Partitioning a permutation graph: algorithms and an application.

In this paper we discuss the problem of partitioning a permutation graph into cliques of bounded size, and describe a real-life application of this problem encountered at a manufacturing company. We formulate the problem as an integer program, and present two exact algorithms for solving it. The first algorithm is a branch-and-price algorithm based on the integer programming formulation; the second one is an algorithm based on the concept of bounded clique-width. The latter algorithm was motivated by the structure present in the real-life instances. Test results are given, both for real-life instances and randomly generated instances. As far as we are aware, this is the first implementation of an algorithm based on bounded clique-width.Algorithms; Analysis of algorithms; Branch-and-price; Companies; Integer programming; Manufacturing; Real life; Size; Structure;

Fast and robust estimation of the multivariate errors in variables model.

In the multivariate errors in variable models one wishes to retrieve a linear relationship of the form y = ß x + a, where both x and y can be multivariate. The variables y and x are not directly measurable, but observed with measurement error. The classical approach to estimate the multivariate errors in variable model is based on an eigenvector analysis of the joint covariance matrix of the observations. In this paper a projection-pursuit approach is proposed to estimate the unknown parameters. Focus is on projection indices based on half-samples. These will lead to robust estimators, which can be computed using fast algorithms. Consistency of the procedure is shown, without needing to make distributional assumptions on the x-variables. A simulation study gives insight in the robustness and the efficiency of the procedure.Algorithms; Consistency; Covariance; Efficiency; Errors in variables; Estimator; Matrix; Measurement; Model; Models; Multivariate statistics; Principal component analysis; Projection-pursuit; Robust estimation; Robustness; Simulation; Studies; Variables;

Container Loading Problems: A State-of-the-Art Review

Container loading is a pivotal function for operating supply chains efficiently. Underperformance results in unnecessary costs (e.g. cost of additional containers to be shipped) and in an unsatisfactory customer service (e.g. violation of deadlines agreed to or set by clients). Thus, it is not surprising that container loading problems have been dealt with frequently in the operations research literature. It has been claimed though that the proposed approaches are of limited practical value since they do not pay enough attention to constraints encountered in practice.In this paper, a review of the state-of-the-art in the field of container loading will be given. We will identify factors which - from a practical point of view - need to be considered when dealing with container loading problems and we will analyze whether and how these factors are represented in methods for the solution of such problems. Modeling approaches, as well as exact and heuristic algorithms will be reviewed. This will allow for assessing the practical relevance of the research which has been carried out in the field. We will also mention several issues which have not been dealt with satisfactorily so far and give an outlook on future research opportunities

Improved Layout Structure with Complexity Measures for the Manufacturer’s Pallet Loading Problem (MPLP) Using a Block Approach

Purpose: The purpose of this paper is to study the Manufacturers pallet-loading problem (MPLP), by loading identical small boxes onto a rectangle pallet to maximise the pallet utilization percentage while reducing the Complexity of loading. Design/methodology/approach: In this research a Block approach is proposed using a Mixed integer linear programming (MILP) model that generates layouts of an improved structure, which is very effective due to its properties in grouping boxes in a certain orientation along the X and Y axis. Also, a novel complexity index is introduced to compare the complexity for different pallet loading, which have the same pallet size but different box arrangements. Findings: The proposed algorithm has been tested against available data-sets in literature and the complexity measure and graphical layout results clearly demonstrate the superiority of the proposed approach compared with literature Manufacturers pallet-loading problem layouts. Originality/value: This study aids real life manufactures operations when less complex operations are essential to reduce the complexity of pallet loading

A literature review on the Pallet Loading Problem Una revisión literaria del Problema de Carga del Pallet

Actualmente, las empresas enfrentan una competencia agresiva, por lo que implementar estrategias para alcanzar la competitividad es elemental. En este sentido, en Logística, el uso adecuado de los recursos es imprescindible. El impacto en la ganancia que tienen el almacenaje y el transporte, conlleva la implementación de acciones para contrarrestarlo. Un paletizado efectivo puede contribuir a reducir costos. El Problema de Carga del Pallet (PLP) procura la optimización del espacio del pallet para lograr cargar máxima de producto debidamente empacado. El uso práctico y beneficios del PLP han dado pie a su estudio en la búsqueda su solución. Este artículo presenta una revisión literaria de 30 estudios para mostrar las características principales y los métodos de solución propuestos para proveer la base teórica y las maneras como se ha tratado el PLP. Con el entendimiento de estas propuestas de solución, se busca tener el sustento para elaborar un modelo nuevo.Nowadays, businesses face a fierce competition. Hence, the search for strategies to achieve competitiveness is elemental. For that purpose, in Logistics, the proper use of resources is a must. Storing and transportation cause impact the overall profit, making it necessary to take actions to lower their effect. An efficient palletizing can contribute to reduce costs. The Pallet Loading Problem (PLP) focuses on finding space optimization to load the maximum quantity of packed product onto the pallet. The PLP’s practical use and benefits have made it subject of study throughout time. This article presents a literature review of 30 approaches to show the main characteristics and the solution methods researchers have proposed. The objective of this revision consists of providing the theoretical basis and the way the PLP has been treated. Thus, the understanding of these solution approaches can help in the development of a new proposed model

Metaheuristics for the Vehicle Routing Problem with Loading Constraints

We consider a combination of the capacitated vehicle routing problem and a class of additional loading constraints involving a parallel machine scheduling problem. The work is motivated by a real-world transportation problem occurring to a wood-products retailer, which delivers its products to a number of customers in a specific region. We solve the problem by means of two different metaheuristics algorithms: a Tabu Search and an Ant Colony Optimization. Extensive computational results are given for both algorithms, on instances derived from the vehicle routing literature and on real-world instances

Modelling and Optimisation of Space Allocation and layout Problems

This thesis investigates the development of optimisation-based, decision-making frameworks for allocation problems related to manufacturing, warehousing, logistics, and retailing. Since associated costs with these areas constitute significant parts to the overall supply chain cost, mathematical models of enhanced fidelity are required to obtain optimal decisions for i) pallet loading, ii) assortment, and iii) product shelf space, which will be the main research focus of this thesis. For the Manufactures Pallet loading problems (MPLP), novel single- and multi-objective Mixed Integer Linear Programming (MILP) models have been proposed, which generate optimal layouts of improved 2D structure based on a block representation. The approach uses a Complexity Index metric, which aids in comparing 2 pallet layouts that share the same pallet size and number of boxes loaded but with different box arrangements. The proposed algorithm has been tested against available data-sets in literature. In the area of Assortments (optimal 2D packing within given containers) , an iterative MILP algorithm has been developed to provide a diverse set of solutions within pre-specified range of key performance metrics. In addition, a basic software prototype, based on AIMMS platform, has been developed using a user-friendly interface so as to facilitate user interaction with a visual display of the solutions obtained. In Shelf- Space Allocation (SSAP) problem, the relationship between the demand and the retailer shelf space allocated to each item is defined as space elasticity. Most of existing literature considers the problem with stationary demand and fixed space elasticities. In this part of the thesis, a dynamic framework has been proposed to forecast space elasticities based on historical data using standard time-series methodologies. In addition, an optimisation mathematical model has been implemented using the forecasted space elasticities to provide the retailer with optimal shelf space thus resulting into closer match between supply and demand and increased profitability. The applicability and effectiveness of the proposed framework is demonstrated through a number of tests and comparisons against literature data-sets