OPERATIONS RESEARCH: OPTIMIZATION TECHNIQUES, LINEAR AND NONLINEAR PROGRAMMING, INTEGER LINEAR PROGRAMMING, GRAPH THEORY, ALGORITHMS FOR FINDING SHORTEST PATHS ON GRAPHS. LEARNING OUTCOMES OF COURSE CONSIST OF THE ACHIEVEMENT OF RESULTS AND DEMONSTRATION TECHNIQUES, AS WELL AS THE ABILITY TO SOLVE EXERCISES AND TO USE THE CALCULUS INSTRUMENTS. THE COURSE’S MAIN AIM, STARTING FROM THE BASIC KNOWLEDGE OF MATHEMATICS AND LINEAR ALGEBRA, CONSIST IN DEALING WITH PROBLEMS OF LINEAR AND NON-LINEAR PROGRAMMING, GRAPH THEORY, AND PROVIDING AND DEVELOPING USEFUL TOOLS FOR A SCIENTIFIC APPROACH TO PROBLEMS AND PHENOMENA THAT STUDENTS ENCOUNTER IN THE PURSUIT OF THEIR STUDIES. THE THEORETICAL PART OF THE COURSE WILL BE PRESENTED IN A RIGOROUS BUT CONCISE WAY AND ACCOMPANIED BY A PARALLEL EXERCISE ACTIVITIES DESIGNED TO PROMOTE THE UNDERSTANDING OF CONCEPTS. KNOWLEDGE AND UNDERSTANDING UNDERSTANDING OF THE TERMINOLOGY USED IN OPERATIONS RESEARCH; KNOWLEDGE OF DEMONSTRATION METHODS; KNOWLEDGE OF THE FUNDAMENTAL CONCEPTS OF OPERATIONS RESEARCH. APPLYING KNOWLEDGE AND UNDERSTANDING KNOWING HOW TO APPLY THEOREMS AND RULES DESIGNED TO SOLVE PROBLEMS. KNOWING HOW TO CONSISTENTLY BUILD SOME DEMONSTRATIONS. KNOWING HOW TO BUILD METHODS AND PROCEDURES FOR THE RESOLUTION OF PROBLEMS. KNOWING HOW TO PERFORM COMPLEX CALCULATIONS IN THE CONTEXT OF LINEAR PROGRAMMING, NONLINEAR, AND GRAPH THEORY. MAKING JUDGEMENTS KNOWING HOW TO IDENTIFY THE MOST APPROPRIATE METHODS TO EFFICIENTLY SOLVE AN OPERATIONAL RESEARCH PROBLEM. TO BE ABLE TO FIND SOME OPTIMIZATIONS TO THE SOLVING PROCESS OF AN OPERATIONAL RESEARCH PROBLEM. COMMUNICATION SKILLS ABILITY TO WORK IN GROUPS. ABILITY TO ORALLY PRESENT A TOPIC RELATED TO MATHEMATICS. LEARNING SKILLS SKILL OF APPLYING THE ACQUIRED KNOWLEDGE TO DIFFERENT CONTEXTS FROM THOSE PRESENTED DURING THE COURSE. SKILL TO DEEPEN THE TOPICS DEALT WITH BY USING MATERIALS DIFFERENT THAN THOSE PROPOSED.

