Markov and Markov-Regenerative <scp>pert</scp> Networks

Kulkarni, Vidyadhar G.; Adlakha, Veena

doi:10.1287/opre.34.5.769

Cited by 159 publications

(109 citation statements)

References 17 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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“…For Markovian PERT networks, Kulkarni and Adlakha [23] describe an exact method for deriving the distribution and moments of the earliest project completion time using continuous-time Markov chains (CTMCs), where it is assumed that each activity is started as soon as its predecessors are completed (an early-start schedule).…”

Section: Policy Classmentioning

confidence: 99%

“…, n − 1); we consider more general distributions in The problem of finding an optimal scheduling policy corresponds to optimizing a discounted criterion in a continuous-time Markov decision chain (CTMDC) on the state space Q, with Q containing all the states of the system that can be visited by the transitions (which are called feasible states); the decision set is described below. We apply a backward stochastic dynamic-programming (SDP) recursion to determine optimal deci-sions based on the CTMC described in Kulkarni and Adlakha [23]. The key instrument of the SDP recursion is the value function F (·), which determines the expected NPV of each feasible state at the time of entry of the state, conditional on the hypothesis that optimal decisions are made in all subsequent states and assuming that all 'past' modules (with all activities past) were successful.…”

Section: The Exponential Casementioning

confidence: 99%

Project planning with alternative technologies in uncertain environments

Creemers

Reyck

Leus

2015

European Journal of Operational Research

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Abstract:We investigate project scheduling with stochastic activity durations to maximize the expected net present value. Individual activities also carry a risk of failure, which can cause the overall project to fail. In the project planning literature, such technological uncertainty is typically ignored and project plans are developed only for scenarios in which the project succeeds. To mitigate the risk that an activity's failure jeopardizes the entire project, more than one alternative may exist for reaching the project's objectives. We propose a model that incorporates both the risk of activity failure and the possible pursuit of alternative technologies. We find optimal solutions to the scheduling problem by means of stochastic dynamic programming. Our algorithms prescribe which alternatives need to be explored, and how they should be scheduled. We also examine the impact of the variability of the activity durations on the project's value.

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“…For Markovian PERT networks, Kulkarni and Adlakha (1986) Kulkarni and Adlakha (1986) as a starting point to develop scheduling procedures that maximize an expected-NPV (eNPV) objective. All aforementioned studies, however, assume unlimited resources and exponentially distributed activity durations.…”

Section: Markov Decision Chainmentioning

confidence: 99%

Minimizing the Expected Makespan of a Project with Stochastic Activity Durations Under Resource Constraints

Creemers

2015

SSRN Journal

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The resource-constrained project scheduling problem (RCPSP) has been widely studied. A fundamental assumption of the basic type of RCPSP is that activity durations are deterministic (i.e., they are known in advance). In reality, however, this is almost never the case. In this article we illustrate why it is important to incorporate activity duration uncertainty, and develop an exact procedure to optimally solve the stochastic resource-constrained scheduling problem (SRCPSP). A computational experiment shows that our approach works best when solving small-to medium-sized problem instances where activity durations have a moderate-to-high level of variability. For this setting, our model outperforms the existing state-of-the-art. In addition, we use our model to assess the optimality gap of existing heuristic approaches, and investigate the impact of making scheduling decisions also during the execution of an activity rather than only at the end of an activity.

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Markov and Markov-Regenerative pert Networks

Cited by 159 publications

References 17 publications

On Calculating Activity Slack in Stochastic Project Networks

On Calculating Activity Slack in Stochastic Project Networks

Project planning with alternative technologies in uncertain environments

Minimizing the Expected Makespan of a Project with Stochastic Activity Durations Under Resource Constraints

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