An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> Abstract This paper is concerned with the development of a heuristic algorithm (MALB) for the general solution of large single-model assembly line balancing problems. It is based on the optimum-seeking backtracking method proposed by Mansoor (1964). Excellent results were obtained from tests taken over a wide range of large ALB problems. Over a third of the tests yielded a 100% line efficiency and the overall computation time was 22 sec on an IBM 7040/7044. <s> BIB001 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> The degree of complexity of a critical path network may be classified by calculating a Coefficient of Network Complexity. It is defined as the quotient of activities squared divided by events or preceding work items squared divided by work items. Three distinct contributions are offered. First, the CNC may serve as an indicator of the attention spent in planning the project. Second, the CNC may be used to derive a predictor of network computer processing time. Third, the CNC value suggests the appropriate processing scheme. <s> BIB002 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> Individual characteristics of multiple-constrained resource, project scheduling problems are examined in an attempt to predict the solution obtainable with heuristic methods. Difficulties encountered in performing this type of research are described, and several multiple regression models are developed for predicting heuristic performance. Both single and multiple project data are examined, and results reported demonstrate the efficacy of determining beforehand the method used for problem solution. <s> BIB003 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> The concept of the restrictiveness of project networks is defined to reflect the degree to which precedence requirements eliminate possible scheduling sequences. A suitable measure of restrictiveness is presented, as published related materials are shown not to apply. To extend the computational feasibility of the concept to larger networks, three indirect estimators of the measure are introduced. Relationships between these and related statistical properties of networks are shown. Finally, an algorithm to generate random networks with a specified restrictiveness is given. <s> BIB004 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> Abstract The measurement of the ‘complexity’ of activity networks seems to be needed in order to estimate the computing requirements and/or to validly compare alternative heuristic procedures. This paper critically evaluates past contributions to the problem, and explores the underlying concepts of measurement. It suggests that the objective of analysis of the network is a determining factor in the process of measurement, and discusses three different objectives; they are: to determine the critical path assuming deterministic time estimates; to determine the probability distribution function of project completion assuming random durations of the activities; and to determine the optimal schedule under limited availability of a single resource. It proposes the form of the measure of network complexity for each objective, and explicitly exhibits the form of the measure relative to the first objective based on a sample of 104 networks. <s> BIB005 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> Two dynamic programming approaches for treating sequencing problems—one proposed by Schrage and Baker and the other by Lawler—are discussed in the context of an assembly line balancing problem. A variant of the Schrage-Baker method is proposed to extend its range of applicability. The three approaches are compared using randomly generated test problems. We find that Lawler's “reaching”-based approach is superior to the other two “pulling”-based alternatives in both time and storage requirements. Based on the empirical results, we present time and space estimates for solving problems of different sizes and order strengths, and discuss the relative merits of the three procedures. <s> BIB006 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> The paper describes an algorithm for the generation of a general class of precedence- and resource-constrained scheduling problems. Easy and hard instances for the single- and multi-mode resource-constrained project scheduling problem are benchmarked by using the state of the art (branch-and-bound-) procedures. The strong impact of the chosen parametric characterization of the problems is shown via an in-depth computational study. The results provided, demonstrate that the classical benchmark instances used by several researchers over decades belong to the subset of the very easy ones. In addition it is shown that hard instances, being far more smaller in size than presumed in the literature, may not be solved to optimality even within a huge amount of computational time. <s> BIB007 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> Algorithms for series-parallel graphs can be extended to arbitrary two-terminal dags if node reductions are used along with series and parallel reductions. A node reduction contracts a vertex with unit in-degree (out-degree) into its sole incoming (outgoing) neighbor. This paper gives an $O(n^{2.5} )$ algorithm for minimizing node reductions, based on vertex cover in a transitive auxiliary graph. Applications include the analysis of PERT networks, dynamic programming approaches to network problems, and network reliability. For NP-hard problems one can obtain algorithms that are exponential only in the minimum number of node reductions rather than the