Last update: 13/03/2018

Abstract

In this mini-course we will examine the application of modern OR techniques in solving real-world problems in Argentina and Chile over the last 15 years. Among the cases we will consider are the design and algorithmic solution of combinatorial auctions, the scheduling of sports leagues and other “sports analytics” problems, rubbish collection and street-cleaning in various cities, and the logistics, transport and production planning problems in the salmon farming industry. In each case we will review the techniques employed and the difficulties we face in finding solutions for a variety of everyday situations that arise in government, private industry and non-profit organisations.

Resumen

Collaboration among different agents (companies, players) is an effective way to improve logistic operations. The current state-of-the-art includes collaborative approaches for a variety of well-known problems such as the classic transportation problem, the traveling salesman problem, and inventory pooling. A current trend is to study such collaborative situations as cooperative games. In this mini-course we will overview concepts, models, methods and applications in the intersection of logistics and cooperative game theory. These include, for example, the use of linear programming to model stability conditions and to design cost allocation methods, and the use of integer programming to group players in coalitions.

Resumen

Extremal graph theory has its origins in Mantel's theorem from 1907 which determines the maximum number of edges a graph can have without containing a triangle. In other words, this result determines the average degree that is necessary to ensure the graph has a triangle. During the past century, a number of results and conjectures in this direction have emerged, using bounds on the minimum or average degree to ensure the appearance of certain subgraphs of a certain size, such as complete graphs (Turán 1941), complete bipartite graphs (Erdös-Stone 1946), Hamilton cycles (Dirac 1952), trees (Erdös-Sos conjecture 1962), among others. The regularity lemma, proved by Szemerédi in 1975 transformed the area. It exposes structural information of all large enough graphs, and today constitutes one of the most used tools in the field.

In this course, we give a gentle introduction to the area of extremal graph theory, surveying the most important classical results and open problems, and proving some of the important theorems. At the end of the course, we will have a quick glimpse at the regularity lemma, and how it works, without going into tedious details.

This course needs no previous knowledge (except for some basic mathematical concepts, such as induction).

Abstract

In this mini-course we will discuss some classical models of bargaining theory, including the Nash Demand Game, the Ultimatum Game, the Nash Bargaining Solution and the Offer-Counteroffer Game. In addition, we will analyze some applications to bargaining processes conducted under polarized environment such as pacemaking and peacekeeping, negotiations with negative externalities, collective bargaining and strikes.

Abstract

A usually-effective strategy for solving NP-hard combinatorial optimization problems consists in modeling such problems as integer programs. However, general algorithms for integer programs usually suffer from performance issues, depending on the instance size and model structure. In this case, we can study the convex hull of feasible solutions of the model, with the objective of enhancing general algorithms with the addition of knowledge on this polyhedron. In this short course we will cover such topics, including the theoretical analysis of valid inequalities and the design of separation procedures.

**Antonio Mauttone: "***Models and Algorithms for Public Transportation Network Design*"
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Abstract

We will discuss the application of Operational Research methodologies to some strategic and tactical planning problems in public transportation regarding network design. In the first part of the mini-course, we will provide a unified view of existing public transport network optimization models and solution methods. We deal with problems related to both infrastructure building (bus rapid transit corridors, railways, metro) and service design (routes and frequencies). Several mathematical programming formulations will be explained, paying attention to the modeling of physical and economic constraints as well as to the modeling of system performance from the viewpoint of the different stakeholders involved. In the second part of the mini-course we will present some specific developments regarding route and frequency optimization, including both exact and heuristic approaches and applications to several real cases.

Abstract

The main objective of this mini-course is to provide students with an overview of empirical methods to conduct research in disciplines related to Management Science, including Operations Management, Quantitative Marketing, Applied Industrial Economics, and interdisciplinary research among these fields. This course does not substitute the formal training of a statistics and econometrics courses. A typical statistics and econometrics class will cover in detail the mechanics and statistical properties of different estimators, which is beyond the scope of this class. However, many times students fulfill their statistics/econometrics classes without a clear understanding on how to apply these methods to answer an empirical research question. This course aims to fill that gap by providing a problem-oriented approach, where the focus is on learning how to identify a suitable empirical strategy to tackle a research question. Because of the limited time, this course does not cover in detail the properties and implementation of the econometric methods used, and students are encouraged to learn those details by taking a series of statistics/econometrics class.

Abstract

In Spain and many parts around the world, many attempts have been made to apply OR in agriculture by introducing decision support systems on the farm. There is a gap between theory and practice as the number of papers proposing OR models to solve agricultural problems is not corresponded with the adoption in field conditions. In this talk, different introductory projects of decision support systems are described and critical success factors and pitfalls are analyzed. Most innovations in information technology (IT) make decision support systems on operational level more successful than the ones working on the tactical/strategic level. Systems with clear financial benefits have of course good potential. However, this is unclear for most systems. The central question for these systems is: does the decision-maker have a problem? If not, an application for solving this ‘problem’ will never be a success. End user involvement as well as close participation of the future marketing organization are also considered to be crucial.

Resumen

Given a class A of graphs and a decision problem X belonging to NP, we say that a full complexity dichotomy of A was obtained if one describes a partition of A into subclasses such that X is classified as polynomial or NP-complete when restricted to each subclass. The concept of full complexity dichotomy is particularly interesting for the investigation of NP-complete problems: as we partition a class A into NP-complete subclasses and polynomial subclasses, it becomes clearer why the problem is NP-complete in A. The class C of graphs that do not contain a cycle with a unique chord was studied by Trotignon and Vušković who proved a structure theorem which led to solving the vertex-colouring problem in polynomial time. We apply the structure theorem to study the complexity of edge-colouring and total-colouring, and show that even for graph classes with strong structure and powerful decompositions, the edge-colouring problem may be difficult. We discuss several surprising complexity dichotomies found in subclasses of C, and the concepts of separating class and of separating problems.

ELAVIO 2018