Taguchi method is one of the most popular approaches for design optimization such that performance characteristics become robust to uncontrollable noise variables. However, most previous Taguchi method applications have addressed a single-characteristic problem. Problems with multiple characteristics are more common in practice. The multi-criteria decision making(MCDM) problem is to select the optimal one among multiple alternatives by integrating a number of criteria that may conflict with each other. Representative MCDM methods include TOPSIS(Technique for Order of Preference by Similarity to Ideal Solution), GRA(Grey Relational Analysis), PCA(Principal Component Analysis), fuzzy logic system, and so on. Therefore, numerous approaches have been conducted to deal with the multi-characteristic design problem by combining original Taguchi method and MCDM methods. In the MCDM problem, multiple criteria generally have different measurement units, which means that there may be a large difference in the physical value of the criteria and ultimately makes it difficult to integrate the measurements for the criteria. Therefore, the normalization technique is usually utilized to convert different units of criteria into one identical unit. There are four normalization techniques commonly used in MCDM problems, including vector normalization, linear scale transformation( max-min, max, or sum). However, the normalization techniques have several shortcomings and do not adequately incorporate the practical matters. For example, if certain alternative has maximum value of data for certain criterion, this alternative is considered as the solution in original process. However, if the maximum value of data does not satisfy the required degree of fulfillment of designer or customer, the alternative may not be considered as the solution. To solve this problem, this paper employs the desirability function that has been proposed in our previous research. The desirability function uses upper limit and lower limit in normalization process. The threshold points for establishing upper or lower limits let us know what degree of fulfillment of designer or customer is. This paper proposes a new design optimization technique for multi-characteristic design problem by integrating the Taguchi method and our desirability functions. Finally, the proposed technique is able to obtain the optimal solution that is robust to multi-characteristic performances.

Conventional data envelopment analysis (DEA) models require that inputs and outputs are given as crisp values. Very often, however, some of inputs and outputs are given as imprecise data where they are only known to lie within bounded intervals. While a typical approach to addressing this situation for optimization models such as DEA is to conduct sensitivity analysis, it provides only a limited ex-post measure against the data imprecision. Robust optimization provides a more effective ex-ante measure where the data imprecision is directly incorporated into the model. This study aims to apply robust optimization approach to DEA models with imprecise data. Based upon a recently developed robust optimization framework which allows a flexible adjustment of the level of conservatism, we propose two robust optimization DEA model formulations with imprecise data; multiplier and envelopment models. We demonstrate that the two models consider different risks regarding imprecise efficiency scores, and that the existing DEA models with imprecise data are special cases of the proposed models. We show that the robust optimization for the multiplier DEA model considers the risk that estimated efficiency scores exceed true values, while the one for the envelopment DEA model deals with the risk that estimated efficiency scores fall short of true values. We also show that efficiency scores stratified in terms of probabilistic bounds of constraint violations can be obtained from the proposed models. We finally illustrate the proposed approach using a sample data set and show how the results can be used for ranking DMUs.

  According to the automated manufacturing processes followed by the development of computer manufacturing technologies, products or quality characteristics produced on the processes have measured and recorded automatically. Much amount of data daily prod

저등급 석탄인 갈탄(lignite)을 순환 유동층 가스화기(circulating fluidized bed gasifier)의 효과적인 가스화를 위한 공급탄으로 제조하기 위하여 모든 조건들은 동일하고 스크린의 크기만을 변경하여 목적하는 입도분포 특성을 달성하는 최적조건을 찾기 위한 실험을 수행하였다. 가스화기 공급탄은 0.045~1 mm 크기로 85 wt% 이상이 요구되며 이러한 입도분포를 갖는 공급탄을 제조하기 위해서는 경제적이면서도 효과적인 공정 설계가 반드시 필요하다. 따라서 본 연구는 중국산 갈탄을 해머밀로 효과적으로 분쇄하기 위하여 다구치 설계를 사용하였으며, 설계조건에 따른 실험결과 및 통계분석 결과 95% 유의수준에서 1차 스크린의 크기는 3 mm, 2차 스크린의 크기는 1.3 mm인 경우가 최적화된 조건인 것으로 나타났다.