THE COURSE AIMS AT THE ACQUISITION OF THE BASIC ELEMENTS OF OPERATIONS RESEARCH: OPTIMIZATION TECHNIQUES, LINEAR AND NONLINEAR PROGRAMMING, INTEGER LINEAR PROGRAMMING, GRAPH THEORY, ALGORITHMS FOR FINDING SHORTEST PATHS ON GRAPHS. LEARNING OUTCOMES OF COURSE CONSIST OF THE ACHIEVEMENT OF RESULTS AND DEMONSTRATION TECHNIQUES, AS WELL AS THE ABILITY TO SOLVE EXERCISES AND TO USE THE CALCULUS INSTRUMENTS. THE COURSE’S MAIN AIM, STARTING FROM THE BASIC KNOWLEDGE OF MATHEMATICS AND LINEAR ALGEBRA, CONSIST IN DEALING WITH PROBLEMS OF LINEAR AND NON-LINEAR PROGRAMMING, GRAPH THEORY, AND PROVIDING AND DEVELOPING USEFUL TOOLS FOR A SCIENTIFIC APPROACH TO PROBLEMS AND PHENOMENA THAT STUDENTS ENCOUNTER IN THE PURSUIT OF THEIR STUDIES. THE THEORETICAL PART OF THE COURSE WILL BE PRESENTED IN A RIGOROUS BUT CONCISE WAY AND ACCOMPANIED BY A PARALLEL EXERCISE ACTIVITIES DESIGNED TO PROMOTE THE UNDERSTANDING OF CONCEPTS.
KNOWLEDGE AND UNDERSTANDING
UNDERSTANDING OF THE TERMINOLOGY USED IN OPERATIONS RESEARCH;
KNOWLEDGE OF DEMONSTRATION METHODS;
KNOWLEDGE OF THE FUNDAMENTAL CONCEPTS OF OPERATIONS RESEARCH.
APPLYING KNOWLEDGE AND UNDERSTANDING
KNOWING HOW TO APPLY THEOREMS AND RULES DESIGNED TO SOLVE PROBLEMS.
KNOWING HOW TO CONSISTENTLY BUILD SOME DEMONSTRATIONS.
KNOWING HOW TO BUILD METHODS AND PROCEDURES FOR THE RESOLUTION OF PROBLEMS.
KNOWING HOW TO PERFORM COMPLEX CALCULATIONS IN THE CONTEXT OF LINEAR PROGRAMMING, NONLINEAR, AND GRAPH THEORY.
MAKING JUDGEMENTS
KNOWING HOW TO IDENTIFY THE MOST APPROPRIATE METHODS TO EFFICIENTLY SOLVE AN OPERATIONAL RESEARCH PROBLEM.
TO BE ABLE TO FIND SOME OPTIMIZATIONS TO THE SOLVING PROCESS OF AN OPERATIONAL RESEARCH PROBLEM.
COMMUNICATION SKILLS
ABILITY TO WORK IN GROUPS.
ABILITY TO ORALLY PRESENT A TOPIC RELATED TO MATHEMATICS.
LEARNING SKILLS
SKILL OF APPLYING THE ACQUIRED KNOWLEDGE TO DIFFERENT CONTEXTS FROM THOSE PRESENTED DURING THE COURSE.
SKILL TO DEEPEN THE TOPICS DEALT WITH BY USING MATERIALS DIFFERENT THAN THOSE PROPOSED.

	Prerequisites
	FOR THE SUCCESSFUL ACHIEVEMENT OF THE GOALS, STUDENT IS RECOMMENDED TO HAVE BASIC KNOWLEDGE OF MATHEMATICS, LINEAR ALGEBRA AND ANALYTIC GEOMETRY.