number of vertices. This gives improvements if the underlying graph is nearly series-parallel. <s> BIB008 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> Exact and heuristic procedures are often developed to obtain optimal and near-optimal solutions to decision problems modeled as activity networks. Testing the accuracy and efficiency of these procedures requires the use of activity networks with various sizes, structures, and parameters. The size of the network is determined by its number of nodes and arcs, where the structure is chosen from the set of all structures for the specified network size. The network parameters depend on the nature of the decision problem. Often, it is desirable for test problems to be generated at random from the space of all feasible networks. This paper deals with the problem of generating the size and structure of the network at random from the space of all feasible networks. It develops a theory which guarantees the randomness of the network structure. The theory is the basis for two methods. One can be used to generate dense networks, where the other is used to generate nondense networks. The methods, which are practical a... <s> BIB009 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> This document contains a bibliography of recent research relating to project risk management, bringing together relevant research scattered across a range of publications. It considers how success or failure can be defined for a project (more than simple time/cost/technical target achievement). It looks at the historical evidence of projects, illustrating failure to achieve targets. What risk means to a project, and how a project team perceive, identify and quantify risk is considered — often the crucial credibility-point in practice. Techniques are discussed for the analysis of risk, to schedule (including analytical and more generally applicable simulation techniques), cost and technical achievement, both separate analyses and the first steps towards an integrated analysis. Success for project participation depends on who bears the risks, and the vital role of risk analysis in informing the contractual allocation of risk is explored. Finally, the management structures and procedures needed to manage risk are discussed. <s> BIB010 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> Abstract We offer a methodology, and the relevant software, to generate source-terminal directed project nets of specified number of nodes, number of activities, complexity index, and ranges of costs and resources utilization. <s> BIB011 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> In a PE RT network, the importance of each activity needs to be assessed in order to identify those that warrant more attention from the project management. For this purpose, two measures are frequently used: criticality index; and uncertainty importance measure. While the former is used to identify which activity's expected duration to decrease in order to decrease the expected project completion time, the latter can be used to identify those that deserve more attention in reducing the magnitude of the uncertainty (variability) in the project completion time ( T ). This paper defines an uncertainty-importance measure of an activity, or of a pair of activities, and develops a method for evaluating the defined measure under the assumption that the durations of activities are independently and symmetrically distributed. The method utilizes Taguchi tolerance design technique with modifications. First, PE RT networks are classified into two types: Type A with a dominantly longer path than the others, and Type... <s> BIB012 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> Foreword. 1. A Systemic Introduction to Project Management. 2. Basic Models for Project Management. 3. Structural Modelling of Projects Networks. 4. Morphology and Simulation of Project Networks. 5. Duration of Projects. 6. Scheduling of Project Networks. 7. The Assessment and Evaluation of Projects. 8. The Optimal Scheduling of a Project in Terms of its Duration. Annex 1: Developed Software. Annex 2: Main Notation. References. Index. <s> BIB013 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> Abstract The risk of the duration of a project exceeding a certain limit has been studied since the early papers proposing the PERT method but no results are available relating the statistical distribution of the total duration with the morphological features of the network. In this paper, a set of indicators is proposed to describe the morphology of the project network and an experimental research is carried out to relate the distribution of the total duration with such indicators. A random generator of project networks is used as well as a model to produce graphical representations of the network. Major results are presented showing how sensitive are the parameters of the distribution of the total duration to the morphology of the network, allowing the project manager to estimate the risk of delay in terms of the proposed indicators. Thus, these results can be used as a decision aid to select alternative designs for the project network taking into account the correspondent risk of delay. <s> BIB014 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> Abstract Traditionally the `importance' of an activity in the PERT model of projects is measured by its `criticality index', which is defined as the probability that the activity will be on the longest path. An insightful discussion by Williams (1992, Journal of Operational Research Society 43, 353–357) revealed that the classical criticality index is not