## 1 Introduction  
Projects ending later and costing more than planned are widespread phenomena in the construction industry [1; 2]. Numerous causes were identified in the construction management literature [3; 4; 5]. Among them, one cause that is persistently identified in late projects is poor planning and project control practices [6].  
Paradoxically, extensive research focused for quite some time on the development of enhanced project planning tools, such as the project evaluation and review technique (PERT) [7], stochastic network analysis (SNA) [8], and artificial intelligence and statistical learning techniques [9]. Additionally, in recent years, project monitoring and control techniques also gained more research attention, including critical chain management [10], earned value management [11], and schedule risk analysis [12].  
However, most of the advanced techniques above were not successfully adopted by construction management practitioners [13]. Currently, classical deterministic scheduling techniques such as the Gantt chart [14] and the critical path method (CPM) [15] still occupy a prominent position in the daily practice of construction management [16]. Indeed, deterministic techniques have some important advantages. They are easier to learn, and their outputs are easier to understand and communicate. The amount of input information they require is generally much lower than other advanced techniques. Additionally, the calculations they involve are also significantly less computer-intensive and do not generally require advanced training to implement them.  
However, deterministic scheduling techniques also suffer from serious limitations [16]. In a recent study, [PERSON] et al. [17] broke down the core assumptions of some classical scheduling techniques and exemplified why they consistently underestimate the project duration even when accurate input information is available. Their findings were not new, but they emphasized that deterministic techniques' major source of inaccuracy stems from neglecting and/or not properly handling activity duration variability. Duration variability is defined here as the difference between the actual (final) duration and the planned (initial) duration of a project activity.  
Hence, the purpose of this paper is to propose some mathematical expressions that approximate the average project duration and the project duration standard deviation when its activities have some variability (virtually all real-life projects). Our estimates are compared against the analogous PERT project duration estimates. It is shown how, at the expense of minimal additional calculation and from the very same input information, our estimates largely outperform the PERT estimates. This allows bridging the accuracy gap that separates deterministic techniques from more complex techniques.  
The paper is structured as follows: Section 2_Background_ describes the activity duration variability and the merge event bias, which are the major source and consequence, respectively, of inaccuracy in all deterministic techniques. In Section 3_Research methods_, the mathematical expressions proposed are presented and all their subcomponents are justified. Section 4_Application example_ describes how all the calculations can be easily implemented step by step. Section 5_Analysis_ and Section 6_Results_ describe how the two expressions were tested with a diverse and representative artificial network dataset. Section 7_Discussions_ comments on how the expressions can be used in real contexts to improve the reliability of project management tasks in general, and the accuracy of some complementary scheduling techniques in particular. Then, Section 8_Conclusions_ summarizes the paper's contributions, highlighting the research limitations and proposing future avenues of research.