35192 - Resources Optimization M

Learning outcomes

The course presents the most effective heuristic algorithms for solving decision-making problems related to the optimal planning and management of resources in complex systems. Students will learn how to analyse the computational performance of these algorithms and their application to real-world problems in logistics and transportation.

Course contents

Recommended prerequisites

Students are expected to be familiar with the basic concepts of Operations Research, with particular reference to linear and integer programming models, graphs and networks, basic algorithms, implementation of computational procedures and computational complexity analysis.

Students are also expected to be able to understand lectures and teaching material in English, as the course is taught in English.

Course programme

The course deals with models, algorithms and heuristic techniques for solving decision-making problems related to the optimal planning and management of resources in complex systems. The course contents are organized into the following topics:

1. Review of integer programming

   Integer linear programming models and formulations; continuous relaxation; surrogate relaxation; Lagrangian relaxation; interpretation of bounds and their role in evaluating heuristic solutions.

2. Network optimization

   Path, tree and flow problems; mathematical formulations and basic algorithms; applications to logistics and transportation problems.

3. Constructive heuristics and local search

   Constructive algorithms; neighborhood structures; improvement criteria; local search. Application examples on classical combinatorial optimization problems, including the knapsack problem, the traveling salesman problem, the bin packing problem and the vehicle routing problem.

4. Metaheuristics

   Multi-start methods, Tabu Search, Simulated Annealing, Iterated Local Search, Variable Neighborhood Search, Ruin and Recreate, Genetic Algorithms and Ant Systems. For each methodology, the course discusses the underlying algorithmic principles, the main implementation choices and the criteria used to assess performance.

5. Heuristic and metaheuristic algorithms from the literature

   Analysis of methods proposed for relevant combinatorial optimization problems in resource planning, with emphasis on computational comparison, solution quality and computing times.

6. Applications to real-world cases

   Modelling and solution of application problems in logistics, transportation and operations management. Critical discussion of computational results and decision-making implications.

Exercises, computational examples and case-study discussions may be proposed during the course in order to connect the theoretical aspects of the algorithms with their practical application.

Readings/Bibliography

Required material

The teaching material provided by the instructor and made available on the Virtuale platform is required for exam preparation.

Recommended readings

• S. Martello, P. Toth, Knapsack Problems: Algorithms and Computer Implementations, J. Wiley, 1990.
• E. Aarts, J.K. Lenstra, eds., Local Search in Combinatorial Optimization, J. Wiley, 1997.
• G. Gutin, A. Punnen, eds., The Traveling Salesman Problem and Its Variations, Kluwer, 2002.
• P. Toth, D. Vigo, eds., The Vehicle Routing Problem, SIAM Monographs on Discrete Mathematics and Applications, 2002.
• C. Barnhart, G. Laporte, eds., Transportation, Handbooks in Operations Research and Management Science, North Holland, 2007.

Further readings

Additional scientific papers, book chapters or bibliographic references may be suggested during the course to further investigate specific algorithms, application problems or case studies.

Slides, exercise material, additional references and operational information will be made available on Virtuale.

Teaching methods

The course consists of classroom lectures, complemented by application examples, guided exercises and case-study discussions.

The teaching activities combine:

• theoretical presentation of models, algorithms and metaheuristics;
• analysis of numerical and computational examples;
• discussion of application cases in logistics, transportation and resource management;
• comparison of different algorithmic strategies in terms of solution quality, computing time and scalability.

The teaching activities are designed to develop the ability to connect mathematical formulations, algorithmic choices and the interpretation of computational results.

If computer laboratory activities are included, attendance at such activities requires prior participation in the University safety training modules for study places, according to the procedures indicated by the Degree Programme.

Assessment methods

The assessment is aimed at verifying:

• knowledge of the main models and algorithms presented in the course;
• the ability to apply heuristic and metaheuristic methods to combinatorial optimization problems;
• the ability to critically analyze the computational performance of an algorithm;
• the ability to connect models, solution methods and real-world applications.

There are two alternative assessment methods:

• intermediate tests, for students who intend to take the assessment during the course;
• regular exam, for students who do not take or do not pass the intermediate tests.

In both cases, the exam consists of a written test and an oral test, with equivalent weight in the final grade.

The written test lasts 1 hour and consists of 3 questions, which may include exercises, theoretical questions and short modelling or algorithmic analysis problems.

The oral test consists of 2 questions answered in writing with pen and paper, followed by an oral discussion. The test assesses the ability to justify the proposed solutions, connect the different topics covered in the course and critically discuss methods, assumptions and results.

Intermediate tests

The intermediate tests consist of:

• an intermediate written test, held approximately halfway through the course programme;
• an intermediate oral test, held at the end of the course programme.

The intermediate written test covers only the first part of the programme. The intermediate oral test covers only the second part of the programme.

Regular exam

Students who do not take the intermediate tests, do not complete them or do not obtain a passing grade must take the regular exam.

The regular exam consists of:

• a written test covering the whole programme;
• an oral test covering the whole programme.

Tools allowed during the tests

During the written and oral tests, the use of books, notes, electronic devices or artificial intelligence tools is not allowed, unless explicitly authorized by the instructor before the test.

The possible use of a calculator will be specified in the exam paper.

Assessment criteria

The final grade is expressed on a scale of 30.

For the intermediate tests, the final grade takes into account the written test on the first part of the programme and the oral test on the second part of the programme.

For the regular exam, the final grade takes into account the written test and the oral test, both covering the whole programme.

The indicative grading criteria are as follows:

• 18-19: limited knowledge of the main topics, sufficient ability to apply methods only to simple problems, overall understandable presentation.
• 20-24: adequate knowledge of the fundamental topics, ability to apply methods and algorithms to standard cases, correct presentation.
• 25-29: broad and solid knowledge of the course contents, good autonomous analytical ability, appropriate use of technical terminology and ability to connect theory and applications.
• 30-30L: complete and in-depth preparation, critical analytical ability, autonomy in connecting models, algorithms and computational results, full command of technical language.

Students with disabilities or specific learning disorders

Students with temporary or permanent disabilities or specific learning disorders are invited to contact the relevant University office in due time. Any adaptations must be proposed by the competent office and submitted sufficiently in advance for approval by the instructor, who will assess their compatibility with the learning outcomes of the course.

Use of generative artificial intelligence in exams

As far as assessment is concerned, the use of generative artificial intelligence is not allowed in controlled examination settings. Any unauthorized use constitutes a breach of academic integrity.

For non-assessed individual study activities, artificial intelligence may be used as a support tool to understand concepts, reformulate explanations or generate self-assessment questions. Students remain responsible for critically checking the accuracy of AI-generated content against the official course material.

Teaching tools

Teaching material will be made available on the Virtuale platform.

The teaching tools may include:

• lecture slides and instructor’s notes;
• exercise sheets;
• numerical examples and case studies;
• possible code fragments or pseudocode;
• additional bibliographic references;
• self-assessment material for exam preparation.

Students are expected to check Virtuale regularly for updates, additional material and information about exercises, intermediate tests and exams.

Generative artificial intelligence may be used as a support tool for individual study and non-assessed activities, for example to reformulate concepts, generate self-assessment questions or clarify theoretical steps. Students remain responsible for critically verifying the accuracy of generated content and comparing it with the official course material.

Office hours

See the website of Paolo Paronuzzi