Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69777220171001Payment scheduling under project crashing based on project progressفشردهسازی پروژه در مسئله زمانبندی پرداخت براساس پیشرفت پروژه39562455710.22067/ijnao.v7i2.46395ENM.Mortazavi NejadDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.H.R.TareghianDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.Z.SariDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.Journal Article19700101In this paper, we address a new problem in the context of project payment scheduling when project activities are allowed to be crashed with the purpose of maximizing the contractors net present value (NPV). We assume that the contractor is paid at some pre-specified points of time according to the volume of work performed. Upon completion of activities, the cost of their execution is paid. Two different approaches are used to determine the volume of work performed at so called review points. In the first approach, only completed activities are considered. In the second approach, any portions of the activities that are executed are considered. To increase the volume of work performed at the review points, the contractor may decide to crash some activities and as such possibly increases his NPV. As activity crashing costs the contractor money, a compromise needs to be made. Two mathematical models are developed to study each approach and hence help the contractor to make the best decision. These models offer a means of investigating whether it is advisable to crash some activities and are therefore of practical importance. It is shown that the contractor may increase his NPV, even when he pays for the activity crashing costs. The performance of the mathematical models is illustrated using a numerical example.https://ijnao.um.ac.ir/article_24557_9ad8b3c758bef4a639c8ee52e718adcb.pdf