This paper builds upon earlier work from the decision/risk analysis area in presenting simple, easy-to-use approximations for the mean and variance of PERT activity times. These approximations offer significant advantages over the PERT formulas currently being taught and used, as well as over recently proposed modifications. For instance, they are several orders of magnitude more accurate than their PERT counterparts in estimating means and variances of beta distributions if the data required for all methods are obtained accurately. Moreover, they utilize probability data that can be assessed more reliably than those required by the PERT formulas, while still requiring just three points from each activity time probability distribution. Using the proposed approximations can significantly improve the accuracy of probability statements about project completion time, and their use complements ongoing efforts to improve PERT analyses of networks involving multiple critical paths.PERT, three-point approximations, activity time estimation, project management

Saaty's analytic hierarchy proces\ a\se\wd a[tributc irnportance by soliciting decision makers' (DM) importance ratius to cornpute weight>. Saaty suggested :i decision rule lor accepting DM judgments based on ii con5istency measure derived from the DM's importance ratios. This paper Investigates the distribtition of random inconsistency and dccision rule implications. Stricter consistency requircments lor three-and lour-attribute criteria inatriccs are suggested..Cuhjecr .4reas: Decic.ion .4naly.si.s and I)eci.rion f'rocrsses. THE ANALY'I'IC HIEXARCHY PROCESSThe analytic hierarchy process (AHP) [7] 181 is a popular tool used by decision analysts to aid decision makers (DMs) in niultiattribute decisions. Zahedi's [lh] introduction and literature review is recommended for detailed information. In AHP, the hierarchy's first level i y the general objective for the decision. A typical hierarchy's second level has several attributes (criteria) that contribute to the general objective. Lower levels subdivide the attributes. Further levels relate the available alternatives lo each attribute or subdivision. This paper's terminology relates to the second level of the hierarchy, although the results apply to all levels. The brief discussion that follows emphasizes background items for the new work to be presented. AHP IpdtaFor each pair of attributes, the DM is asked, "What is the relative importance of this attribute with respect to that one?" The answers are importance ratios. The traditional A H P pairwise cornparison scale 191 has 17 importance ratios: the integers from 1 to 9 and the 8 reciprocals I'rorn 112 t o 119. For example, ratio I means the attributes are about equally importailt, 9 nieans the first is extremely more important than the second, and 115 means the second attribute is strongly more important than the first. Saaty [6] introduced a crireria matrix, C, to hold the importance ratios. For example, after attributes D, E, and 1; are identified a DM might provide the ratios shown i n the following matrix: A t t r b 1 11 t e S

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