A survey of variants and extensions of the resource-constrained project scheduling problem <s> Logical Dependencies <s> 1 Basic Concepts.- 1.1 Directed Graphs and Project Networks.- 1.2 GERT Networks.- 1.3 Assumptions and Structural Problems.- 1.4 Complete and GERT Subnetworks.- 2 Temporal Analysis of GERT Networks.- 2.1 Activation Functions and Activation Distributions.- 2.2 Evaluation of Admissible GERT Networks.- 2.3 Computation of Some Quantities Important to Time Planning.- 2.4 Evaluation Methods for Admissible GERT Networks.- 3 STEOR Networks and EOR Networks.- 3.1 Markov Chains and Markov Renewal Processes.- 3.2 STEOR Networks and Markov Renewal Processes.- 3.3 Basic Properties of Admissible EOR Networks.- 3.4 Coverings of Admissible EOR Networks.- 3.5 Properties and Computation of Activation Functions and Activation Numbers.- 3.6 The MRP Method.- 4 Reducible GERT Networks.- 4.1 STEOR-Reducible Subnetworks.- 4.2 Cycle Reduction.- 4.3 Nodes Which Belong Together.- 4.4 Basic Element Structures.- 4.5 BES Networks.- 4.6 Evaluation Methods for BES Networks and General Admissible GERT Networks.- 5 Scheduling with GERT Precedence Constraints.- 5.1 Deterministic Single-Machine Scheduling.- 5.2 Stochastic Single-Machine Scheduling with GERT Precedence Constraints: Basic Concepts.- 5.3 Stochastic Single-Machine Scheduling with GERT Precedence Constraints: Optimality Criteria and Complexity.- 5.4 List Schedules and Sequences of Activity Executions.- 5.5 Minimum Flow-Time Scheduling in FOR Networks.- 5.6 A Flow-Time Scheduling Example.- 5.7 Minimizing the Maximum Expected Lateness in FOR Networks.- 5.8 Essential Histories and Scheduling Policies for Min-Sum Problems in General GERT Networks.- 5.9 Elements of Dynamic Programming.- 5.10 Determination of an Optimal Scheduling Policy for the General Min-Sum Problem.- 6 Cost Minimization for STEOR and FOR Networks.- 6.1 STEOR Networks with Time-Dependent Arc Weights.- 6.2 Cost Minimization in STEOR Networks: Basic Concepts.- 6.3 A Dynamic Programming Approach.- 6.4 The Value-Iteration and Policy-Iteration Techniques.- 7 Cost and Time Minimization for Decision Project Networks.- 7.1 Decision Project Networks.- 7.2 Cost Minimization.- 7.3 Randomized Actions.- 7.4 Multiple Executions of Projects.- 7.5 Time Minimization.- References. <s> BIB001 </s> A survey of variants and extensions of the resource-constrained project scheduling problem <s> Logical Dependencies <s> In this paper, a new approach to the problem of scheduling of design activities with precedence and multiple resource constraints is proposed. In addition to the AND type relationship, OR and EXCLUSIVE OR relationships may also exist between design activities. In order to handle these logical relationships, IDEF3 is used for network representation. A large network of design activities can be arranged in different levels of abstraction. A procedure is proposed to transform an IDEF3 model into a set of alternative precedence networks. In the networks selected, the activities that are resource independent are grouped with a partitioning procedure. In order to increase the efficiency of the search for the best schedule, a procedure based on the Christofides et al. (1987) reduction procedure is introduced to determine a lower bound on the completion time of the hierarchically structured design activity network. > <s> BIB002 </s> A survey of variants and extensions of the resource-constrained project scheduling problem <s> Logical Dependencies <s> This paper describes how the Resource-Constrained Project Scheduling Problem (RCPSP) can be used as a basis for real-time decision support in the disruption management of the aircraft turnaround, the most typical airport ground process. For this purpose, the RCPSP is extended by the possibility to describe alternative activities, which can be used to model potential process modifications. An evolutionary approach is presented for solving this generalized problem, considering both basic rescheduling possibilities as well as the option of exchanging activities. The work presented in this paper is based on the results of a study conducted in collaboration with Deutsche Lufthansa AG, concerned with the analysis of the elementary requirements of decision support systems for turnaround process management. <s> BIB003
Several researchers, e.g., Elmaghraby  and Belhe and Kusiak BIB002 , have extended the precedence network concept by adding logical nodes. In the RCPSP, an activity node which has several successor nodes implies that this activity must be finished before any of the successors may be started. This controls the temporal arrangement of the activities. As all successor activities must be executed, the activity nodes can be viewed as logical "AND" nodes. Extending this concept, some activity nodes might be declared as logical "OR" nodes, implying that at least one successor activity of an "OR" node has to be performed. Analogously, "XOR" (exclusive-or) nodes induce that exactly one successor activity must be executed. These network extensions are, for example, useful to model research and development projects: After an "XOR"-activity "test prototype" has been performed, either activity "modify prototype" or activity "start production" is executed, depending on the outcome of the test. In the project management literature, networks with logical nodes are mostly treated in connection with stochastic concepts, see Neumann BIB001 . Another type of logical dependencies has been proposed by Kuster and Jannach BIB003 . A socalled mutual exclusion relationship between activities i and j implies that if i is executed then j shall not be executed. Analogously, a mutual inclusion relationship between activities i and j means that if i is executed then j shall be executed as well. The resulting problem is used for scheduling ground processes on airports such as fueling, cleaning and catering.