On duality in linear fractional programming

In this paper, a dual of a given linear fractional program is defined and the weak, direct and converse duality theorems are proved. Both the primal and the dual are linear fractional programs. This duality theory leads to necessary and sufficient conditions for the optimality of a given feasible solution. A unmerical example is presented to illustrate the theory in this connection. The equivalence of Charnes and Cooper dual and Dinkelbach’s parametric dual of a linear fractional program is also established.

Nonnegative integral solution of linear equations

A method to obtain a nonnegative integral solution of a system of linear equations, if such a solution exists is given. The method writes linear equations as an integer programming problem and then solves the problem using a combination of artificial basis technique and a method of integer forms.

MPI parallel programming of mixed integer optimization problems using CPLEX with COIN-OR

The aim of this technical report is to present some detailed explanations in order to help to understand and use the Message Passing Interface (MPI) parallel programming for solving several mixed integer optimization problems. We have developed a C++ experimental code that uses the IBM ILOG CPLEX optimizer within the COmputational INfrastructure for Operations Research (COIN-OR) and MPI parallel computing for solving the optimization models under UNIX-like systems. The computational experience illustrates how can we solve 44 optimization problems which are asymmetric with respect to the number of integer and continuous variables and the number of constraints. We also report a comparative with the speedup and efficiency of several strategies implemented for some available number of threads.

Inference in Credal Networks Through Integer Programming

A credal network associates a directed acyclic graph with a collection of sets of probability measures; it offers a compact representation for sets of multivariate distributions. In this paper we present a new algorithm for inference in credal networks based on an integer programming reformulation. We are concerned with computation of lower/upper probabilities for a variable in a given credal network. Experiments reported in this paper indicate that this new algorithm has better performance than existing ones for some important classes of networks.

Multilinear and Integer Programming for Markov Decision Processes with Imprecise Probabilities

Markov Decision Processes (MDPs) are extensively used to encode sequences of decisions with probabilistic effects. Markov Decision Processes with Imprecise Probabilities (MDPIPs) encode sequences of decisions whose effects are modeled using sets of probability distributions. In this paper we examine the computation of Γ-maximin policies for MDPIPs using multilinear and integer programming. We discuss the application of our algorithms to “factored” models and to a recent proposal, Markov Decision Processes with Set-valued Transitions (MDPSTs), that unifies the fields of probabilistic and “nondeterministic” planning in artificial intelligence research. 

New insights on integer-programming models for the kidney exchange problem

In recent years several countries have set up policies that allow exchange of kidneys between two or more incompatible patient–donor pairs. These policies lead to what is commonly known as kidney exchange programs. The underlying optimization problems can be formulated as integer programming models. Previously proposed models for kidney exchange programs have exponential numbers of constraints or variables, which makes them fairly difficult to solve when the problem size is large. In this work we propose two compact formulations for the problem, explain how these formulations can be adapted to address some problem variants, and provide results on the dominance of some models over others. Finally we present a systematic comparison between our models and two previously proposed ones via thorough computational analysis. Results show that compact formulations have advantages over non-compact ones when the problem size is large.

Binary integer programming formulations for scheduling in market-driven foundries

This paper describes the development and solution of binary integer formulations for production scheduling problems in market-driven foundries. This industrial sector is comprised of small and mid-sized companies with little or no automation, working with diversified production, involving several different metal alloy specifications in small tailor-made product lots. The characteristics and constraints involved in a typical production environment at these industries challenge the formulation of mathematical programming models that can be computationally solved when considering real applications. However, despite the interest on the part of these industries in counting on effective methods for production scheduling, there are few studies available on the subject. The computational tests prove the robustness and feasibility of proposed models in situations analogous to those found in production scheduling at the analyzed industrial sector. (C) 2010 Elsevier Ltd. All rights reserved.

Planejamento de reativos em sistemas de energia elétrica através de um algoritmo de Branch-and-Bound não linear

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

New integer programming models for balanced multi-country kep

Le persone che soffrono di insufficienza renale terminale hanno due possibili trattamenti da affrontare: la dialisi oppure il trapianto di organo. Nel caso volessero seguire la seconda strada, oltre che essere inseriti nella lista d'attesa dei donatori deceduti, possono trovare una persona, come il coniuge, un parente o un amico, disposta a donare il proprio rene. Tuttavia, non sempre il trapianto è fattibile: donatore e ricevente possono, infatti, presentare delle incompatibilità a livello di gruppo sanguigno o di tessuto organico. Come risposta a questo tipo di problema nasce il KEP (Kidney Exchange Program), un programma, ampiamente avviato in diverse realtà europee e mondiali, che si occupa di raggruppare in un unico insieme le coppie donatore/ricevente in questa stessa situazione al fine di operare e massimizzare scambi incrociati di reni fra coppie compatibili. Questa tesi approffondisce tale questione andando a valutare la possibilità di unire in un unico insieme internazionale coppie donatore/ricevente provenienti da più paesi. Lo scopo, naturalmente, è quello di poter ottenere un numero sempre maggiore di trapianti effettuati. Lo studio affronta dal punto di vista matematico problematiche legate a tale collaborazione: i paesi che eventualmente accettassero di partecipare a un simile programma, infatti, devono avere la garanzia non solo di ricavarne un vantaggio, ma anche che tale vantaggio sia equamente distribuito fra tutti i paesi partecipanti.