always informative or intuitively appealing. In a recent study by Cho and Yum (1997, International Journal of Production Research 35, 2737–2757), a new `Uncertainty Importance Measure' is defined to measure the effect of the variability in an activity duration on the variability of the overall project duration. They propose Taguchi's sampling technique as a method for analyzing the network. The main contribution of this paper is to study the impact of changing the mean duration of an activity on the variability of the project duration. On the way to accomplish this, we further investigate the accuracy of Taguchi's sampling method for approximating the mean and standard deviation of the project duration, and propose steps that could result in computational savings in large networks. <s> BIB015 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> Abstract Project scheduling has long been an area of intensive research, but until recently most efforts have been dedicated to developing solution procedures and generalizing models, with little work done on generating problem instances. Additionally, if labor time regulations have to be taken into consideration, the classical resource-constrained project scheduling problem (RCPSP) cannot be used for many problems in manpower scheduling. This paper introduces several extensions to the RCPSP aimed at modeling such problems, and a problem instance generator based on the project generator ProGen incorporating these extensions. Thus, it becomes possible to thoroughly test solution procedures for, e.g., audit-staff scheduling, crew scheduling and timetabling problems. Preliminary computational results are given that were obtained with a greedy randomized solution method using priority rules specifically tailored to the generalized model. <s> BIB016 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> Abstract A review of the issues related to activity criticality and the sensitivity of the mean and variance of project completion time to changes in the mean and variance of individual activities is presented. The methodologies proposed range over the analytical, Monte Carlo sampling, and statistical sampling, in particular the use of Taguchi orthogonal arrays. <s> BIB017 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> The problem of designing a contract mechanism to allocate the component subprojects of a large project to a pool of contractors has important implications for project success. Our research analytically addresses issues involved in diversifying risk for the project owner by partitioning the project and assigning the subprojects to multiple contractors whose performance characteristics are imperfectly known. We begin by giving a precise analytical treatment of the effect of activity variance on expected project duration, characterizing the cases when an increase in activity variance pushes up the expected project duration. In the case of a homogeneous project consisting of serial subprojects, we show that disaggregating the project and assigning the subprojects to the contractors on a piecemeal basis reduces variance of project duration while leaving the mean unchanged. On the other hand, in the case of a homogeneous project consisting of parallel subprojects, aggregating the subprojects and assigning the aggregated project to one of the contractors reduces mean project duration. <s> BIB018 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> Abstract We put forward a fuzzy way of measuring the criticality of project activities and of the whole project. In the proposed approach both the decision maker attitude and the project network structure are taken into account. The criticality measure obtained may serve as a measure of risk or of the supervision effort needed and can help in making the decision whether to accept or to reject the project. Its numerical implementation is as difficult as that of the classical CPM method. <s> BIB019 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> Abstract The performance of methods to manage projects depends heavily on the features of their project networks. This is particularly true for methods devoted to project scheduling, risk analysis and resources allocation. Therefore, a long line of research has been developed to generate benchmark sets of project networks and several sets have been proposed in the literature. Unfortunately, no comparative analyses of their features were published and hence serious doubts about the comparability of results using different benchmark sets can be raised. In this paper, a multi-dimensional taxonomy for the morphology of project networks is used and four benchmark sets are evaluated: Patterson collection of problems (Patterson JH. A comparison of exact approaches for solving the multiple constrained resource, project scheduling problem. Management Science 1984;30:854–867) and the sets produced by the generators due to Agrawal et al. Agrawal MK, Elmaghraby SE, Herroelen WS. DAGEN a generator of testsets for project activity nets. European Journal of Operational Research 1996;90:376–382, Kolisch et al. Kolisch R, Sprecher A, Drexl A. Characterization and generation of a general class of resource — constrained project scheduling problems. Management Science 1995;41:1693–1703, Tavares Tavares LV. Advanced models in project management. Kluwer, 1999 and Tavares et al. Tavares LV, Antunes Ferreira JA, Coelho JS. The risk of delay of a project in terms of the morphology of its network. European Journal of Operational Research 1999;119:510–537. Original results about the lack of representativeness of these sets are obtained showing