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11
Integrated variance reduction strategies for simulation
 Operations Research
, 1996
"... We develop strategies for integrated use of certain wellknown variance reduction techniques to estimate a mean response in a finitehorizon simulation experiment. The building blocks for these integrated variance reduction strategies are the techniques of conditional expectation, correlation induc ..."
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Cited by 29 (2 self)
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We develop strategies for integrated use of certain wellknown variance reduction techniques to estimate a mean response in a finitehorizon simulation experiment. The building blocks for these integrated variance reduction strategies are the techniques of conditional expectation, correlation induction (including antithetic variates and Latin hypercube sampling), and control variates; and all pairings of these techniques are examined. For each integrated strategy, we establish sufficient conditions under which that strategy will yield a smaller response variance than its constituent variance reduction techniques will yield individually. We also provide asymptotic variance comparisons between many of the methods discussed, with emphasis on integrated strategies that incorporate Latin hypercube sampling. An experimental performance evaluation reveals that in the simulation of stochastic activity networks, substantial variance reductions can be achieved with these integrated strategies. Both the theoretical and experimental results indicate that superior performance is obtained via joint application of the techniques of conditional expectation and Latin hypercube sampling. Subject classifications: Simulation, efficiency: conditioning, control variates, correlation inArea of review: Simulation.
A heuristic for optimizing stochastic activity networks with applications to statistical digital circuit sizing
 IEEE Transactions on Circuits and SystemsI
, 2004
"... A deterministic activity network (DAN) is a collection of activities, each with some duration, along with a set of precedence constraints, which specify that activities begin only when certain others have finished. One critical performance measure for an activity network is its makespan, which is th ..."
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Cited by 12 (4 self)
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A deterministic activity network (DAN) is a collection of activities, each with some duration, along with a set of precedence constraints, which specify that activities begin only when certain others have finished. One critical performance measure for an activity network is its makespan, which is the minimum time required to complete all activities. In a stochastic activity network (SAN), the durations of the activities and the makespan are random variables. The analysis of SANs is quite involved, but can be carried out numerically by Monte Carlo analysis. This paper concerns the optimization of a SAN, i.e., the choice of some design variables that affect the probability distributions of the activity durations. We concentrate on the problem of minimizing a quantile (e.g., 95%) of the makespan, subject to constraints on the variables. This problem has many applications, ranging from project management to digital integrated circuit (IC) sizing (the latter being our motivation). While there are effective methods for optimizing DANs, the SAN optimization problem is much more difficult; the few existing methods cannot handle largescale problems.
A SimulationBased Process Model for Managing Complex Design Projects
 IEEE Trans. Eng. Manage
, 2005
"... Abstract—This paper presents a process modeling and analysis technique for managing complex design projects using advanced simulation. The model computes the probability distribution of lead time in a stochastic, resourceconstrained project network where iterations take place among sequential, para ..."
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Cited by 10 (0 self)
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Abstract—This paper presents a process modeling and analysis technique for managing complex design projects using advanced simulation. The model computes the probability distribution of lead time in a stochastic, resourceconstrained project network where iterations take place among sequential, parallel, and overlapped tasks. The model uses the design structure matrix representation to capture the information flows between tasks. We use a simulationbased analysis to account for many realistic aspects of design process behavior which were not possible in previous analytical models. We propose a heuristic for the stochastic, resourceconstrained project scheduling problem in an iterative project network. The model can be used for better project planning and control by identifying leverage points for process improvements, and for evaluating alternative planning and execution strategies. An industrial example is provided to illustrate the utility of the model. Index Terms—Design iteration, design structure matrix, process modeling, project management, project simulation.
A Study of Approximating the Moments of the Job Completion Time in PERT Networks
, 1995
"... this paper. The project starts at the initial node and ends at the terminal node. A path is a set of nodes connected by arrows which begin at the initial node and end at the terminal node. This collection of arcs, nodes and paths is collectively called an activity network. A project is deemed comple ..."
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Cited by 4 (0 self)
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this paper. The project starts at the initial node and ends at the terminal node. A path is a set of nodes connected by arrows which begin at the initial node and end at the terminal node. This collection of arcs, nodes and paths is collectively called an activity network. A project is deemed complete if work along all paths is complete. After the development of the network, the next major planning step is the estimation of activity and project times. Typical methods for estimating activity times have been to use point estimates or some sort of range or distribution. The type of method used depends on the situation facing the project manager. Hershauer and Nabielsky (1972) categorize the situations into three major categories, viz., certainty, risk, and uncertainty. They further subdivide these categories based on availability of knowledge regarding the mode, range and distribution of the time estimates. They then map the situation and estimations to the appropriate methods to be adopted. If activity times are deterministic, the duration of the project completion time is determined by the length of the longest path in the network. However, this becomes complicated when activity times are stochastic in nature. We assume a scenario equivalent to Hershauer and Nabielsky's risk categorynamely, a common distribution situation. For a stochastic activity network, Kulkarni and Adlakha (1986) have identified three important measures of performance: (a) Distribution of the project completion time.
