LEARNING OUTCOMES

The course provides students the basics of operations research, which are most relevant to the strategic and operational planning of enterprises. The course aims to develop optimization models and provide mathematical programming methods, both exact and heuristic, for decision-makers. Students are also provided with the necessary knowledge to understand the structure of an optimization algorithm and to implement it with Python. Emphasis is given to logistics and transportation problems. Students will evaluate the acquiring of their skills by examining, developing and analyzing case studies in a computer classroom using the spreadsheet optimization tool of Excel and ad-hoc software environments. By the end of the course, students will have the skills necessary to identify the methodological approach needed to address a decision-making problem and the ability to apply that method to determine the good solutions.

AIMS AND LEARNING OUTCOMES

The course provide students the operations research and decision support methods, which are the most relevant to the strategic decisions, for the planning and controlling. Problem solving skills will also be provided. The course is aimed at developing optimization models and providing methods for decision-making problems. The resolution of strategic decision problems can be addressed using a variety of techniques. The focus of the course is on mathematical modeling techniques for decision problems and algorithmic techniques aimed at a faster resolution of this type of problem. At the end of the course, students will be able to use linear programming to model strategic problems. Further, using tools such as  Spreadsheet tool of Excel and Python, students can design and implement solution approaches to the decision problem of both exact and heuristic types. Among the main Operation Research techniques, students will acquire skills in Linear programming, Integer Linear Programming, heuristic and meta-heuristic algorithms to face relevant strategic problems, as Facility location, Optimal routes and connections problems, Decision problems with Boolean variables, Decision problems with more than one objective.

PREREQUISITES

Recommended:

• Algebra,
• Analytic geometry,
• Programming,
• Basic Microsoft Excel.

   

TEACHING METHODS

The course includes frontal lessons held in the computer classroom, to give students the opportunity to formulate, solve and analyze together with the teachers the proposed problems. If it is not possible to carry out activities in the presence, due to changes in health conditions, the teaching methods decided by the University will be adopted. For any updates, please refer to Aulaweb.

SYLLABUS/CONTENT

Consistent with the objectives previously illustrated in the course, the following topics are covered

1. Introduction to Operations Research (OR).
   • The origin of OR. The role of the Air force group in the II world war period. The OR modelling approach: main components of a decision problem. Continue and discrete optimization problems.
2. Introduction to Linear Programming (LP).
   • LP problem formulations. The Simplex method. Formulation and solution of LP problems with Excel
3. Inroduction to programming. Logic circuits. Programming languages.
4. Python basic concepts:
   • Getting Started, first program "hello world".
   • Variables and Input.
   • Conditional statements. Iteration statements.
   • Functions Modules and Classes
   • Strings, Lists, Dictionaries
5. Use LP solvers in Python:
   • Define decision variables,
   • Create the objective function,
   • Add constraints to the model,
   • Analysis of the solutions.
6. Decision problems with Boolean variables.
   • Either-or constraint.
   • The fixed charge problem.
   • Covering problems.
7. Strategic decision problems (1):
   • Facility location problem: definition, location in the space, property of the network, facility location in networks, strategic nodes in a network (center, median and p-median).
   • LP formulation. Basic heuristic approach. Facility location game. 
8. Data structure:
   • Graph data structure
   • Data manipulation and storage.
   • Develop a parser.
   • Test cases creation.
   • Binary variables with Python.
9. Algorithms and complexity classes (concepts):
   • Exact, heuristic, meta-heuristic.
   • Constructive Algorithms, Greedy Algorithms, selection function. Enhanced Greedy.
   • The bin packing problem, constructive algorithm, greedy algorithm
   • Implementation of the proposed algorithms.        
10. Strategic decision problems (2):
    • Optimal routes and connections problems on networks. Optimal path problem. External factors (reliability, sustainability, geopolitics) in route definition problems. Case study: merchant ship routes. Network design problem.
11. Local Search:
    • Definition of neighborhood,
    • Implementation of a neighborhood.
    • Escape from the local minima, the Tabu Search, the tabu list, the reactive tabu list.
    • Implementation of a Local Search.
12. Genetic Algorithms:
    • Chromosome, population, crossover, mutation, selection function.
    • Population diversity, speciation heuristic and strong mutation.
    • Memetic Algorithms.
    • Implementation of a Genetic Algorithm
13. Decision problems with more than one objective: multi-objective optimization approaches; Pareto optimal solutions. Some examples.

RECOMMENDED READING/BIBLIOGRAPHY

The following books and articles are suggested.

• Hillier, Lieberman, “Introduction to Operations Research”, McGraw Hill, 2016.
• J.F.McCloskey, “OR FORUM- The Beginnings of Operations Research: 1934-1941”, Operations Research, V.35, N.1, 1987, 143-152.
• J.F.McCloskey, “OR FORUM- British Operational Research in World War II””, Operations Research, V.35, N.3, 1987, 453-469.
• A. L. Jaimes, S. Zapotecas-Martinez, C.A. Coello, “An introduction to multiobjective optimization techniques”, in Optimization in Polymer Processing, A. Gaspar-Cunha, J.A. Covas (Editors), Nova Science Publishers, 29-57 (2009)
• M. Ehrgott, “Multicriteria optimization”, Springer, Berlin-Heidelberg (2005)
• M. ¨Ozlen, M. Azizoˇglu, “Multi-objective integer programming: A general approach for generating all non-dominated solutions”, European Journal of Operational Research, 199, 25-35 (2009)
• G. Ghiani, G. Laporte, R. Musmanno, "Introduction to logistics systems" , Wiley (2004)
• Downey, A., et al. "Thinking python. 2.0". Green Tea Press Supplemental Material:, 2012.