The paper deals with the investigation of the critical factor of the supply chain concerning time factor. The literature review can give a background to understand and handle the reasons and consequences of the growing importance of time. By using utility functions to represent the value of various delivery-times for the different participants in the supply chain, including the final customers, it proves through the Kano-model, that the choices, behaviour and willingness of payment of time-sensitive and non time-sensitive consumers are different for varying lead times, so for optimization soft computing techniques must be applied. As the functions are not linear and significant uncertainty must be handled as well, the use of fuzzy numbers is necessary. The features of fuzzy power functions are investigated, and a parametric approaches is presented that can be an efficient approximation of the values calculated on the basis of extension principle. © 2009 IEEE.