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Engineering design evaluation is characterized by imprecise (vague) importance and satisfaction levels of criteria, which are better treated as fuzzy variables rather than as subjective crisp variables. Nevertheless, operations on fuzzy numbers tend to increase unnecessarily the imprecision when they are combined for some applications, particularly, when a fuzzy-weighted average (FWA) is calculated. This paper proposes a novel method of operating on fuzzy numbers to obtain a fuzzyweighted average of desirability levels during design evaluation. The method produces overall desirability levels less imprecise and more realistic than those of the conventional FWA. Furthermore, the balance points of these fuzzy numbers seem to be more credible than those of the FWA. An example is presented, which demonstrates the advantages of the method developed. IntroductionDesign is a main concern in modern manufacturing companies. Enterprises need to invest in designing because they have to develop new products to remain competitive in the market of today and operate at a pro® t. However, not only by carrying out design will manufacturing companies be pro® table and competitive, but also they need to improve the eOE ectiveness of the design activity. For many years, manufacturing companies tended to concentrate on improving manufacturing processes (Birmingham et al. 1997), but now they realise the potential of improvements and cost reduction during the design process. A study conducted by Lotter (1986) indicates that as much as 75% of the costs of a product is de® ned during the design stage. Therefore, it is here, in the execution and management of the design process, that signi® cant, potential reductions of cost can be made.To exploit all the potential of the design activity, companies have to understand well how to carry out this process; however, what they face is a very complex and not well understood design. Time to introduce a new product or artefact into the market and the design and manufacturin g costs have to be maintain at a minimum; also, the product has to have the right quality in order that the company can have success. Then, designers have to explore divergently such that several design solutions are considered to select the best design, that is, the design that satis® es the need with the lower costs and time to market, and the best quality.

As variables in the design evaluation stage are imprecise (fuzzy), tools, such as fuzzy set theory, should be used. This paper presents several fuzzy approaches to design evaluation. Weights of criteria and performance levels are captured by fuzzy numbers, and the overall performance of an alternative is calculated through the new fuzzy weighted average. Different approaches to express and calculate performance are discussed. Two metrics for measuring performance levels per criterion of a solution are proposed. Also, a new type of fuzzy goal is suggested. Finally, a novel way of comparing the overall performance of a design candidate by drawing an aggregate profile of performance is proposed. It is concluded that fuzzy set theory is a powerful and flexible tool for dealing with the imprecision in different types of problems in design evaluation.

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Agregar un nuevo canal de ventas genera nuevos desafíos en términos de gestión de inventarios debido a la diferencia de tamaño de los pedidos y tiempos de cumplimiento además de la incertidumbre en la demanda de ambos canales. El objetivo es diseñar un modelo de gestión de inventarios mixto compuesto por un modelo de reaprovisionamiento conjunto para el canal tradicional de tiendas minoristas y un modelo de revisión continua con para el canal Online, ambos con demanda estocástica, por la diferencia que presentan en su gestión operativa. Se desarrollo un método heurístico para la solución del problema y para su validación se evaluaron ejemplos numéricos donde se encontró una reducción de 11% en el costo de la política de inventario del almacén de doble canal con el modelo propuesto el cual busca representar una aproximación de la gestión como lo es el reaprovisionamiento conjunto en los minoristas.