that misleading conclusions can be deduced. The last set is, by far, that one covering most extensively the morphologic space of instances which could be foreseen because the generation of networks is carried out in terms of an wider range of parameters. This conclusion is quite useful for project managers willing to assess alternative methods to solve their problems based on project networks. <s> BIB020 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> In this paper, we describe RanGen, a random network generator for generating activity-on-the-node networks and accompanying data for different classes of project scheduling problems. The objective is to construct random networks which satisfy preset values of the parameters used to control the hardness of a problem instance. Both parameters which are related to the network topology and resource-related parameters are implemented. The network generator meets the shortcomings of former network generators since it employs a wide range of different parameters which have been shown to serve as possible predictors of the hardness of different project scheduling problems. Some of them have been implemented in former network generators while others have not. <s> BIB021 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> In project management, the project duration can often be compressed by accelerating some of its activities at an additional expense. This is the so-called time–cost tradeoff problem which has been extensively studied in the past. However, the discrete version of the problem which is of great practical relevance, did not receive much attention so far. Given a set of modes (time–cost pairs) for each activity, the objective of the discrete time–cost tradeoff problem is to select a mode for each activity so that the total cost is minimized while meeting a given project deadline. ::: ::: The discrete time–cost tradeoff problem is a strongly -hard optimization problem for general activity networks. In terms of what current state-of-art algorithms can do, instances with (depending on the structure of the network and the number of processing alternatives per activity) no more than 20–50 activities can be solved to optimality in reasonable amount of time. Hence, heuristics must be employed to solve larger instances. To evaluate such heuristics, lower bounds are needed. This paper provides lower and upper bounds using column generation techniques based on “network decomposition”. Furthermore, a computational study is provided to demonstrate that the presented bounds are tight and that large and hard instances can be solved in short run-time. <s> BIB022 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> This paper focuses on the application of the techniques of discretization to obtain an approximated probability density function (pdf) for the completion time of large-size projects, in which we allow any type of pdf for the duration of activities. In this study, we improve the techniques of discretization in the following two ways: first, we propose to replace the max operation with an approximation procedure to save significant computational loading; and second, to reduce the error from assuming independence between paths using a simple heuristic rule. To evaluate the performance of our proposed algorithm, we randomly generated 20 sets of 100-node instances in our numerical experiments. Taking the results from a Monte Carlo simulation using 20,000 samples as a benchmark, we demonstrate that the proposed algorithm significantly outperforms the PERT model and Dodin's [B.M. Dodin, Approximating the distribution function in stochastic networks, Comput. Oper. Res. 12 (3) (1985) 251-264] algorithm in both the running time and the precision aspects. <s> BIB023 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> This paper evaluates and compares different network generators to generate project scheduling problem instances based on indicators measuring the topological network structure. We review six topological network indicators in order to describe the detailed structure of a project network. These indicators were originally developed by [L.V. Tavares, J.A. Ferreira and J.S. Coelho, The risk of delay of a project in terms of the morphology of its network, European Journal of Operational Research 119 (1999), 510–537] and have been modified, or sometimes completely replaced, by alternative indicators to describe the network topology. The contribution of this paper is twofold. Firstly, we generate a large amount of different networks with four project network generators. Our general conclusions are that none of the network generators are able to capture the complete feasible domain of all networks. Additionally, each network generator covers its own network-specific domain and, consequently, contributes to the generation of data sets. Secondly, we perform computational results on the well-known resource-constrained project scheduling problem to prove that our indicators are reliable and have significant, predictive power to serve as complexity indicators. <s> BIB024 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> The interest in activity sensitivity from both the academics and the practitioners lies in the need to focus a project manager's attention on those activities that influence the performance of the project. When management has a certain feeling of the relative sensitivity of the various parts (activities) on the project objective, a better management's focus and a more accurate response during project tracking should positively contribute to the overall performance of the project. In the current