A new model for the multi-mode resource-constrained project scheduling problem with discount cash flows

This paper presents a mathematical model for the multi-mode resource-constrained project scheduling problem with maximizing the net present value of project. The proposed model is inspired by MRCPSP-GPR. Firstly, we presented an exact model solving MRCPSP_GPR then we expanded the model to estimate other cost-related options, penalty-related expenditure is a case in point. As a result of estimating different factors which impact on project scheduling such as reward and penalty of finishing the project, managers can efficiently make a better decision. For better adaptation with real conditions, we consider two payment methods in two objective functions. The adjusted schedule by proposed model and solving time was logical. Moreover, to verify the proposed model, a numerical example is solved in small size and the related computational results are illustrated in terms of schedules. In addition, computational results with a set of 36 test problems in various sizes are reported and the results analyzed