Necessary Criticality of Paths in Networks with Imprecise Durations and Time lags

This research deals with the problems of the necessarily critical paths in the networks with imprecise durations and time lags, represented by intervals or fuzzy numbers. So far, the related problems have been solved when the activity durations are imprecise, by several authors. However, they do not consider the impressions in time lags in their models. In this paper, we assume that the time lags of the precedence relations are imprecise (intervals or fuzzy). In the case of interval, it is shown that both problems of asserting whether a given path is necessarily critical and the problem of determining an arbitrary necessarily critical path are not difficult to be resolved. Then, the interval durations and time lags are generalized into fuzzy numbers. For this purpose, we implement an algorithm for calculating the degree of necessary criticality of a path. Then, a linear programming (LP) approach is proposed to determine this degree for L-L type fuzzy numbers of the model. This LP model is simpler than the previously algorithms and the results are more robust. The proposed approach can determine the paths that are necessary critical with maximum degree.