	Contents
	MODELS OF OPERATIONS RESEARCH: THE MODELING APPROACH. OPTIMIZATION MODELS. (HOURS LECTURE/PRACTICE/LABORATORY 3/1/-) CONTINUOUS OPTIMIZATION: ONE-DIMENSIONAL OPTIMIZATION. ONE-DIMENSIONAL OPTIMIZATION METHODS. MULTIDIMENSIONAL NOT-CONSTRAINED OPTIMIZATION. OPTIMALITY CONDITIONS. DIRECT CLIMBING METHODS. THE GRADIENT METHOD. MULTIDIMENSIONAL CONSTRAINED OPTIMIZATION. ADMISSIBLE DIRECTION METHODS. (HOURS 4/2/-) LINEAR PROGRAMMING: INTRODUCTION TO LINEAR PROGRAMMING. GRAPHICAL REPRESENTATION OF A PROGRAMMING LINEAR PROBLEM . THE CONSTRAINTS. THE DOMAIN OF ELIGIBILITY. THE OBJECTIVE FUNCTION. GRAPHICAL METHODS. EXAMPLES OF LINEAR PROGRAMMING MODELS. GRAPHICAL SOLUTION OF A PROGRAMMING LINEAR PROBLEM OF P.L. IN TWO VARIABLES. DESCRIPTION OF THE SIMPLEX ALGORITHM. (HOURS 12/4/-) DUALITY IN LINEAR PROGRAMMING: FUNDAMENTAL RESULTS OF THE DUALITY THEORY. INTERPRETATION OF DUALITY. (HOURS 3/1/-) INTEGER PROGRAMMING: FORMULATION AND SOLUTION OF INTEGER LINEAR PROGRAMMING PROBLEMS. FORMULATION OF A PROBLEM P.L.I. THE BRANCH AND BOUND METHOD. APPLICATION OF THE BRANCH AND BOUND METHOD. AN INTEGER LINEAR PROGRAMMING PROBLEM. (HOURS 10/4/-) ELEMENTS OF GRAPH THEORY: GRAPH DESIGN. VERTEX-VERTEX ADJACENCY MATRIX. ARC-VERTEX ADJACENCY MATRIX. LISTS P-S. (HOURS 7/3/-) THE PROBLEM OF THE MINIMUM PATH: CLASSIFICATION OF MINIMUM PATH PROBLEMS AND ALGORITHMS. MINIMUM PATH MODELING. THE MINIMUM PATH OF ACYCLIC GRAPHS. TOPOLOGICAL SORT OF AN ACYCLIC GRAPH. ALGORITHM FOR THE MINIMUM PATHS ON ACYCLIC GRAPHS. MINIMUM PATH OF CYCLIC GRAPHS: DIJKSTRA'S ALGORITHM. (HOURS 4/2/-) TOTAL HOURS 43/17/-

Contents

MODELS OF OPERATIONS RESEARCH: THE MODELING APPROACH. OPTIMIZATION MODELS. (HOURS LECTURE/PRACTICE/LABORATORY 3/1/-)
CONTINUOUS OPTIMIZATION: ONE-DIMENSIONAL OPTIMIZATION. ONE-DIMENSIONAL OPTIMIZATION METHODS. MULTIDIMENSIONAL NOT-CONSTRAINED OPTIMIZATION. OPTIMALITY CONDITIONS. DIRECT CLIMBING METHODS. THE GRADIENT METHOD. MULTIDIMENSIONAL CONSTRAINED OPTIMIZATION. ADMISSIBLE DIRECTION METHODS. (HOURS 4/2/-)
LINEAR PROGRAMMING: INTRODUCTION TO LINEAR PROGRAMMING. GRAPHICAL REPRESENTATION OF A PROGRAMMING LINEAR PROBLEM . THE CONSTRAINTS. THE DOMAIN OF ELIGIBILITY. THE OBJECTIVE FUNCTION. GRAPHICAL METHODS. EXAMPLES OF LINEAR PROGRAMMING MODELS. GRAPHICAL SOLUTION OF A PROGRAMMING LINEAR PROBLEM OF P.L. IN TWO VARIABLES. DESCRIPTION OF THE SIMPLEX ALGORITHM. (HOURS 12/4/-)
DUALITY IN LINEAR PROGRAMMING: FUNDAMENTAL RESULTS OF THE DUALITY THEORY. INTERPRETATION OF DUALITY. (HOURS 3/1/-)
INTEGER PROGRAMMING: FORMULATION AND SOLUTION OF INTEGER LINEAR PROGRAMMING PROBLEMS. FORMULATION OF A PROBLEM P.L.I. THE BRANCH AND BOUND METHOD. APPLICATION OF THE BRANCH AND BOUND METHOD. AN INTEGER LINEAR PROGRAMMING PROBLEM. (HOURS 10/4/-)
ELEMENTS OF GRAPH THEORY: GRAPH DESIGN. VERTEX-VERTEX ADJACENCY MATRIX. ARC-VERTEX ADJACENCY MATRIX. LISTS P-S. (HOURS 7/3/-)
THE PROBLEM OF THE MINIMUM PATH: CLASSIFICATION OF MINIMUM PATH PROBLEMS AND ALGORITHMS. MINIMUM PATH MODELING. THE MINIMUM PATH OF ACYCLIC GRAPHS. TOPOLOGICAL SORT OF AN ACYCLIC GRAPH. ALGORITHM FOR THE MINIMUM PATHS ON ACYCLIC GRAPHS. MINIMUM PATH OF CYCLIC GRAPHS: DIJKSTRA'S ALGORITHM. (HOURS 4/2/-)
TOTAL HOURS 43/17/-

