An Integrated Model for Multi-Mode Resource-Constrained Multi-Project Scheduling Problems Considering Supply Management with Sustainable Approach in the Construction Industry under Uncertainty Using Evidence Theory and Optimization Algorithms

In this study, the multi-mode resource-constrained multi-project scheduling problems (MMRCMPSPs) considering supply management and sustainable approach in the construction industry under uncertain conditions have been investigated using evidence theory to mathematical modeling and solving by multi-objective optimization algorithms. In this regard, a multi-objective mathematical model has been proposed, in which the first objective function aims to maximize a weighted selection of projects based on economic, environmental, technical, social, organizational, and competitive factors; the second objective function is focused on maximizing profit, and the third objective function is aimed at minimizing the risk of supply management. Moreover, various components, such as interest rates, carbon penalties, and other implementation limitations and additional constraints, have also been considered in the modeling and mathematical relationships to improve the model's performance and make it more relevant to real-world conditions and related issues, leading to better practical applications. In the mathematical modeling adopted, the processing time of project activities has been considered uncertain, and the evidence theory has been utilized. This method can provide a flexible and rational approach based on evidence and knowledge in the face of uncertainty. In addition, to solve the proposed multi-objective mathematical model, metaheuristic optimization algorithms, such as the differential evolution (DE) algorithm based on the Pareto archive, have been used, and for evaluating the results, the non-dominated sorting genetic algorithm II (NSGA-II) has also been employed. Furthermore, the results have been compared based on multi-objective evaluation criteria, such as quality metric (QM), spacing metric (SM), and diversity metric (DM). It is worth noting that to investigate the performance and application of the proposed model, multiple evaluations have been conducted on sample problems with different dimensions, as well as a case study on residential apartment construction projects by a contracting company. In this respect, the answers obtained from solving the model using the multi-objective DE algorithm were better and superior to the NSGA-II algorithm and had a more favorable performance. Generally, the results indicate that using the integrated multi-objective mathematical model in the present research for managing and scheduling multi-mode resource-constrained multi-project problems, especially in the construction industry, can lead to an optimal state consistent with the desired objectives and can significantly improve the progress and completion of projects.