Solving Lotsizing Problems on Parallel Identical Machines Using Symmetry Breaking Constraints

Production planning on multiple parallel machines is an interesting problem, both from a theoretical and practical point of view. The parallel machine lotsizing problem consists of finding the optimal timing and level of production and the best allocation of products to machines. In this paper we look at how to incorporate parallel machines in a Mixed Integer Programming model when using commercial optimization software. More specifically, we look at the issue of symmetry. When multiple identical machines are available, many alternative optimal solutions can be created by renumbering the machines. These alternative solutions lead to difficulties in the branch-and-bound algorithm. We propose new constraints to break this symmetry. We tested our approach on the parallel machine lotsizing problem with setup costs and times, using a network reformulation for this problem. Computational tests indicate that several of the proposed symmetry breaking constraints substantially improve the solution time, except when used for solving the very easy problems. The results highlight the importance of creative modeling in solving Mixed Integer Programming problems.Mixed Integer Programming;Formulations;Symmetry;Lotsizing

A hybrid genetic algorithm for solving a layout problem in the fashion industry.

As of this writing, many success stories exist yet of powerful genetic algorithms (GAs) in the field of constraint optimisation. In this paper, a hybrid, intelligent genetic algorithm will be developed for solving a cutting layout problem in the Belgian fashion industry. In an initial section, an existing LP formulation of the cutting problem is briefly summarised and is used in further paragraphs as the core design of our GA. Through an initial attempt of rendering the algorithm as universal as possible, it was conceived a threefold genetic enhancement had to be carried out that reduces the size of the active solution space. The GA is therefore rebuilt using intelligent genetic operators, carrying out a local optimisation and applying a heuristic feasibility operator. Powerful computational results are achieved for a variety of problem cases that outperform any existing LP model yet developed.Fashion; Industry;

Solving Lotsizing Problems on Parallel Identical Machines Using Symmetry Breaking Constraints

Production planning on multiple parallel machines is an interesting problem, both from a theoretical and practical point of view. The parallel machine lotsizing problem consists of finding the optimal timing and level of production and the best allocation of products to machines. In this paper we look at how to incorporate parallel machines in a Mixed Integer Programming model when using commercial optimization software. More specifically, we look at the issue of symmetry. When multiple identical machines are available, many alternative optimal solutions can be created by renumbering the machines. These alternative solutions lead to difficulties in the branch-and-bound algorithm. We propose new constraints to break this symmetry. We tested our approach on the parallel machine lotsizing problem with setup costs and times, using a network reformulation for this problem. Computational tests indicate that several of the proposed symmetry breaking constraints substantially improve the solution time, except when used for solving the very easy problems. The results highlight the importance of creative modeling in solving Mixed Integer Programming problems

Análisis del proceso productivo de una empresa de confecciones: Modelación y simulación

Modeling and simulation of small industrial systems, has become important in the decision-making processes, because it allows small companies to make their production decisions. This article analyses a company engaged in the manufacture of men’s outwear with average weekly production of 490 units. The motivation of this study lies in the interest the company owners have to increase its productivity; for this reason, a model of the real system with Arena® tool was developed. With this model, it was possible to recognize the process parts that cause delays and bottlenecks and from there it was suggested a valid solution scenario. This paper shows the results of real system simulation and proposes two scenarios which provide an increase in the productivity.El modelado y simulación de pequeños sistemas industriales ha adquirido gran importancia en los procesos de toma de decisiones, toda vez que les permite a microempresas fundamentar sus decisiones de producción. Este artículo hace un análisis de una empresa dedicada a la confección de ropa exterior masculina con una producción semanal promedio de 490 prendas. La motivación del estudio radica en el interés de incrementar su productividad; por esto, se desarrolló un modelo del sistema real con la herramienta Arena®, logrando identificar las partes de los procesos responsables de atrasos y “cuellos de botella” que permitieron plantear el escenario de solución. Este documento muestra los resultados de la simulación del sistema real y una comparación con un escenario de mejora que presentó un aumento en la productividad

The Review of Mark Planning Problem

Mark planning is one of the most important planning processes in garment industry. The major function is to generate a set of markers which is used as cutting guidelines or cutting templates in a cutting process. In other words, this process can be seen as a planning step of a cutting process which determines what sequence and how many parts will be cut. For the academic point of view, mark planning has been of interests for more than 15 years. Many papers were published with various objective functions, problem scenarios, and constraints. Therefore, a summarization of these papers representing key contents of each paper will be useful for researchers who are interested in this type of problem. The purpose of this paper is to introduce an exhaustive review of mark planning papers which is composed of three sections: the relevant background, the summary of papers, and the relationship between objective functions which is cost combinations and major garment characteristics. In conclusion, future researches should go forward the trend of integration between this process and other relevant processes in the production chain, e.g. cut scheduling, assembly planning, marker making

Alternative formulations for a layout problem in the fashion industry

In this paper we propose alternative IP models for solving the layout problem in the fashion industry as described in Degraeve and Vandebroek (1998). Before cutting, several layers of cloth are put on a cutting table and several templates, indicating how to cut all material for a specific size, are fixed on top of the stack. The problem consists of finding good combinations of templates and the associated height of the stack of cloth to satisfy demand while minimizing total waste. Computational results indicate that our alternative models outperform the originally proposed model. We also discuss how the new models can be adapted for the multicolor version of the problem..status: publishe