Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 365697, 18 pages
Research Article

A Modified PSO Algorithm for Minimizing the Total Costs of Resources in MRCPSP

1Department of Industrial Engineering, Sharif University of Technology, Tehran 11365-8639, Iran
2Department of Industrial Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran

Received 6 September 2011; Revised 4 December 2011; Accepted 30 December 2011

Academic Editor: Yi-Chung Hu

Copyright © 2012 Mohammad Khalilzadeh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce a multimode resource-constrained project scheduling problem with finish-to-start precedence relations among project activities, considering renewable and nonrenewable resource costs. We assume that renewable resources are rented and are not available in all periods of time of the project. In other words, there is a mandated ready date as well as a due date for each renewable resource type so that no resource is used before its ready date. However, the resources are permitted to be used after their due dates by paying penalty costs. The objective is to minimize the total costs of both renewable and nonrenewable resource usage. This problem is called multimode resource-constrained project scheduling problem with minimization of total weighted resource tardiness penalty cost (MRCPSP-TWRTPC), where, for each activity, both renewable and nonrenewable resource requirements depend on activity mode. For this problem, we present a metaheuristic algorithm based on a modified Particle Swarm Optimization (PSO) approach introduced by Tchomté and Gourgand which uses a modified rule for the displacement of particles. We present a prioritization rule for activities and several improvement and local search methods. Experimental results reveal the effectiveness and efficiency of the proposed algorithm for the problem in question.