A Lagrangian-based heuristic for the capacitated lot-sizing problem in parallel machines

This paper addresses the capacitated lot-sizing problem involving the production of multiple items on unrelated parallel machines. A production plan should be determined in order to meet the forecast demand for the items, without exceeding the capacity of the machines and minimize the sum of production, setup and inventory costs. A heuristic based on the Lagrangian relaxation of the capacity constraints and subgradient optimization is proposed. Initially, the heuristic is tested on instances of the single machine problem and results are compared with heuristics from the literature. For parallel machines and small problems the heuristic performance is tested against optimal solutions, and for larger problems it is compared with the lower bound provided by the Lagrangian relaxation. (c) 2005 Elsevier B.V. All rights reserved.17521070108

A network flow model for the capacitated lot-sizing problem

The lot-sizing problem considered in this paper consists in planning the production of multiple items on a single machine over a finite planning horizon divided into time periods. The objective of the problem is to determine a minimum cost production plan that meets the forecast demand for the items. The mathematical model considers setup time and setup cost, and is represented as a minimum cost network how problem. A branch-and-bound method is proposed for solving the model.:The performance of the method is evaluated by using numerical experiments for various demand patterns and values of cost parameters. (C) 1999 Elsevier Science Ltd. All rights reserved.27227528

Semantic Wordification of Document Collections

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Word clouds have become one of the most widely accepted visual resources for document analysis and visualization, motivating the development of several methods for building layouts of keywords extracted from textual data. Existing methods are effective to demonstrate content, but are not capable of preserving semantic relationships among keywords while still linking the word cloud to the underlying document groups that generated them. Such representation is highly desirable for exploratory analysis of document collections. In this paper we present a novel approach to build document clouds, named ProjCloud that aim at solving both semantical layouts and linking with document sets. ProjCloud generates a semantically consistent layout from a set of documents. Through a multidimensional projection, it is possible to visualize the neighborhood relationship between highly related documents and their corresponding word clouds simultaneously. Additionally, we propose a new algorithm for building word clouds inside polygons, which employs spectral sorting to maintain the semantic relationship among words. The effectiveness and flexibility of our methodology is confirmed when comparisons are made to existing methods. The technique automatically constructs projection based layouts the user may choose to examine in the form of the point clouds or corresponding word clouds, allowing a high degree of control over the exploratory process.313311451153Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

A Generic Decision Support Tool for Lot-Sizing and Scheduling Problems with Setup and Due Dates

Decision support tools are essential to help in the management of industrial systems at different levels: strategic, to design the system; tactical to plan activities or assign resources; operational to schedule activities. In this paper, we present a generic and modular decision support tool to solve different planning, assignment, scheduling or lot-sizing problems. To the best of our knowledge, such generic tool does not exist. The methodology is illustrated by solving a real world lot-sizing and scheduling problem from a plastic injection company