A Cross Entropy-Based Heuristic for the Capacitated Multi-Source Weber Problem with Facility Fixed Cost: Cross entropy for continuous location problems

This paper investigates a capacitated planar location-allocation problem with facility fixed cost. A zone-based fixed cost which consists of production and installation costs is considered. A nonlinear and mixed integer formulation is first presented. A powerful three stage Cross Entropy meta-heuristic with novel density functions is proposed. In the first stage a covering location problem providing a multivariate normal density function for the associated stochastic problem is solved. The allocation values considering a multinomial density function are obtained in the second stage. In the third stage, single facility continuous location problems are solved. Several instances of various sizes are used to assess the performance of the proposed meta-heuristic. Our approach performs well when compared with the optimizer GAMS which is used to provide the optimal solution for small size instances and lower/upper bounds for some of the larger ones

Algoritmo genético para solucionar el problema de dimensionamiento y programación de lotes con costos de alistamiento dependientes de la secuencia

The main purpose of this paper is to develop a hybrid genetic algorithmin order to determine the lot sizes and their production scheduling in asingle machine manufacturing system for multi-item orders, the objectivefunction minimizes the sum of holding costs, tardy costs and setup costs.The problem considers a set of orders to be processed each one with itsown due date. Each order must be delivered complete. In the schedulingare considered sequence dependent setup times. The proposed hybridgenetic algorithm has embedded a heuristic that is used to calculate itsfitness function. The heuristic method presents a modification on theoptimal timming algorithm in which are involved sequence dependentset up times. A design of experiments is developed in order to assess thealgorithm performance, which is also tested using random-generateddata and results are compared with those generated by an exact method.The results show that the algorithm achieves a good performance in bothsolution quality and time especially for large instances.El objetivo de este artículo es desarrollar un algoritmo genético el cualpermita determinar los tamaños de lote de producción y su programaciónen un sistema de manufactura de una máquina para órdenesmultiproducto, cuya función objetivo minimiza la suma de los costosde inventario por terminaciones tardías y de alistamiento. El problemacontempla un conjunto de órdenes a ser procesadas con sus respectivasfechas de entrega. Cada orden debe ser entregada en su totalidad. Dentrode la programación de los trabajos se consideran tiempos de alistamientodependientes de la secuencia. En la metaheurística implementada se utilizade manera embebida un método heurístico para el cálculo de la funciónde adaptación. El método heurístico presentado es una variación delOptimal Timming Algorithm el cual involucra los tiempos de alistamientodependientes de la secuencia. Se desarrolla un diseño de experimentospara probar el desempeño del algoritmo utilizando instancias generadasde forma aleatoria y comparando sus soluciones contra las encontradaspor un método exacto. Los resultados muestran que el algoritmo lograun buen desempeño tanto en tiempo de ejecución como en calidad de lasolución especialmente en instancias grandes.

Optimal staffing under an annualized hours regime using Cross-Entropy optimization

This paper discusses staffing under annualized hours. Staffing is the selection of the most cost-efficient workforce to cover workforce demand. Annualized hours measure working time per year instead of per week, relaxing the restriction for employees to work the same number of hours every week. To solve the underlying combinatorial optimization problem this paper develops a Cross-Entropy optimization implementation that includes a penalty function and a repair function to guarantee feasible solutions. Our experimental results show Cross-Entropy optimization is efficient across a broad range of instances, where real-life sized instances are solved in seconds, which significantly outperforms an MILP formulation solved with CPLEX. In addition, the solution quality of Cross-Entropy closely approaches the optimal solutions obtained by CPLEX. Our Cross-Entropy implementation offers an outstanding method for real-time decision making, for example in response to unexpected staff illnesses, and scenario analysis

Large-Scale Optimisation in Operations Management: Algorithms and Applications

The main contributions of this dissertation are the design, development and application of optimisation methodology, models and algorithms for large-scale problems arising in Operations Management. The first chapter introduces constraint transformations and valid inequalities that enhance the performance of column generation and Lagrange relaxation. I establish theoretical connections with dual-space reduction techniques and develop a novel algorithm that combines Lagrange relaxation and column generation. This algorithm is embedded in a branch-and-price scheme, which combines large neighbourhood and local search to generate upper bounds. Computational experiments on capacitated lot sizing show significant improvements over existing methodologies. The second chapter introduces a Horizon-Decomposition approach that partitions the problem horizon in contiguous intervals. In this way, subproblems identical to the original problem but of smaller size are created. The size of the master problem and the subproblems are regulated via two scalar parameters, giving rise to a family of reformulations. I investigate the efficiency of alternative parameter configurations empirically. Computational experiments on capacitated lot sizing demonstrate superior performance against commercial solvers. Finally, extensions to generic mathematical programs are presented. The final chapter shows how large-scale optimisation methods can be applied to complex operational problems, and presents a modelling framework for scheduling the transhipment operations of the Noble Group, a global supply chain manager of energy products. I focus on coal operations, where coal is transported from mines to vessels using barges and floating cranes. Noble pay millions of dollars in penalties for delays, and for additional resources hired to minimize the impact of delays. A combination of column generation and dedicated heuristics reduces the cost of penalties and additional resources, and improves the efficiency of the operations. Noble currently use the developed framework, and report significant savings attributed to it

