Catálogo de publicaciones - libros

FLOPC++ is an open source algebraic modeling language implemented as a C++ class library. It allows linear optimization problems to be modeled in a declarative style, similar to algebraic modeling languages, such as GAMS and AMPL, within a C++ program. The project is part of COmputational INfrastructure for Operations Research (COIN-OR) and uses its Open Solver Interface (OSI) to achieve solver independence.

In this paper, we consider two-machine permutation flow shop scheduling problem to minimize the makespan in which some of the jobs have to be processed with no-wait in process. We also consider precedence constraints which impose some jobs to be processed before or after some others. We propose a constructive algorithm to find a feasible solution. We also develop a Tabu Search algorithm to solve this problem. Our computational analysis indicates its good performance.

We consider a generalization of the Steiner tree problem on graphs suitable for the design of the last mile in fiber optic networks and propose a multi commodity flow formulation for the exact solution of this problem. Some experimental results are discussed.

This paper continues the investigation of the cycle polytope of a directed graph begun by Balas and Oosten [2]. Given a digraph G = ( N,A ) and the collection C of its simple directed cycles, the cycle polytope defined on G is P _ C ≔ conv { X ^ C : C ∈ C }, where χ ^C is the incidence vector of C . According to the integer programming formulation given in [2], P _ C is the convex hull of points x ∈ℝ satisfying (1) $$ x(\delta ^ + (i)) - x(\delta ^ - (i)) = 0{\text{ }}for{\text{ all }}i \in N $$ , (2) $$ x(\delta ^ + (i)) \leqslant 1{\text{ }}for{\text{ all }}i \in N $$ , (3) $$ \begin{array}{*{20}c} { - x(S,N\backslash S) + x(\delta ^ + (i)) + x(\delta ^ + (j)) \leqslant 1{\text{ }}for{\text{ all }}S \subseteq N,2 \leqslant |S| \leqslant n - 2,} \\ {i \in S,j \in N\backslash S} \\ \end{array} $$ , (4) $$ \sum\limits_{i = 1}^{n - 1} {\sum\limits_{j = i + 1}^n {x_{\pi (i)\pi (j)} } \geqslant 1{\text{ for all permutations }}\pi {\text{ of }}N} $$ , (5) $$ x_{ij} \in \{ 0,1\} {\text{ }}for all (i,j) \in A $$

In this paper, we deal with modelling robust design problems via conic optimization. A robust design problem deals with finding a robust optimal solution of an uncertain design problem. The uncertain data is assumed to belong to a so-called uncertainty set $$ \mathcal{U} $$ . Uncertainty means that the data is not known exactly at the time when the solution has to be determined. In order to find a robust optimal solution, we use the robust optimization (RO) methodology of Ben-Tal and Nemirovskii. We demonstrate this on the robust shortest path problem (RSPP), the robust maximum flow problem (RMFP) and the robust resistance network topology design (RNTD) problem.

Several hard optimization problems of finding spanning connected subgraphs with extreme total edge weight are considered. A number of results on constructing polynomial algorithms with performance guarantees for these problems is presented.^1

In multidimensional poverty measurement k ≥ 2 different quantitative basic needs variables y _j, j = 1... k have to be considered. Let the respective variables be substitutable. Then for a single person i = 1... n poverty can be aggregated across variables as follows: (1) $$ C_{1i}^* = \left( {\frac{1} {k}\sum\limits_{j = 1}^k {p_{ij}^{*\alpha } } } \right)^{\frac{1} {\alpha }} ,\alpha \geqslant 2 $$ (see Kocklaeuner (2002) with respect to an unidimensional ethical poverty index aggregating poverty across persons).

We consider a model for a financial market where the asset prices satisfy a stochastic differential equation. For the volatility no new source of randomness is introduced, but the volatility at each time depends deterministically on all previous price fluctuations. Such non-constant volatility models preserve the completeness of the market while they allow for many attractive features.

We intend to optimize harvesting of two populations within a business cycle of an economy with appropriate means. The simulation model we have in mind concentrates on the problem of profit maximization within an interdependent system. Furthermore, we deal with the task of explaining phenomena of the typical behavior of the subjects while operating a complex system, e.g., a market, a company, ...

Variable selection in cross-country growth regression models is currently a major open research topic and has inspired theoretical and empirical literature, see [6]. There are two categories of research problems that are intimately connected. The first problem is model uncertainty and the second is data heterogeneity. Recent literature aims to overcome the first problem by applying Bayesian Model Averaging (BMA) approaches in finding important, robust and significant variables to explain economic growth. While BMA offers an appealing approach to handle model uncertainty very little research has been undertaken to consider the problem of data heterogeneity. In this paper we analyze the issue of data heterogeneity on the basis of the exclusion of countries, i.e. we will take a closer look at the robustness of approaches when countries are eliminated from the data set. We will show that results of BMA are very sensitive to small variations in data. As an alternative to BMA in the cross-country growth regression debate we suggest the use of “classical” Bayesian Model Selection (BMS). We will argue that there is much in favor of BMS and will show that BMS is less sensitive in the identification of important, robust and significant variables when small variations in data are made. Our empirical results are undertaken on the most frequently used data set in the cross-country growth debate provided by [4].