Resumo em Inglês:

This paper presents an overview of our research in combinatorial optimization problems. Over the last three decades, our team has been studying mostly optimization problems that arise in industrial environments through the elaboration and solution of mathematical decision models. In addition to elaborating innovative models, we have improved upon existing solutions to complex problems, helping decision makers and researchers to better understand complex industrial systems. Our work has focused on the development of computationally more efficient algorithms that improve on existing methods by improving the solution quality or reducing the computation effort to obtain good solutions. While some of our earlier work became less necessary with the speed up of the computational facilities, the search for improved solution quality and reduced computational effort continues. After reviewing our findings on lot sizing, production scheduling, cutting problems, pattern sequencing, tool switches in flexible manufacturing machines and integrated cutting and sequencing problems, we propose topics for future study.

Resumo em Inglês:

Internet-based customization tools can be used to design service encounters that maximize customers' utility in the present or explore their tastes to provide more value in the future, where these two goals conflict with each other. Maximizing expected customer satisfaction in the present leads to slow rates of learning that may limit the ability to provide quality in the future. An emphasis on learning can lead to unsatisfied customers that will not only forego purchasing in the current period, but, more seriously, never return if they lose trust in the service provider's ability to meet their needs. This paper describes service design policies that balance the objectives of learning and selling by characterizing customer lifetime value as a function of knowledge. The analysis of the customization problem as a dynamic program yields three results. The first result is the characterization of customization policies that quantify the value of knowledge so as to adequately balance the expected revenue of present and future interactions. The second result is an analysis of the impact of operational decisions on loyalty, learning, and profitability over time. Finally, the quantification of the value of knowing the customer provides a connection between customer acquisition and retention policies, thus enhancing the current understanding of the mechanisms connecting service customization, value creation, and customer lifetime value.

Resumo em Inglês:

A recent optimal control problem in the area of economics has mathematical properties that do not fall into the standard optimal control problem formulation. In our problem the state value at the final time the state, y(T) = z, is free and unknown, and additionally the Lagrangian integrand in the functional is a piecewise constant function of the unknown value y(T). This is not a standard optimal control problem and cannot be solved using Pontryagin's Minimum Principle with the standard boundary conditions at the final time. In the standard problem a free final state y(T) yields a necessary boundary condition p(T) = 0, where p(t) is the costate. Because the integrand is a function of y(T), the new necessary condition is that y(T) should be equal to a certain integral that is a continuous function of y(T). We introduce a continuous approximation of the piecewise constant integrand function by using a hyperbolic tangent approach and solve an example using a C++ shooting algorithm with Newton iteration for solving the Two Point Boundary Value Problem (TPBVP). The minimising free value y(T) is calculated in an outer loop iteration using the Golden Section or Brent algorithm. Comparative nonlinear programming (NP) discrete-time results are also presented.

Resumo em Inglês:

Value-Focused Thinking (VFT) provides a systematic approach to structure complex decisions for subsequent analysis. It is a powerful complement to decision analysis and its application has been growing in recent years. This paper discusses the application of VFT in Brazil to three problems in different contexts: water management, information system/information technology (IS/IT) strategic planning, and the disposal of plaster waste. This article describes how the VFT approach was used to structure these decision problems and identify alternatives to stall them, which led to developing qualitative and quantitative models for evaluating the alternatives, and discusses how such structures can be used in other similar problems.

Resumo em Inglês:

In this paper we present a brief overview of 10 years of research on Parametric Data Envelopment Analysis (DEA). We begin with a brief introduction to DEA. Then, we present the central problem of how to distribute a new and total fixed variable (input or output) across all DMUs (Decision Making Units) present in the analysis. We then tell the history of the developments in Parametric DEA, beginning with its first conception in 2002, moving onward to the current research. We conclude with a brief discussion of future perspectives.

Resumo em Inglês:

This paper presents the Clustering Search (CS) as a new hybrid metaheuristic, which works in conjunction with other metaheuristics, managing the implementation of local search algorithms for optimization problems. Usually the local search is costly and should be used only in promising regions of the search space. The CS assists in the discovery of these regions by dividing the search space into clusters. The CS and its applications are reviewed and a case study for a problem of capacitated clustering is presented.

Resumo em Inglês:

The second smallest Laplacian eigenvalue of a graph G is called algebraic connectivity, denoted a(G). The ordering of trees via this graph invariant is frequently studied in the literature. In this paper, we present a new invariant, the Internal Degree Sequence (IDS), that also supports an accurate evaluation of the connectivity of trees. We compare the IDS with a(G) for all elements in six classes of trees known to have the largest algebraic connectivity and we show that the IDS provides a strict total ordering of the elements of these classes. This result is also proved for a subclass of trees of diameter 4.