A New Bi-Objective Model for a Multi-Mode Resource-Constrained Project Scheduling Problem with Discounted Cash Flows and four Payment Models

The aim of a multi-mode resource-constrained project scheduling problem (MRCPSP) is to assign resource(s) with the restricted capacity to an execution mode of activities by considering relationship constraints, to achieve pre-determined objective(s). These goals vary with managers or decision makers of any organization who should determine suitable objective(s) considering organization strategies. In this paper, we present a new bi-objective model for the MRCPSP that maximizes the net present value (NPV) and minimizes the holding cost of activities completed by the projects’ completion time. For better adoption with real conditions, we consider four different payment models for positive cash flow. To verify the proposed model, a number of numerical examples are solved in small sizes and the related computational results are illustrated in terms of schedules. Finally, a meta-heuristic algorithm based on simulated annealing (SA) is utilized to solve our four payment proposed models in various sizes and the obtained results were analyzed.