A survey of variants and extensions of the resource-constrained project scheduling problem <s> Dedicated Resources <s> We study scheduling problems with multiple modes and dedicated resources arising in production and project management, which constitute a special class of the general multimode resource-constrained project scheduling problem. A task may require simultaneously a set of discrete, renewable resources to be processed and the processing can be performed in different modes, that is with different resource sets, processing times, or costs. Precedence constraints can exist among tasks. The total budget that can be allocated to the project can be limited. The problem consists of identifying a mode for each task and a starting time for its processing respecting precedence, resource, and budget constraints. A graph model and an iterative solution scheme are presented. Specific heuristic algorithms for the cases with and without budget constraints are given and computational results are discussed. <s> BIB001 </s> A survey of variants and extensions of the resource-constrained project scheduling problem <s> Dedicated Resources <s> In this paper we describe an exact algorithm to solve a preemptive project scheduling problem with scarce resources. As most of the scheduling problems also the studied one is NP-hard. Many different approaches, such as mathematical programming, heuristics, simulating annealing, etc., have been presented to solve this class of intractable problems. In our approach we consider a graph-theoretical method based on new coloring techniques. In particular, given a disjunctive graph we examine the correspondences between an assignment of time windows (i.e. activities starting time and finishing time) and an assignment of colors to the activities of a project, defining when an exact weighted coloring is an optimal preemptive schedule. We present computational results on randomly generated test problems of the branch and bound algorithm proposed. From the results obtained emerges that the possibility to manage hard problems using new coloring techniques seems to be more efficient than others, referring in particular to the performances of the algorithm proposed. <s> BIB002 </s> A survey of variants and extensions of the resource-constrained project scheduling problem <s> Dedicated Resources <s> Interval capacity consistency tests consider the resource capacities available and required within certain time intervals. The goal of the tests is to draw conclusions that allow to rule out inadmissible activity start times or sequences. The tests can be effectively used to reduce the search space of difficult time- and resource-constrained scheduling problems. They have successfully been applied in algorithms for solving idealised problems such as the classical job shop scheduling problem (JSP) or the resource-constrained project scheduling problem (RCPSP) as well as for solving industrial scheduling problems. For instance, it seems fair to say that the advances in modern branch and bound algorithms for the JSP that have been made in the last decade can to a large extent be attributed to the effect of interval consistency tests, some of which are also known under the names of immediate selection, edge finding, and energetic reasoning. The tests can also serve to derive tight lower bounds for makespan minimisation problems. <s> BIB003 </s> A survey of variants and extensions of the resource-constrained project scheduling problem <s> Dedicated 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> BIB004
Dedicated resources are resources that can be assigned to only one activity at a time. They can be expressed by a renewable resources with an availability of one unit per period, R k = 1. Consequently, they are included in the RCPSP as a special case. Project scheduling problems with dedicated resources are studied in Bianco et al. BIB001 BIB002 . Dorndorf et al. BIB003 refer to the RCPSP with dedicated resources as disjunctive scheduling problem, see also Dorndorf et al.  . In the notation of Brucker et al. BIB004 , dedicated resources can be covered by setting α = PS; Rm, 1, 1 which means that we have m renewable resources with a capacity of one unit and a request of at most one unit.