Analysis of the Uncapacitated Dynamic Lot Size Problem

In this paper we provide worst case error bounds for several heuristics for the uncapacitated dynamic lot size problem. We propose two managerially oriented procedures and show that they have a relative worst case error bound equal to two, and develop similar analyses for methods known as the "Silver and Meal" heuristics, the part period balancing heuristics, and economic order quantity heuristics (expressed in terms of a time supply of demand).We also present results on aggregation and partitioning of the planning horizon

Solving Medium-Density Subset Sum Problems in Expected Polynomial Time: An Enumeration Approach

The subset sum problem (SSP) can be briefly stated as: given a target integer $E$ and a set $A$ containing $n$ positive integer $a_j$, find a subset of $A$ summing to $E$. The \textit{density} $d$ of an SSP instance is defined by the ratio of $n$ to $m$, where $m$ is the logarithm of the largest integer within $A$. Based on the structural and statistical properties of subset sums, we present an improved enumeration scheme for SSP, and implement it as a complete and exact algorithm (EnumPlus). The algorithm always equivalently reduces an instance to be low-density, and then solve it by enumeration. Through this approach, we show the possibility to design a sole algorithm that can efficiently solve arbitrary density instance in a uniform way. Furthermore, our algorithm has considerable performance advantage over previous algorithms. Firstly, it extends the density scope, in which SSP can be solved in expected polynomial time. Specifically, It solves SSP in expected $O(n\log{n})$ time when density $d \geq c\cdot \sqrt{n}/\log{n}$, while the previously best density scope is $d \geq c\cdot n/(\log{n})^{2}$. In addition, the overall expected time and space requirement in the average case are proven to be $O(n^5\log n)$ and $O(n^5)$ respectively. Secondly, in the worst case, it slightly improves the previously best time complexity of exact algorithms for SSP. Specifically, the worst-case time complexity of our algorithm is proved to be $O((n-6)2^{n/2}+n)$, while the previously best result is $O(n2^{n/2})$.Comment: 11 pages, 1 figur

Bun splitting: a practical cutting stock problem

We describe a new hierarchical 2D-guillotine Cutting Stock Problem. In contrast to the classic cutting stock problem, waste is not an issue. The problem relates to the removal of a defective part and assembly of the remaining parts into homogeneous size blocks. The context is the packing stages of cake manufacturing. The company's primary objective is to minimise total processing time at the subsequent, packing stage. This objective reduces to one of minimising the number of parts produced when cutting the tray load of buns. We offer a closed form optimization approach to this class of problems for certain cases, without recourse to mathematical programming or heuristics. The methodology is demonstrated through a case study in which the number of parts is reduced by almost a fifth, and the manufacturer's subsidiary requirement to reduce isolated single bun parts and hence customer complaints is also satisfied

Joint pricing and ordering policies for deteriorating item with retail price-dependent demand in response to announced supply price increase

[[abstract]]Recently, due to rapid economic development in emerging nations, the world's raw material prices have been rising. In today's unrestricted information environment, suppliers typically announce impending supply price increases at specific times. This allows retailers to replenish their stock at the present price, before the price increase takes effect. The supplier, however, will generally offer only limited quantities prior to the price increase, so as to avoid excessive orders. The retail price will usually reflect any supply price increases, as market demand is dependent on retail price. This paper considers deteriorating items and investigates (1) the possible effects of a supply price increase on retail pricing, and (2) ordering policies under the conditions that special order quantities are limited and demand is dependent on retail price. The purpose of this paper is to determine the optimal special order quantity and retail price to maximize profit. Our theoretical analysis examines the necessary and sufficient conditions for an optimal solution, and an algorithm is established to obtain the optimal solution. Furthermore, several numerical examples are given to illustrate the developed model and the solution procedure. Finally, a sensitivity analysis is conducted on the optimal solutions with respect to major parameters.[[incitationindex]]SCI[[booktype]]紙

A genetic algorithm for the one-dimensional cutting stock problem with setups

This paper investigates the one-dimensional cutting stock problem considering two conflicting objective functions: minimization of both the number of objects and the number of different cutting patterns used. A new heuristic method based on the concepts of genetic algorithms is proposed to solve the problem. This heuristic is empirically analyzed by solving randomly generated instances and also practical instances from a chemical-fiber company. The computational results show that the method is efficient and obtains positive results when compared to other methods from the literature. © 2014 Brazilian Operations Research Society

Caracterização de uso e cobertura da terra na Amazônia utilizando imagens duais multitemporais do COSMO-SkyMed

The use of radar imagery is an alternative source of information to support the monitoring of the Amazon region, since the optical images have imaging limitations in tropical areas due to the occurrence of clouds. Therefore, the goal of this study is to analyze the radar images in X-band multi-temporal polarized obtained by COSMO-SkyMed satellite (COnstellation of small Satellites for Mediterranean basin Observation), in the intensity mode, isolated and/or combined with textural information, to thematic characterization of land use/land cover in the Humaitá, Amazonas State region. The methodology used includes: analysis of the dual images obtained during two subsequent acquisitions, in order to explore the potential of the dataset as a quad-pol intensity; extraction of textural attributes from the co-occurrence matrix (Gray Level Co-occurrence Matrix) and subsequent contextual classification; statistical assessment of the thematic performance of the intensity and textural images, isolated and in polarized groups. Within the results achieved, the group formed only by the intensity images presented a better performance if compared to those containing the textural attributes. In this discrimination, the classes involved were forest, alluvial forest, reforestation, savannah, pasture and burned areas, yielding 66% overall accuracy and a Kappa value of 0.55. The results showed that X band images, from COSMO-SkyMed, StripMap mode (Ping-Pong), multi-polarized, presents a moderate potential to characterize and monitor the dynamics of land use/land land cover in the Brazilian Amazon.A utilização de imagens de radar é fonte alternativa de informações para subsidiar o monitoramento da região amazônica, visto que as imagens ópticas têm limitações de imageamento em zonas tropicais face a ocorrência de nuvens. Por conseguinte este trabalho teve como objetivo analisar a capacidade das imagens-radar de banda X multitemporais e polarizadas obtidas pelo satélite COSMO-SkyMed (COnstellation of small Satellites for Mediterranean basin Observation), no modo intensidade, isoladamente e agregados às informações texturais, na caracterização temática de uso e cobertura da terra no município de Humaitá/AM. A metodologia empregada consistiu daanálise das imagens duais obtidas em duas aquisições subsequentes, de forma a explorar a potencialidade do conjunto de dados na forma quad-pol intensidade; extração dos atributos texturais a partir da matriz de coocorrência (Gray Level Co-occurrence Matrix) e posterior classificação contextual; avaliação estatística de desempenho temático das imagens intensidade e texturais, isoladas e em grupos polarizados. Dentre os vários resultados alcançados, foi verificado que o grupo formado somente pelas imagens intensidade apresentou o melhor desempenho, comparado àqueles contendo os atributos texturais. Nesta separabilidade, estavam envolvidas as classes de floresta, floresta aluvial, reflorestamento, savana, pasto e queimada, obtendo-se 66% de acurácia total e valor Kappa de 0,55. Os resultados mostraram que as imagens de banda X do COSMO-SkyMed, modo StripMap (Ping-Pong), multipolarizadas, têm potencial moderado para a caracterização e monitoramento da dinâmica de uso e cobertura da terra na Amazônia brasileira