Modeling and Solution Procedure for a Preemptive Multi-Objective Multi-Mode Project Scheduling Model in Resource Investment Problems

Document Type : Original Manuscript


1 MSc, Department of Industrial Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 Associate Professor, Department of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran


In this paper, a preemptive multi-objective multi-mode project scheduling model for resource investment problem is proposed. The first objective function is to minimize the completion time of project (makespan);the second objective function is to minimize the cost of using renewable resources. Non-renewable resources are also considered as parameters in this model. The preemption of activities is allowed at any integer time units, and for each activity, the best execution mode is selected according to the duration and resource. Since this bi-objective problem is the extension of the resource-constrained project scheduling problem (RCPSP), it is NP-hard problem, and therefore, heuristic and metaheuristic methods are required to solve it. In this study, Non-dominated Sorting Genetic AlgorithmII (NSGA-II) and Non-dominated Ranking Genetic Algorithm (NRGA) are used based on results of Pareto solution set.We also present a heuristic method for two approaches of serial schedule generation scheme (S-SGS) and parallel schedule generation scheme (P-SGS) in the developed algorithm in order to optimize the scheduling of the activities.The input parameters of the algorithm are tuned with Response Surface Methodology (RSM). Finally, the algorithms are implemented on some numerical test problems, and their effectiveness is evaluated.


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