An exact decomposition technique for the deadline-constrained discrete time/cost trade-off problem with discounted cash flows

Abstract

This paper addresses the deadline-constrained discrete time/cost trade-off problem with discounted cash flows in project scheduling optimization. Our objective is to optimize the net present value (NPV) of cash flows by selecting execution modes for activities while considering project deadlines. To address this problem, we propose an adapted model that combines the activity-on-node representation of the project network with the milestone activity payment system commonly used in real-world scenarios. This enhanced model accurately depicts project dynamics, enabling improved decision-making in NPV optimization. To solve the problem, we employ the generalized benders decomposition technique, which provides an exact solution approach to handle the computational complexity of the problem. Our approach introduces three types of feasibility cuts. The first type eliminates infeasible solutions by analyzing subproblem infeasibility. The second type enhances the generation of high-quality optimality cuts by iteratively introducing constraints to the master problem, utilizing dominated paths in the project network graph. Lastly, the third type targets the elimination of inferior infeasible solutions. Additionally, we generate a comprehensive dataset encompassing various scenarios and parameter ranges from existing literature. This dataset serves as a valuable resource for further research, with online accessibility and the latest solutions available for approximately 32,400 generated instances. Through our research, we demonstrate the superiority of our proposed solution procedure compared to existing methods in the field. By considering the specific requirements of project scheduling with NPV optimization and project deadlines, our approach contributes to more effective project planning and decision-making in real-world contexts.