An evolutionary search procedure for optimizing time–cost performance of projects under multiple renewable resource constraints Reza Zamani ⇑ SISAT, Faculty of Engineering and Information Sciences, Wollongong University, Building 39, Wollongong, NSW 2522, Australia article info Article history: Received 28 September 2011 Received in revised form 24 April 2013 Accepted 11 July 2013 Available online 19 July 2013 Keywords: Project management Resource constrained Time–cost trade-off Multimode projects Overall cost minimization Evolutionary computation abstract This paper presents an effective procedure for optimizing time–cost performance of multi-mode resource constrained project scheduling problems in which activities are subject to finish-start precedence con- straints under renewable limited resources. Associated with each execution mode of activities, there exists a direct cost, a processing time, and a set of required renewable resources. In optimizing time–cost performance, the procedure treats the cost as a non-renewable resource whose limit can affect the dura- tion of the project and balances cost versus time through the notion of priority-rank. This is performed by the use of a module which handles multimode projects, and since the procedure has to call this module with different limits on the cost, the effectiveness of this module plays a key role in the overall efficiency. For this reason, an effective evolutionary search technique has been developed to create the basis of this module. For testing its effectiveness, this module has been tested on 552 largest multimode benchmark instances of the PSPLIB and the results are promising: For over 98% of instances, the module finds the best available solutions in the literature. The module also produces a solution for one of these benchmark instances that is better than all of the current solutions in the literature. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Market globalization is a major force to build sophisticated soft- ware applications for the planning, organizing, and controlling of enterprise projects. One of the major functions of these software applications is to provide project mangers with an analysis of cost– time performance of their projects (Raymond & Bergeron, 2008). Pro- ject scheduling is a branch of scheduling aimed at developing algo- rithms handling such complexities in project management. Scheduling is defined as the allocation of resources over time to perform a collection of activities (Baker, 1974). In theory, the sched- uling phase begins after the planning phase, in which the planner identifies (i) a collection of activities to be carried out, and (ii) the le- vel of resources required in the project to handle these activities. Theoretically, planning decisions correspond to long range commit- ments and scheduling decisions cannot be made unless the restric- tions imposed by planning commitments have been identified. In practice, however, planning is intensively intertwined with schedul- ing, and a versatile resource is required to facilitate their interaction, with monetary resources playing the role of such a versatile re- source. It is from this intensive interaction between scheduling and planning phases that resource-constrained scheduling and monetary issues become highly intervened. In Kolisch and Padman (2001), for project scheduling problems four components have been considered, namely activities, re- sources, precedence relations, and performance measures. Each of these components has several varieties. For instance, resources can be renewable, non-renewable, doubly constrained, or partially renewable. In project scheduling, objectives can be any combina- tion of (i) makespan minimization, (ii) cost minimization, (iii) weighted-delays minimization, (iv) net-present-value maximiza- tion, and (v) optimum levelling of resource usage (Kolisch & Pad- man, 2001). Because of the key role of project scheduling in the success of organizations, an extensive array of research on various aspects of project scheduling has been accomplished. By using the concept of versatile resource, the application of multimode resource constrained project scheduling problem, MRCPSP, can be extended to the problems in which the minimum, or in precise term a high-quality, overall cost of the project is sought. With the aim of facilitating interactions between planning and scheduling phases, a versatile resource, as a financial resource, can be sent to the rescue when the execution of an activity needs to be expedited, optimizing time–cost performance of the project by balancing the time versus the cost of project completion. While other resources represent some objects and their amounts are determined by planners, a versatile resource represents an arti- fact and is merely used by schedulers for time-cost trade-off pur- poses. In effect, a versatile resource can be considered as a facilitating resource that can be sent to the rescue whenever an 0360-8352/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.cie.2013.07.010 ⇑ Tel.: +61 2 42213648. E-mail address: reza@uow.edu.au Computers & Industrial Engineering 66 (2013) 451–460 Contents lists available at ScienceDirect Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie