Modification in Chen and Tsai’s method for solving time–cost trade-off problems of project networks in fuzzy environments

Chen and Tsai [Eur J Oper Res 212:386–397, 2011] proposed a method to find the lower and upper bound of α-cut of the minimum total fuzzy crash cost and optimal fuzzy activity times of the project networks in fuzzy environments and used the values of lower and upper bounds, corresponding to different values of α, to obtain the minimum total fuzzy crash cost and the optimal fuzzy activity times. In this paper, it is pointed out that in the α-cut of optimal fuzzy activity times, obtained by using the existing method, the lower bound is not necessarily less than the upper bound. Also, some modifications in the existing method are suggested so that in the α-cut of optimal fuzzy activity time, the lower bound is always less than or equal to upper bound.