A survey of variants and extensions of the resource-constrained project scheduling problem <s> Nonrenewable and Doubly Constrained Resources <s> This paper presents a general model of resource allocation problems based on the concept of the system of the complex of operations type. Using the terminology of this model, a classification of particular allocation problems has been made and examples of an exact formulation of new problems have been given. Attention has been paid to the practical interpretation of assumptions and results. Some desired directions of further development in the theory and application of the considered problems have been indicated. <s> BIB001 </s> A survey of variants and extensions of the resource-constrained project scheduling problem <s> Nonrenewable and Doubly Constrained Resources <s> Abstract The paper deals with the allocation of different categories of resources in a network project under multiple conflicting criteria including project duration or maximum lateness, and several cost criteria. The resource requirements of the splittable activities are assumed to be discrete, i.e., assuming arbitrary values from given finite sets for particular resource types and categories. Two approaches for solving the problem, using multiobjective linear programming in specific ways, are described. Reduction of the number of activity preemptions, as a secondary project performance measure, is considered. <s> BIB002 </s> A survey of variants and extensions of the resource-constrained project scheduling problem <s> Nonrenewable and Doubly Constrained Resources <s> Abstract Project scheduling is concerned with single-item or small batch production where scarce resources have to be allocated to dependent activities over time. Applications can be found in diverse industries such as construction engineering, software development, etc. Also, project scheduling is increasingly important for make-to-order companies where the capacities have been cut down in order to meet lean management concepts. Likewise, project scheduling is very attractive for researchers, because the models in this area are rich and, hence, difficult to solve. For instance, the resource-constrained project scheduling problem contains the job shop scheduling problem as a special case. So far, no classification scheme exists which is compatible with what is commonly accepted in machine scheduling. Also, a variety of symbols are used by project scheduling researchers in order to denote one and the same subject. Hence, there is a gap between machine scheduling on the one hand and project scheduling on the other with respect to both, viz. a common notation and a classification scheme. As a matter of fact, in project scheduling, an ever growing number of papers is going to be published and it becomes more and more difficult for the scientific community to keep track of what is really new and relevant. One purpose of our paper is to close this gap. That is, we provide a classification scheme, i.e. a description of the resource environment, the activity characteristics, and the objective function, respectively, which is compatible with machine scheduling and which allows to classify the most important models dealt with so far. Also, we propose a unifying notation. The second purpose of this paper is to review some of the recent developments. More specifically, we review exact and heuristic algorithms for the single-mode and the multi-mode case, for the time–cost tradeoff problem, for problems with minimum and maximum time lags, for problems with other objectives than makespan minimization and, last but not least, for problems with stochastic activity durations. <s> BIB003
The basic RCPSP features only one type of resources which is called renewable because it is avialable in each period with its full capacity. In project scheduling problems with multiple modes (MPS|prec|C max , see Section 2.4), often three different kinds of resources are considered, namely renewable, nonrenewable, and doubly constrained resources. This resource categorization has been developed by Słowiński BIB002 and Wȩglarz BIB001 . Renewable resources such as manpower and machines are limited on a per-period basis. In contrast, nonrenewable resources have a limited capacity for the entire project, an example would be a budget for the project. While renewable resources are already part of the basic (singlemode) RCPSP, nonrenewable ones need only be considered in a multi-mode environment. In the classification scheme of Brucker et al. BIB003 , we propose to reflect a multi-mode problem with both renewable and nonrenewable resource with α = MPS; R; N. This slightly modifies the original notation of Brucker et al. BIB003 , but it enables us to integrate further resource categories throughout the following sections. Doubly constrained resources are limited both for each period and for the whole project (money is an example if both the budget and the per-period cashflow of the project are limited). As a doubly constrained resource can be incorporated by a renewable and a nonrenewable resource, doubly constrained resources do not enhance the expressive power of the problem setting and need not be considered explicitly.