عنوان مقاله [English]
Project scheduling is an important task in project management. The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled and be subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling, which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. Resource-constrained project scheduling is concerned with the allocation of time intervals to the processing of activities. The execution of activities requires the use of scarce resources. Resource investment problem (RIP) is known as the problem of minimizing renewable resource costs subject to a project due date. A resource Renting problem (RRP) is a project-scheduling problem in which the availability levels of the rented resources are considered as decision variables, and the goal is to find a schedule and resource renting such that some objective functions are optimized. In this paper, we considered a resource renting problem with a discounted cash flow, in which the goal is to maximize the net present value of the project cash flows. We considered Interest Rate in this model, and this caused the model to be more real. In recent works, RRP was a NP-hard problem, and solving this problem with exact method took a long time. In addition, it was clear that the exact methods were not able to solve medium or large instances; thus, we developed a heuristic method to solve the problem. Most of the work in project scheduling used genetic algorithm for obtaining qualified solution in a reasonable time. Also, we developed a genetic algorithm for this problem such that it produced optimum and near optimum solution for this problem.Results show that as interest rate increases, since the cost of resource usage should reduce, scheduling of work and start times shift later. It shows that adding interest rate to the model makes the problem more real and useful for real projects.