Solving the multi-response problem in Taguchi method by benevolent formulation in DEA

The Taguchi method is an efficient approach for optimizing a single quality response. In practice, however, most products/processes have more than one quality response of main interest. Recently, the multi-response problem in the Taguchi method has gained a considerable research attention. This research, therefore, proposes an efficient approach for solving the multi-response problem in the Taguchi method utilizing benevolent formulation in data envelopment analysis (DEA). Each experiment in Taguchi’s orthogonal array (OA) is treated as a decision making unit (DMU) with multiple responses set inputs and/or outputs. Each DMU is evaluated by benevolent formulation. The ordinal value of the DUM’s efficiency is then used to decide the optimal factor levels for multi-response problem. Three frequently-investigated case studies are adopted to illustrate the proposed approach. The computational results showed that the proposed approach provides the largest total anticipated improvement among principal component analysis (PCA), DEA based ranking approach (DEAR) and other techniques in literature. In conclusion, the proposed approach may provide a great assistant to practitioners for solving the multi-response problem in manufacturing applications on the Taguchi method.