	Teaching Methods
	THE COURSE COVERS THEORETICAL LESSONS, DURING WHICH ALL COURSE CONTENTS WILL BE PRESENTED BY LECTURES, AND CLASSROOM EXERCISES DURING WHICH THE MAIN TOOLS NECESSARY FOR THE RESOLUTION OF EXERCISES RELATED TO TEACHING CONTENTS WILL BE PROVIDED.

	Verification of learning
	THE FINAL EXAM IS DESIGNED TO EVALUATE AS A WHOLE: •THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED DURING THE COURSE •THE MASTERY OF THE MATHEMATICAL LANGUAGE IN THE WRITTEN AND ORAL PROOFS •THE SKILL OF PROVING THEOREMS •THE SKILL OF SOLVING EXERCISES •THE SKILL TO IDENTIFY AND APPLY THE BEST AND EFFICIENT METHOD IN EXERCISES SOLVING •THE ABILITY TO APPLY THE ACQUIRED KNOWLEDGE TO DIFFERENT CONTEXTS FROM THOSE PRESENTED DURING THE COURSE. THE EXAM CONSISTS OF A WRITTEN PROOF AND AN ORAL INTERVIEW. WRITTEN PROOF: THE WRITTEN PROOF CONSISTS IN SOLVING TYPICAL PROBLEMS PRESENTED IN THE COURSE. IN THE CASE OF A SUFFICIENT PROOF, IT WILL BE EVALUATED BY THREE SCALES. ORAL INTERVIEW: THE INTERVIEW IS DEVOTED TO EVALUATE THE DEGREE OF KNOWLEDGE OF ALL THE TOPICS OF THE COURSE, AND COVERS DEFINITIONS, THEOREMS PROOFS, EXERCISES SOLVING. FINAL EVALUATION: THE FINAL MARK, EXPRESSED IN THIRTIETHS, DEPENDS ON THE MARK OF THE WRITTEN PROOF, WITH CORRECTIONS IN EXCESS OR DEFECT ON THE BASIS OF THE ORAL INTERVIEW.

Verification of learning

THE FINAL EXAM IS DESIGNED TO EVALUATE AS A WHOLE:
•THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED DURING THE COURSE
•THE MASTERY OF THE MATHEMATICAL LANGUAGE IN THE WRITTEN AND ORAL PROOFS
•THE SKILL OF PROVING THEOREMS
•THE SKILL OF SOLVING EXERCISES
•THE SKILL TO IDENTIFY AND APPLY THE BEST AND EFFICIENT METHOD IN EXERCISES SOLVING
•THE ABILITY TO APPLY THE ACQUIRED KNOWLEDGE TO DIFFERENT CONTEXTS FROM THOSE PRESENTED DURING THE COURSE.
THE EXAM CONSISTS OF A WRITTEN PROOF AND AN ORAL INTERVIEW.
WRITTEN PROOF: THE WRITTEN PROOF CONSISTS IN SOLVING TYPICAL PROBLEMS PRESENTED IN THE COURSE. IN THE CASE OF A SUFFICIENT PROOF, IT WILL BE EVALUATED BY THREE SCALES.
ORAL INTERVIEW: THE INTERVIEW IS DEVOTED TO EVALUATE THE DEGREE OF KNOWLEDGE OF ALL THE TOPICS OF THE COURSE, AND COVERS DEFINITIONS, THEOREMS PROOFS, EXERCISES SOLVING.
FINAL EVALUATION: THE FINAL MARK, EXPRESSED IN THIRTIETHS, DEPENDS ON THE MARK OF THE WRITTEN PROOF, WITH CORRECTIONS IN EXCESS OR DEFECT ON THE BASIS OF THE ORAL INTERVIEW.