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Scheduling under nonrenewable resources is one of the challenging issues in project scheduling problems. There are many cases where the projects are subject to some nonrenewable resources. In most of the literature, nonrenewable resources are assumed to be available in full amount at the beginning of the project. However, in practice, it is prevalent that these resources are procured along the project horizon. This paper studies the generalized resource-constrained project scheduling problem (RCPSP) where, in addition to renewable resources, nonrenewable resources are considered, such as budget or consuming materials by the project activities. As the problem is NP-hard, some sub-algorithm... 

In this paper, we develop an approach to optimally allocate a limited nonrenewable resource among the activities of a project, represented by a PERT-Type Network (PTN). The project needs to be completed within some specified due date. The objective is to maximize the probability of project completion on time. The duration of each activity is an arbitrary discrete random variable and also depends on the amount of consumable resource allocated to it. On the basis of the structure of networks, they are categorized as either reducible or irreducible. For each network structure, an analytical algorithm is presented. Through some examples, the algorithms are illustrated  

In the project scheduling literature, nonrenewable resources are assumed to be available in full amount at the beginning of the project. However, in practice, it is very common that these resources are procured along the project horizon according to some pre-scheduled plan. In this paper, we study an extended form of the resource-constrained project scheduling problem that is subject to this type of nonrenewable resources in addition to the renewable resources. In order to solve this problem, we propose a branch and cut algorithm. We incorporate with the algorithm some technics and fathoming rules to shorten the solving process. The algorithm is capable of specifying lower bounds for the...