How green is a lean supply chain?

This article presents a supply chain planning model that can be used to investigate tradeoffs between cost and environmental degradation including carbon emissions, energy consumption and waste generation. The model also incorporates other aspects of real world supply chains such as multiple transport lot sizing and flexible holding capacity of warehouses. The application of the model and solution method is investigated in an actual case problem. Our analysis of the numerical results focuses on investigating relationship between lean practices and green outcomes. We find that (1) not all lean interventions at the tactical supply chain planning level result in green benefits, and (2) an agile supply chain is the greenest and most efficient alternative when compared to strictly lean and centralized situations

Tactical supply chain planning under a carbon tax policy scheme: a case study

Greenhouse gas emissions are receiving greater scrutiny in many countries due to international forces to reduce anthropogenic global climate change. Industry and their supply chains represent a major source of these emissions. This paper presents a tactical supply chain planning model that integrates economic and carbon emission objectives under a carbon tax policy scheme. A modified Cross-Entropy solution method is adopted to solve the proposed nonlinear supply chain planning model. Numerical experiments are completed utilizing data from an actual organization in Australia where a carbon tax is in operation. The analyses of the numerical results provide important organizational and policy insights on (1) the financial and emissions reduction impacts of a carbon tax at the tactical planning level, (2) the use of cost/emission tradeoff analysis for making informed decisions on investments, (3) the way to price carbon for maximum environmental returns per dollar increase in supply chain cost

Penjadwalan Flow Shop untuk Meminimasi Total Tardiness Menggunakan Algoritma Cross Entropy–Algoritma Genetika

Flow shop scheduling problems much studied by several researchers. One problem with scheduling is the tardiness. Total tardiness is the performance to minimize tardiness jobs. it is the right performance if there is a due date. This study proposes the Cross-Entropy Genetic Algorithm (CEGA) method to minimize the mean tardiness in the flow shop problem. In some literature, the CEGA algorithm is used in the case of minimizing the makespan. However, CEGA not used in the case of minimizing total tardiness. CEGA algorithm is a combination of the Cross-Entropy Algorithm which has a function to provide optimal sampling distribution and Genetic Algorithms that have functions to get new solutions. In some numeric experiments, the proposed algorithm provides better performance than some algorithms. For computing time, it is affected by the number of iterations. The higher the iteration, computing requires high time

Algoritmo heurístico basado en listas tabú para la planificación de la producción en sistemas multinivel con listas de materiales alternativas y entornos de coproducción

Maestría en IngenieríaEn esta investigación se presenta el desarrollo un algoritmo heurístico basado en los principios de búsqueda tabú para la solución del problema de lotificación multinivel con restricciones de capacidad, listas de materiales alternativas y entornos de coproducción, basado en la estructura del modelo de Planificación de Materiales y Operaciones Genéricas GMOP propuesto en el año 2013. El algoritmo propuesto utiliza el mecanismo de memoria a corto plazo (Lista Tabú) para la selección de Strokes alternativos para la fabricación de cada producto. La validación del algoritmo se realizó analizando la calidad y los tiempos de obtención de las soluciones. El algoritmo demostró potencial al alcanzar porcentajes de diferencia entre el 10% y 17% con respecto a las soluciones óptimas en los problemas de mayor tamaño y un equilibrio entre calidad y tiempos de solución problemas relativamente pequeños.This research shows the development process of a heuristic algorithm based on the principles of taboo search for the solution of the capacitated multilevel lot sizing problem with alternate bill of materials and co-production environments, based on the structure of the Generic Materials and Operations Planning model (GMOP). The proposed algorithm uses the short-term memory mechanism (Taboo List) for the selection of alternate strokes to produce each product. The validation of the algorithm was carried out analyzing the quality and the solution times. The algorithm demonstrated potential by reaching difference percentages around 10% and 17% compared with optimal solutions in large problems and a balance between quality and solution times when is used in relatively small problems