A LABELCORRECTING TRACING ALGORITHM FOR THE APPROXIMATION OF THE PROBABILITY DISTRIBUTION FUNCTION OF THE PROJECT COMPLETION TIME
"... When facing projects with uncertain factors, most of the project managers are interested to secure the pdf of the completion time of the project so as to have full insights into its randomness. For largesize SAN with general types of pdf for the duration of activities, the project managers must tur ..."
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Cited by 2 (2 self)
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When facing projects with uncertain factors, most of the project managers are interested to secure the pdf of the completion time of the project so as to have full insights into its randomness. For largesize SAN with general types of pdf for the duration of activities, the project managers must turn to the techniques of discretization since the other approaches in the literature become too demanding in computational loading. In this study, we find that there are two problems when applying the techniques of discretization to obtain an approximated probability density function (pdf) of the project completion time in stochastic activity networks. Namely, first, there exists neither exact data structure nor systematic scheme for the computer programming when applying the techniques of discretization; and second, error may arise from assuming independency between subpaths in the activity network. Therefore, we are motivated to propose a LabelCorrecting Tracing Algorithm (LCTA) to improve the techniques of discretization. To evaluate the performance of the proposed LCTA, we randomly generate 20 sets of 100node instances in our numerical experiments. Using the pdf’s resultant from Monte Carlo simulation using 20,000 samples as the benchmark, we compared the pdf’s obtained from the PERT model, Dodin’s [10] algorithm and the proposed LCTA. Based on our experimental results, we conclude that the proposed LCTA significantly outperforms the others in both the run time and the precision aspects.
Evaluation and Optimization of the Robustness of DAG Schedules in Heterogeneous Environments
"... ..."
An efficient Activity Network Reduction Algorithm based on the Label Correcting Tracing Algorithm
"... Abstract—When faced with stochastic networks with an uncertain duration for their activities, the securing of network completion time becomes problematical, not only because of the nonidentical pdf of duration for each node, but also because of the interdependence of network paths. As evidenced by ..."
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Abstract—When faced with stochastic networks with an uncertain duration for their activities, the securing of network completion time becomes problematical, not only because of the nonidentical pdf of duration for each node, but also because of the interdependence of network paths. As evidenced by Adlakha & Kulkarni [1], many methods and algorithms have been put forward in attempt to resolve this issue, but most have encountered this same largesize network problem. Therefore, in this research, we focus on network reduction through a Series/Parallel combined mechanism. Our suggested algorithm, named the Activity Network Reduction Algorithm (ANRA), can efficiently transfer a largesize network into an S/P Irreducible Network (SPIN). SPIN can enhance stochastic network analysis, as well as serve as the judgment of symmetry for the Graph Theory.
SOLVING STOCHASTIC PERT NETWORKS EXACTLY USING HYBRID BAYESIAN NETWORKS
"... In this paper, we describe how a stochastic PERT network can be formulated as a Bayesian network. We approximate such PERT Bayesian network by mixtures of Gaussians hybrid Bayesian networks. Since there exists algorithms for solving mixtures of Gaussians hybrid Bayesian networks exactly, we can use ..."
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In this paper, we describe how a stochastic PERT network can be formulated as a Bayesian network. We approximate such PERT Bayesian network by mixtures of Gaussians hybrid Bayesian networks. Since there exists algorithms for solving mixtures of Gaussians hybrid Bayesian networks exactly, we can use these algorithms to make inferences in PERT Bayesian networks. 1
I.6.6 Simulation and Modeling: Simulation Output Analysis; I.6.6 Simulation and Modeling: Types of Simulation—Monte
"... Figure 1. Visualization of schedule uncertainty analysis using COMPASS. Humans have difficulty evaluating the effects of uncertainty on schedules. People often mitigate the effects of uncertainty by adding slack based on experience and nonstochastic analyses such as the critical path method (CPM). ..."
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Figure 1. Visualization of schedule uncertainty analysis using COMPASS. Humans have difficulty evaluating the effects of uncertainty on schedules. People often mitigate the effects of uncertainty by adding slack based on experience and nonstochastic analyses such as the critical path method (CPM). This is costly as it leads to longer than necessary schedules, and can be ineffective without a clear understanding of where slack is needed. COMPASS is an interactive realtime tool that analyzes schedule uncertainty for a stochastic task network. An important feature is that it concurrently calculates stochastic critical paths and critical tasks. COMPASS visualizes this information on top of a traditional Gantt view, giving users insight into how delays caused by uncertain durations propagate down the schedule. Evaluations with 10 users show that users can use COMPASS to answer a variety of questions about the possible evolutions of a schedule (e.g., what is the likelihood that all activities will complete before a given date?)