Bounding Distributions for a Stochastic Acyclic Network

Kleindorfer, George B.

doi:10.1287/opre.19.7.1586

Cited by 115 publications

(37 citation statements)

References 7 publications

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“…Additional work related to the problem of determining the expected project makespan with stochastic task durations includes papers by Van Slyke (1963) who suggests Monte Carlo Simulation as a viable method for constructing the project makespan distribution, Martin (1965) who defines a network reduction approach for determining the makespan Probability Density Function (PDF), Dodin (1984) who develops a heuristic approach to finding the k most critical paths through a project network, Dodin (1985a) who develops an approximation for the makespan CDF, Kleindorfer (1971); Robillard and Trahan (1976) and Dodin (1985b) who obtain bounds for the makespan PDF and Kulkarni and Adlakha (1986) who develop the makespan distribution for a project network with exponentially distributed task times using a Markov Pert Networks (MPN. Many of these, including Dodin (1985a), developed approximations using discretization of continuous density functions, simplifying the convolution of task densities.…”

Section: Fig 1: It Project Performancementioning

confidence: 99%

On Calculating Activity Slack in Stochastic Project Networks

Mitchell¹

2010

American Journal of Economics and Business Administration

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Problem statement: Identifying critical tasks in a project network is easily done when task times are deterministic, but doing so under stochastic task times is problematic. The few methods that have been proposed contain serious drawbacks which lead to identifying critical tasks incorrectly, leaving project managers without the means to (1) identify and rank the most probable sources of project delays, (2) assess the magnitude of each source of schedule risk, and (3) identify which tasks represent the best opportunities for successfully addressing schedule risk? Approach: In this study we considered the problem of identifying the sources of schedule risk in a stochastic project network. We developed general expressions for determining a task's late starting and ending time distributions. We introduced the concept of stochastic slack and develop a number of metrics that help a project manager directly identify and estimate the magnitude of sources of schedule risk. Finally, we compared critical tasks identified using the activity criticality index to those found using stochastic slack metrics. Results:We have demonstrated that a task may have non-zero probability of negative stochastic slack and that expected total slack for a task may be negative. We also found that while the activity criticality index is effective for calculating the probability that a task is on a critical path, the stochastic slack based metrics discussed in this paper are better predictors of the extent to which a delay in a task will result in a project delay. Conclusion/Recommendations: Project managers should consider using stochastic slack based metrics for assessing project risk and establishing the most likely project schedule outcomes. Given the calculation complexity associated with theoretically exact stochastic slack metrics, effective heuristics are required.

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Section: Fig 1: It Project Performancementioning

confidence: 99%

On Calculating Activity Slack in Stochastic Project Networks

Mitchell¹

2010

American Journal of Economics and Business Administration

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“…Indeed, many techniques for statistical timing analysis are based on those developed in the operations research and management science literature, e.g., criticality analysis (Bowman 1995) and distribution bounding (Kleindorfer 1971, Ludwig et al 2001). …”

Section: Statistical Designmentioning

confidence: 99%

Digital Circuit Optimization via Geometric Programming

Boyd

Kim

Patil

et al. 2005

Operations Research

154

146

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This paper concerns a method for digital circuit optimization based on formulating the problem as a geometric program (GP) or generalized geometric program (GGP), which can be transformed to a convex optimization problem and then very efficiently solved. We start with a basic gate scaling problem, with delay modeled as a simple resistor-capacitor (RC) time constant, and then add various layers of complexity and modeling accuracy, such as accounting for differing signal fall and rise times, and the effects of signal transition times. We then consider more complex formulations such as robust design over corners, multimode design, statistical design, and problems in which threshold and power supply voltage are also variables to be chosen. Finally, we look at the detailed design of gates and interconnect wires, again using a formulation that is compatible with GP or GGP.

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“…Criticality (4)(5)(6)(7)(8) 0.000 0.143 Table 1: Project statistics for the project from Van Slyke [19].…”

Section: Cpm Simulationmentioning

confidence: 99%

“…The second example is a larger project taken from Kleindorfer [8]. The project consists of forty activities distributed over fifty one paths.…”

Section: Example 2: Comparison With Other Worst Case Approachesmentioning

confidence: 99%

Persistence in discrete optimization under data uncertainty

2006

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An important question in discrete optimization under uncertainty is to understand the persistency of a decision variable, i.e., the probability that it is part of an optimal solution. For instance, in project management, when the task activity times are random, the challenge is to determine a set of critical activities that will potentially lie on the longest path. In the spanning tree and shortest path network problems, when the arc lengths are random, the challenge is to pre-process the network and determine a smaller set of arcs that will most probably be a part of the optimal solution under different realizations of the arc lengths. Building on a characterization of moment cones for single variate problems, and its associated semidefinite constraint representation, we develop a limited marginal moment model to compute the persistency of a decision variable. Under this model, we show that finding the persistency is tractable for zero-one optimization problems with a polynomial sized representation of the convex hull of the feasible region. Through extensive experiments, we show that the persistency computed under the limited marginal moment model is often close to the simulated persistency value under various distributions that satisfy the prescribed marginal moments and are generated independently.

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Bounding Distributions for a Stochastic Acyclic Network

Cited by 115 publications

References 7 publications

On Calculating Activity Slack in Stochastic Project Networks

On Calculating Activity Slack in Stochastic Project Networks

Digital Circuit Optimization via Geometric Programming

Persistence in discrete optimization under data uncertainty

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