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 methods for decision-makers. Emphasis is given to logistics and transportation problems. Students will examine, develop and analyze case studies in a computer classroom using ad-hoc software environment. Basic mathematical Game Theory tools to deal with strategic problems characterized by interactions among two or more agents are also presented.

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. Particular emphasis is given to logistics and transportation problems.

The resolution of strategic decision problems can be addressed using a variety of techniques.

In this course we will focus on mathematical modeling techniques for decision problems and on algorithmic techniques aimed at a faster resolution of this type of problem.

At the end of the course the student will be able to use linear programming to model strategic problems. Using tools such as ( Spread sheet Excel, MPL, Python)., the student can design and implement a solution approach to the decision problem of both an exact and heuristic type.

Among the main techniques we will study: Linear programming, Integer Linear Programming, heuristic and meta-heuristic algorithms.

Among the main problems addressed: Facility location, Optimal routes and connections problems, Decision problems with Boolean variables, Decision problems with more than one objective, Decision problems with uncertain outcomes.

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.
   • Introduction to Linear Programming (LP): examples of LP problem formulations. The Simplex method. Formulation and solution with excel
2. Python basic concepts:
   • Getting Started, first program "hello world".
   • Variables and Input.
   • Conditional statements.
   • Iteration statements.
   • Functions Modules and Classes
   • Strings, Lists, Dictionaries
3. Use Pl and PLI solvers in Python:
   • Define decision variables,
   • Create the objective function,
   • Add constraints to the model,
   • Analysis of the solutions.
4. 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. 
5. Data structure:
   • Graph data structure
   • Data manipulation and storage.
   • Develop a parser.
   • Test cases creation.
6. 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.        
7. Strategic decision problems:
   • 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. The minimum spanning tree problem. 
8. 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.
9. Genetic Algorithms:
   • Chromosome, population, crossover, mutation, selection function.
   • Population diversity, speciation heuristic and strong mutation.
   • Memetic Algorithms.
   • Implementation of a Genetic Algorithm
10. Network models for optimizing projects’ time-cost trade off: the critical path; crashing decisions.
11. Decision problems with Boolean variables: Either-or constraints, functions with N possible values. The fixed charge problem. Covering problems. Example of the Boolean variables usage through facility location problems and their main decision components.
12. Decision problems with more than one objective: multi-objective optimization approaches; Pareto optimal solutions. Some examples.
13. Decision problems with uncertain outcomes: 
    • Decision analysis: decision making without and with experimentation, probability tree. Decision trees using Excel. 

RECOMMENDED READING/BIBLIOGRAPHY

we suggest reading the following books and articles.

• 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.
• Robert T. Clemen & Terence Reilly, “Making hard decisions” , 3rd edition
• 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, “A discussion of scalarization techniques for multiple objective integer programming”, Annals of Operations Research, 147, 343-360 (2006)
• 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. Think python. 2.0. Green Tea Press Supplemental Material:, 2012.