research manuscript, a simulation study is performed to measure the ability of four basic sensitivity metrics to dynamically improve the time performance during project execution. We measure the use of sensitivity information to guide the corrective action decision making process to improve a project's time performance, while varying the degree of management's attention. A large amount of simulation runs are performed on a large set of fictitious project networks generated under a controlled design. <s> BIB025 </s> An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management <s> Test Data. <s> Meant to complement rather than compete with the existing books on the subject, this book deals with the project performance and control phases of the project life cycle to present a detailed investigation of the project’s time performance measurement methods and risk analysis techniques in order to evaluate existing and newly developed methods in terms of their abilities to improve the corrective actions decision-making process during project tracking. As readers apply what is learned from the book, EVM practices will become even more effective in project management and cost engineering. Individual chapters look at simulation studies in forecast accuracy, schedule adherence, time sensitivity, activity sensitivity and using top-down or bottom-up project tracking. The book also offers an actual real-life case study, a short tutorial on the EVM use in ProTrack, and conclusions on the relative effectiveness for each technique presented. <s> BIB026
In this section, the generation process to construct a set of project networks that differ from each other in terms of their topological structure is described in detail. Rather than drawing conclusions for a (limited) set of real life projects, the aim is to generate a large set of project networks that spans the full range of complexity BIB005 . This guarantees a very large and diverse set of generated networks that can and might occur in practice such that the results of the simulation studies can be generalised. The generation process relies on the project network generator developed by Vanhoucke et al. BIB024 to generate activity-on-the-node project networks where the set of nodes represents network activities and the set of arcs represents the technological precedence relations between the activities. These authors have proposed a network generator that allows generating networks with a controlled topological structure. They have proven that their generator is able to generate a set of very diverse networks that differ substantially from each other from a topological structure point of view. Moreover, it has been shown in the literature that the structure of a network heavily influences the constructed schedule BIB003 , the risk for delays BIB014 , the criticality of a network  , or the computational effort an algorithm needs to schedule a project BIB005 . In the simulation experiments, the design and structure of the generated networks are varied and controlled, resulting in 4,100 diverse networks with 30 activities. For more information about the specific topological structures and the generation process, the reader is referred to Vanhoucke et al. BIB024 . The constructed data set can be downloaded from http://www.or-as.be/measuringtime. Various research papers dealing with network generators for project scheduling problems have been published throughout the academic literature. Demeulemeester et al. BIB009 have developed a random generator for activity-on-thearc (AoA) networks. These networks are so-called strongly random since they can be generated at random from the space of all feasible networks with a specified number of nodes and arcs. Besides the number of nodes and the number of arcs, no other characteristics can be specified for describing the network topology. Kolisch et al. BIB007 describe ProGen, a network generator for activity-on-the-node (AoN) networks which takes into account network topology as well as resource-related characteristics. Schwindt  extended ProGen to ProGen/Max which can handle three different types of resource-constrained project scheduling problems with minimal and maximal time lags. Agrawal et al. BIB011 recognize the importance of the complexity index as a measure of network complexity and have developed an activity-onthe-arc network generator DAGEN for which this complexity measure can be set in advance. Tavares BIB013 has presented a new generator RiskNet based on the concept of the progressive level by using six morphological indicators (see later in this section). Drexl et al. BIB016 presented a project network generator ProGen/ based on the project generator ProGen, incorporating numerous extensions of the classical resourceconstrained project scheduling problem. Demeulemeester et al. BIB021 have developed an activity-on-the-node network generator RanGen which is able to generate a large amount of networks with a given order strength (discussed later). Due to an efficient recursive search algorithm, RanGen is able to generate project networks with exact predefined values for different topological structure measures. The network generator also takes the complexity index into account. Akkan et al. BIB022 have presented a constraint logic programming approach for the generation of acyclic directed graphs. Finally, Vanhoucke et al. BIB024 have adapted RanGen to an alternative RanGen2 network generator which will be used for the generation of the project networks of the studies that have led to the writing of this paper. It is based on the RiskNet generator of Tavares BIB013 . Neither of