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Earned value management (EVM)–based models for estimating project actual duration (AD) and cost at completion using various methods are continuously developed to improve the accuracy and actualization of predicted values. This study primarily aimed to examine natural gradient boosting (NGBoost-2020) with the classification and regression trees (CART) base model (base learner). To the best of the authors' knowledge, this concept has never been applied to EVM AD forecasting problem. Consequently, the authors compared this method to the single K-nearest neighbor (KNN) method, the ensemble method of extreme gradient boosting (XGBoost-2016) with the CART base model and the optimal equation of EVM, the earned schedule (ES) equation with the performance factor equal to 1 (ES1). The paper also sought to determine the extent to which the World Bank's two legal factors affect countries and how the two legal causes of delay (related to institutional flaws) influence AD prediction models.

In this paper, data from 30 construction projects of various building types in Iran, Pakistan, India, Turkey, Malaysia and Nigeria (due to the high number of delayed projects and the detrimental effects of these delays in these countries) were used to develop three models. The target variable of the models was a dimensionless output, the ratio of estimated duration to completion (ETC(t)) to planned duration (PD). Furthermore, 426 tracking periods were used to build the three models, with 353 samples and 23 projects in the training set, 73 patterns (17% of the total) and six projects (21% of the total) in the testing set. Furthermore, 17 dimensionless input variables were used, including ten variables based on the main variables and performance indices of EVM and several other variables detailed in the study. The three models were subsequently created using Python and several GitHub-hosted codes.

For the testing set of the optimal model (NGBoost), the better percentage mean (better%) of the prediction error (based on projects with a lower error percentage) of the NGBoost compared to two KNN and ES1 single models, as well as the total mean absolute percentage error (MAPE) and mean lags (MeLa) (indicating model stability) were 100, 83.33, 5.62 and 3.17%, respectively. Notably, the total MAPE and MeLa for the NGBoost model testing set, which had ten EVM-based input variables, were 6.74 and 5.20%, respectively. The ensemble artificial intelligence (AI) models exhibited a much lower MAPE than ES1. Additionally, ES1 was less stable in prediction than NGBoost. The possibility of excessive and unusual MAPE and MeLa values occurred only in the two single models. However, on some data sets, ES1 outperformed AI models. NGBoost also outperformed other models, especially single models for most developing countries, and was more accurate than previously presented optimized models. In addition, sensitivity analysis was conducted on the NGBoost predicted outputs of 30 projects using the SHapley Additive exPlanations (SHAP) method. All variables demonstrated an effect on ETC(t)/PD. The results revealed that the most influential input variables in order of importance were actual time (AT) to PD, regulatory quality (RQ), earned duration (ED) to PD, schedule cost index (SCI), planned complete percentage, rule of law (RL), actual complete percentage (ACP) and ETC(t) of the ES optimal equation to PD. The probabilistic hybrid model was selected based on the outputs predicted by the NGBoost and XGBoost models and the MAPE values from three AI models. The 95% prediction interval of the NGBoost–XGBoost model revealed that 96.10 and 98.60% of the actual output values of the testing and training sets are within this interval, respectively.

Due to the use of projects performed in different countries, it was not possible to distribute the questionnaire to the managers and stakeholders of 30 projects in six developing countries. Due to the low number of EVM-based projects in various references, it was unfeasible to utilize other types of projects. Future prospects include evaluating the accuracy and stability of NGBoost for timely and non-fluctuating projects (mostly in developed countries), considering a greater number of legal/institutional variables as input, using legal/institutional/internal/inflation inputs for complex projects with extremely high uncertainty (such as bridge and road construction) and integrating these inputs and NGBoost with new technologies (such as blockchain, radio frequency identification (RFID) systems, building information modeling (BIM) and Internet of things (IoT)).

The legal/intuitive recommendations made to governments are strict control of prices, adequate supervision, removal of additional rules, removal of unfair regulations, clarification of the future trend of a law change, strict monitoring of property rights, simplification of the processes for obtaining permits and elimination of unnecessary changes particularly in developing countries and at the onset of irregular projects with limited information and numerous uncertainties. Furthermore, the managers and stakeholders of this group of projects were informed of the significance of seven construction variables (institutional/legal external risks, internal factors and inflation) at an early stage, using time series (dynamic) models to predict AD, accurate calculation of progress percentage variables, the effectiveness of building type in non-residential projects, regular updating inflation during implementation, effectiveness of employer type in the early stage of public projects in addition to the late stage of private projects, and allocating reserve duration (buffer) in order to respond to institutional/legal risks.

Ensemble methods were optimized in 70% of references. To the authors' knowledge, NGBoost from the set of ensemble methods was not used to estimate construction project duration and delays. NGBoost is an effective method for considering uncertainties in irregular projects and is often implemented in developing countries. Furthermore, AD estimation models do fail to incorporate RQ and RL from the World Bank's worldwide governance indicators (WGI) as risk-based inputs. In addition, the various WGI, EVM and inflation variables are not combined with substantial degrees of delay institutional risks as inputs. Consequently, due to the existence of critical and complex risks in different countries, it is vital to consider legal and institutional factors. This is especially recommended if an in-depth, accurate and reality-based method like SHAP is used for analysis.