Optimizing Three-Dimensional Trade-Off Problem of Time–Cost–Quality over Multi-Mode Projects with Generalized Logic

Clients typically tend to aim for reasonable prices, minimum possible makespans, and the best quality for the construction projects that they engage in. Evidently, weighing the available offers and coming up with an optimal decision can pose challenges for the decision makers. In this regard, the generation of a tool that helps decision makers strike a proper balance among the conflicting project objectives (i.e., time, cost, and quality) is imperative. To this end, this study proposes a method which assists in the selection of the best compromise choices among the options available for each of the project activities. In addition to the time and cost, the proposed method is designed to bring the quality aspect into the equation as well. To quantify the quality, a value referring to the weighted importance and performance of each activity is used. The proposed method is based on a modified multi-objective genetic algorithm (GA) that incorporates the domination concept for the selection of the best solutions out of the potential candidates. The GA-based method is capable of handling an unlimited number of precedence relationships for each activity, and above all, it is able to capture and unravel any type of logical relationship. This very feature significantly improves the practical relevance of this research, as the parallelization of activities is a common practice in real-life projects. Planners benefit from the various types of relationships (i.e., Start to Start, Start to Finish, Finish to Start, and Finish to Finish), and the concept of lag time frequently introduces parallelization into the network. Overlapped activities, in turn, help reduce the unwanted idle times and speed up the project significantly. Accordingly, in order to demonstrate the application and effectiveness of the proposed model, it has been used in the solution of four time–cost–quality (TCQ) trade-off problems, three of which are generated within the context of this paper. The practiced instances include a small benchmark TCQT problem with 18 activities taken from the literature in addition to more complex 29- and 63-activity TCQTPs produced herein based on benchmark time–cost trade-off problems. The performance of the presented approach is ultimately examined over a large-scale, real-case construction project with over four hundred activities and generalized logic in an unprecedented attempt to validate a model in the realm of TCQTPs. The successful results of the experiments reveal the effectiveness of the proposed model and corroborate the feasibility of its application by the planners amidst arduous decision-making processes.