the networks generated by the previously mentioned network generators can be called strongly random because they do not guarantee that the topology is a random selection from the space of all possible networks which satisfy the specified input parameters. Next to the generation of project networks, numerous researchers have spent attention on the topological structure of a project network. The topological structure of a network can be calculated in various ways. Probably the best known measure for the topological structure of activity-on-the-arc networks is the coefficient of network complexity (CNC), defined by Pascoe  as the number of arcs over the number of nodes and redefined by Davies  and Kaimann BIB002  . The measure has been adapted for activity-on-the-node problems by Davis [93] as the number of direct arcs over the number of activities (nodes) and has been used in the network generator ProGen BIB007 . Since the measure relies totally on the count of the activities and the direct arcs of the network and as it is easy to construct networks with an equal CNC value but a different degree of difficulty, Elmaghraby and Herroelen BIB005 questioned the usefulness of the suggested measure. De Reyck and Herroelen  and Herroelen and De Reyck  conclude that the correlation of the CNC with the complexity index is responsible for a number of misinterpretations with respect to the explanatory power of the CNC. Indeed, Kolisch et al. BIB007 and Alvarez-Valdes and Tamarit  had revealed that resource-constrained project scheduling networks become easier with increasing values of the CNC, without considering the underlying effect of the complexity index. In conclusion, the CNC, by itself, fails to discriminate between easy and hard project networks and can therefore not serve as a good measure for describing the impact of the network topology on the hardness of a project scheduling problem. Another well-known measure of the topological structure of an AoN network is the order strength, OS  , defined as the number of precedence relations including the transitive (When two direct or immediate precedence relations exist between activities ( , ) and activities ( , ), then there is also an implicit transitive relation between activities ( , ).) ones but not including the arcs connecting the dummy start or end activity divided by the theoretical maximum number of precedence relations ( * ( −1))/2, where denotes the number of nondummy activities in the network. It is sometimes referred to as the density BIB006 or the restrictiveness BIB004 and is equal to 1 minus the flexibility ratio BIB001 . Herroelen and De Reyck  conclude that the order strength OS, the density, the restrictiveness, and the flexibility ratio constitute one and the same complexity measure. Schwindt  uses the order strength in the problem generator ProGen/Max and argues that this measure plays an important role in predicting the difficulty of different resource-constrained project scheduling problems. De Reyck  verified and confirmed the conjecture that the OS outperforms the complexity index as a measure of network complexity for the resource-constrained project scheduling problem. The complexity index was originally defined by Bein et al. BIB008 for two-terminal acyclic activity-on-the-arc networks as the reduction complexity, that is, the minimum number of node reductions which-along with series and parallel reductions-allow to reduce a two-terminal acyclic network to a single edge. As a consequence, the complexity index measures the closeness of a network to a series-parallel directed graph. Their approach for computing the reduction complexity consists of two steps. First, they construct the so-called complexity graph by means of a dominator and a reverse-dominator tree. Second, they determine the minimal node cover through the use of the maximum flow procedure by Ford and Fulkerson  . De Reyck and Herroelen  adopted the reduction complexity as the definition of the complexity index of an activity network and have proven the complexity index to outperform other popular measures of performance, such as the CNC. Moreover, they also show that the OS, on its turn, outperforms the complexity index. These studies motivated the construction of an AoN problem generator for networks where both the order strength OS and the complexity index can be specified in advance, which has led to the development of the RanGen and RanGen2 generators (see earlier). The topological structure of an activity-on-the-node network used in the three simulation studies is calculated based on four indicators initially proposed by Tavares et al. BIB014 BIB020 and further developed by Vanhoucke et al. BIB024 . These indicators serve as classifiers of project networks by controlling the design and structure of each individual project network. All indicators have been rescaled and lie between 0 and 1, inclusive, denoting the two extreme structures. The logic behind each indicator is straightforward and relies on general topological definitions from the project scheduling literature. Their intuitive meaning is briefly discussed along the following lines. (iv) Topological float (TF) measures the degrees of freedom for each activity as the difference between the progressive and regressive level  for each activity in the project network. TF = 0 when the network structure is 100% dense and no activities can be shifted within its structure. A network with TF = 1 consists of one serial chain of activities without topological float (this chain defines the SP value) while the remaining activities have a maximal float value. [80] present a surrogate