Document Type : Research Paper


1 Department of Industrial Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Rasht Branch, Islamic Azad University, Gilan, Iran.

3 Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran


The Resource-Constrained Project Scheduling Problem (RCPSP) is a general one in scheduling which possesses various applications in production, production scheduling, project managing and other criteria. This issue has been studied since 1960 and is very complicated. In this study, the common presuppositions and limitations regarding such problems will be investigated in addition to their reliability in modelization in order to investigate the possibility of availability of renewable resources using a new attitude. The objective of modelization of RCPSP is quantification of total costs and minimization of delays in projects. Therefore, in order to mathematically modelize RCPSP, non-linear complex integer math programming which transforms into a linear programming model using the features of exponential functions is used. In order to solve the final linear math problem, some experimental examples will be designed in different dimensions, so that the performance and efficiency of the designed model are studied. For solving problems with low dimensions , the Epsilon Constraint multi-objective optimization method is used in an exact optimization software like Lingo. In order to find out the solutions of the ones whose dimensions are high, which exact methods can not solve,the meta-heuristic algorithm called NSGA-II which is a strong one to optimize multi objective problems is used. The results of using these algorithms and the statistical analysis which shows their reliability as 95 percent , indicates that the performance is suitable for genetic algorithms. Therefore this meta-heuristic algorithm has more efficiency and more apposite performance for the recommended model compared with the software of exact optimization. Using the designed math model ,this study can result in decreasing the times of delay in projects and the costs in the scheduling problem and also increasing the reliability when activities are multi-mode.


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