Presentating a multi-objective optimization model for resource-constrained project scheduling regarding financial costs, time delays and the reliability function

The common presuppositions and limitations regarding the Resource Constrained Project Scheduling Problem (RCPSP) were investigated in addition to their reliability in modeling in order to investigate the possibility of availability of renewable resources using a new attitude. The objective of modeling RCPSP was the quantification of total costs and minimization of delays in projects. Hence, in order to mathematically model RCPSP, the first non-linear complex integer math programming was transformed into a linear programming model using the features of exponential functions. To solve the final linear math problem, some experimental examples were designed in different dimensions aiming to study the performance and efficiency of the designed model. For solving low-dimension problems, the exact (epsilon) constraint multi-objective optimization method was used in the Lingo software. A meta-heuristic algorithm called NSGA-II was employed to find solutions for high-dimension problems that the Exact method could not solve. The results of using these algorithms and the statistical analysis (with 95% reliability) indicated that the performance was suitable for the Genetic Algorithm (GA). The calculation error between the Exact method and the meta-heuristic method for the three target categories of total cost, time delay, and reliability was calculated based on the obtained results. The number of errors in calculating the total cost was 26%, 19%, and 5%, respectively. Also, the delay objective function error was equal to 28%, 24%, 12 %, and 14%, respectively. Finally, the reliability objective function error value was equal to 8%, 3%, 29%, and 36%, respectively. Accordingly, it can be concluded that this meta-heuristic algorithm (GA) has more efficiency and more apposite performance for the recommended model compared with the Exact optimization software. The use of the math model designed in this study can result in decreasing the time delays in projects and the costs of scheduling problems, as well as increasing the reliability in multi-mode activities.