indicator of criticality by using a regression model in order to offer a better alternative to the poor performance of the criticality index in predicting the impact of an activity delay on the total project duration. Kuchta BIB019 presents an alternative criticality index based on network information. However, no computational experiments have been performed to show the improvement of the new measure. In Elmaghraby BIB017 , a short overview is given on the advantages and disadvantages of the three sensitivity measures discussed in Williams  . The author conjectures that a relative importance of project activities should be given by considering a combined version of these three sensitivity measures and reviews the more advanced studies that give partial answers on the mentioned shortcomings. More precisely, the paper reviews the research efforts related to the sensitivity of the mean and variance of a project's total duration due to changes in the mean and variance of individual activities. Cho and Yum BIB012 propose an uncertainty importance measure to measure the effect of the variability in an activity's duration on the variability of the overall project duration. Elmaghraby et al. BIB015 investigate the impact of changing the mean duration of an activity on the variability of the project duration. Finally, Gutierrez and Paul BIB018 present an analytical treatment of the effect of activity variance on the expected project duration. Motivated by the heavy computational burden of simulation techniques, various researchers have published analytical methods and/or approximation methods as a worthy alternative. An overview can be found in the study of Yao and Chu BIB023 and will not be discussed in the current research paper. Although not very recently published, another interesting reference related to this topic is the classified bibliography of research related to project risk management written by Williams BIB010 . A detailed study of all sensitivity extensions is outside the scope of this paper, and the reader is referred to the different sources mentioned above. In this section, four sensitivity metrics for activity duration sensitivity will be used in the project control simulation study originally presented by Vanhoucke BIB025 and further discussed in Vanhoucke BIB026 and Vanhoucke  . Three of the four activity duration sensitivity measures have been presented in the criticality study in stochastic networks written by Williams  , while a fourth sensitivity measure is based on the sensitivity issues published in PMBOK  . The four sensitivity metrics used in the simulation are described along the following lines. (i) Criticality index (CI) measures the probability that an activity lies on the critical path. (ii) Significance index (SI) measures the relative importance of an activity taking the expected activity and project duration into account as well as the activity slack. (iii) Schedule sensitivity index (SSI) measures the relative importance of an activity taking the CI as well as the standard deviations of the activity and project durations into account. (iv) Cruciality index (CRI) measures the correlation between the activity duration and the total project duration in three different ways: The aim of the study is to compare the four sensitivity metrics in a project control setting and to test their ability to distinguish between highly and lowly sensitive activities such that they can be used efficiently in a project control setting. Therefore, the scope of the study and the used measurement points and resulting output metrics can be summarised as follows. (i) Scope of the study is to compare and validate four well-known sensitivity metrics for activity duration variations. (ii) Measurement points are activity criticality, activity slack, variability in and correlations between the activity and project durations. The figure can be used to validate the discriminative power of the sensitivity metrics to make a distinction between highly sensitive activities (with a high expected impact) and the other less important activities that require much less attention. Ideally, the number of highly sensitive activities should be low such that only a small part of the project activities require attention while the others can be considered as safe. The criticality index and sensitivity index do not report very good results on that aspect for projects with a medium (SP = 50) to high (SP = 75) number of serial activities, since many (SP = 50) or most (SP = 75) activities are considered to be highly sensitive. The other sensitivity measures SSI and the three versions of CRI perform much better since they show higher upward tails with a low number of activities. The CRI metric has a more or less equal distribution of the number of observations between the lowest and highest values, certainly for the SP = 50 and SP = 75 projects. The SSI clearly shows that a lot of activities are considered as less sensitive for SP = 25 and SP = 50 while only a few activities have much higher (i.e., sensitive) values. Consequently, the SSI and CRI metrics have a higher discriminative power compared to the SI and CI metrics. Similar findings have been reported in Vanhoucke BIB025 . It should be noted that the picture does not evaluate the sensitivity metrics on their ability to measure the real sensitivity of the project activities to forecast the real impact of activity duration changes on the project duration. Moreover, their applicability in a project control setting is also not incorporated in this figure. However, this topic is discussed in the project control experiments of Section 3.4.