## 8 Conclusions  
Deterministic scheduling techniques, such as the Gantt chart and the critical path method, are still the most common in practical settings these days. However, these techniques neglect activity duration variability which exacerbates a phenomenon known as the _merge event bias_. This bias is shared with the PERT duration estimates and is generally translated into average project durations being underestimated and standard deviations being overestimated. More recently, many advanced non-deterministic scheduling techniques were proposed. However, they are significantly more complex and highly computer-intensive, they require extensive precalibration information, and/or practitioners are not adequately trained to implement them. As a result, their adoption in practice is quite limited. In this paper, we proposed a series of empirical expressions that allow construction project schedulers to come up with better estimates of the average project duration (\(\mu_{p}\)) and the project duration standard deviation (\(\sigma_{p}\)). These estimates clearly outperform the analogous classical PERT estimates with the need for neither extra (deterministic) scheduling information nor a substantial additional calculation effort. For testing the superiority of our estimates, a wide and representative benchmark dataset containing 4100 networks (schedules) was employed. The activity durations and their variabilities were modeled with different statistical distributions and different parametrizations. In this study, we commented on some apparent limitations of our estimates and how to overcome them. Finally, we also extensively discussed how the \(\mu_{p}\) and \(\sigma_{p}\) estimates can be used in real construction contexts and/or in combination with other techniques (such as earned value management, and schedule risk analysis) to enhance accuracy or reduce calculation effort. Future avenues of research are plentiful. For example, the current estimates work well with fewer than five critical and subcritical parallel paths (\(N_{p}<5\)). Future expressions may want to use higher-degree polynomials of the variable \(LN(N_{p})\) to improve the accuracy of our \(\mu_{p}\) and \(\sigma_{p}\) estimates. Similarly, the accuracy of the \(\sigma_{p}\) estimate, when lognormal activity duration variability is assumed, could clearly be improved. Future research may want to consider extending the array of estimates that can be (deterministically) calculated. A fine example would be approximating the probability of an activity being critical (the criticality index) with deterministic calculations. This would greatly benefit the field of schedule risk analysis by allowing many metrics to be calculated with computer simulation. The following are available online at [[http://www.mdpi.com/2076-3417/10/2/654/s1](http://www.mdpi.com/2076-3417/10/2/654/s1)]([http://www.mdpi.com/2076-3417/10/2/654/s1](http://www.mdpi.com/2076-3417/10/2/654/s1)): Supplementary A: Real projects dataset characteristics summary and project activity durations log means and log standard deviations; Supplementary B: 4100-project schedule networks and datasets regression results; Supplementary C: Dataset I \(\mu_{p}\) and \(\sigma_{p}\) regression QQ plots and homoscedasticity graphs; Supplementary D: Summary of all datasets \(\mu_{p}\) and \(\sigma_{p}\) regression results with free \(K_{1}\) and \(K_{2}\). Conceptualization, P.B.-P.; methodology, P.B.-P. and A.C.-N.; validation, P.B.-P. and M.V. ; formal analysis, P.B.-P.; investigation, P.B.-P., M.O.-M. and J.Z. ; resources, M.V. ; data curation, M.V. ; writing--original draft preparation, P.B.-P., A.C.-N. and M.V. ; writing--review and editing, P.B.-P., A.C.-N. and M.V. ; supervision, M.O.-M. and A.P.-F.; funding acquisition, P.B.-P., A.C.-N. and A.P.-F. All authors have read and agreed to the published version of the manuscript. The first author acknowledges the Spanish Ministry of Science, Innovation, and Universities for his Ramon y Cajal contract (RYC-2017-22222) co-funded by the European Social Fund.