• International conference on construction engineering and project management
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• 2011.02a
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• pp.395-398
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• 2011

This paper introduces stochastic cash-flow modeling integrated with simulation based scheduling. The system makes use of CPM schedule data exported from commercial scheduling software, computes the best fit probability distribution functions (PDFs) of historical activity durations, assigns the PDFs identified to respective activities, simulates the schedule network, computes the deterministic and stochastic project cash-flows, plots the corresponding cash flow diagrams, and estimates the best fit PDFs of overdraft and net profit of a project. It analyzes the effect of different distributions of activity durations on the distribution of overdrafts and net profits, and improves reliability compared to deterministic cash flow analysis.

• International Journal of Contents
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• v.6 no.3
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• pp.19-24
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• 2010

Task scheduling is an integrated component of computing with the emergence of grid computing. In this paper, we address two different task scheduling models, which are static Round-Robin (RR) and dynamic Fastest Site First (FSF) task scheduling method, using extended timed marked graphs, which is a special case of Stochastic Petri Nets (SPN). Stochastic reward nets (SRN) is an extension of SPN and provides compact modeling facilities for system analysis. We build hierarchical SRN models to compare two task scheduling methods. The upper level model simulates task scheduling and the lower level model implements task serving process for different sites with multiple servers. We compare these two models and analyze their performances by giving reward measures in SRN.

• Journal of the Korean Operations Research and Management Science Society
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• v.4 no.1
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• pp.69-77
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• 1979

A single machine stochastic scheduling problem is considered. Associated with each job is its random processing time and random deferral cost. The criterion is to order the jobs so as to minimize the sum of the deferral costs. The expected sum of the deferral costs is theroretically derived under the stochastic situation for each of several scheduling decision rules which are well known for the deterministic environment. It is also shown that certain stochastic problems can be reduced to equivalent deterministic problems. Two examples are illustrated to show the expected total deferral costs.

• International conference on construction engineering and project management
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• 2015.10a
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• pp.169-173
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• 2015

The linear scheduling method or line-of-balance (LOB) is a popular choice for projects that involve repetitive tasks during project execution. The method, however, produces deterministic schedule that does not convey a range of potential project outcomes under uncertainty. This results from the fact the basic scheduling parameters such as crew production rates are estimated to be deterministic based on single-point value inputs. The current linear scheduling technique, therefore, lacks the capability of reflecting the fluctuating nature of the project operation. In this paper the authors address the issue of how the variability of operation and production rates affects schedule outcomes and show a more realistic description of what might be a realistic picture of typical projects. The authors provide a solution by providing a more effective and comprehensive way of incorporating the crew performance variability using a Monte Carlo simulation technique. The simulation outcomes are discussed in terms of how this stochastic approach can overcome the shortcomings of the conventional linear scheduling technique and provide optimum schedule solutions.

• Management Science and Financial Engineering
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• v.18 no.2
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• pp.5-11
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• 2012

In this paper, stochastic scheduling problems are considered when processing times and due dates follow arbitrary distributions and due dates are either common or exchangeable. For maximizing the expected number of early jobs, two policies, one, based on pairwise comparisons of the processing times, and the other, based on survivabilities, are introduced. In addition, it is shown that the former guarantees optimal solutions when the processing times and due dates are deterministic and that the latter guarantees optimal solutions when the due dates follow exponential distributions. Then a new approach, exploiting the two policies, is proposed and analyzed which turns out to give better job sequences in many situations. In fact, the new approach guarantees optimal solutions both when the processing times and due dates are deterministic and when the due dates follow exponential distributions.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.183-199
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• 2007

In this paper we research the problem in which the objective is to minimize the sum of squared deviations of job expected completion times from the due date, and the job processing times are stochastic. In the problem the machine is subject to stochastic breakdowns and all jobs are preempt-repeat. In order to show that the replacing ESSD by SSDE is reasonable, we discuss difference between ESSD function and SSDE function. We first give an express of the expected completion times for both cases without resampling and with resampling. Then we show that the optimal sequence of the problem V-shaped with respect to expected occupying time. A dynamic programming algorithm based on the V-shape property of the optimal sequence is suggested. The time complexity of the algorithm is pseudopolynomial.

• Journal of the Korean Operations Research and Management Science Society
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• v.20 no.1
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• pp.179-193
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• 1995

A multi-objective, single-stage scheduling problem with stochastic processing times is considered where the objective is to simultaneously minimize the expected value and the variance of total flowtime, and the mean probability of tardiness. In cases where processing times follow normal distributions, a method using pairwise interchange of two jobs(PITJ) is proposed to generate a set of the approximate efficient schedules. The efficient schedules are not dominated by the criterion vectors of any other permutation schdules in the feasible region. Numerical experiments performed to ascertain the effectiveness of PITJ algorithm are also reported in the results.

• Proceedings of the IEEK Conference
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• 2008.06a
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• pp.197-198
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• 2008

In this paper, we study an opportunistic scheduling scheme for the OFDMA system with streaming services. The service is modeled by using the appropriate utility function. We formulate a stochastic optimization problem that aims at maximizing network utility while satisfying the QoS requirement of each user. The problem is solved by using the dual approach and the stochastic sub-gradient algorithm.

• International conference on construction engineering and project management
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• 2009.05a
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• pp.393-399
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• 2009

This paper introduces an automated tool named Advanced Stochastic Schedule Simulation System (AS4). The system automatically integrates CPM schedule data exported from Primavera Project Planner (P3) and historical activity duration data obtained from a project data warehouse, computes the best fit probability distribution functions (PDFs) of historical activity durations, assigns the PDFs identified to respective activities, computes the optimum number of simulation runs, simulates the schedule network for the optimum number of simulation runs, and estimates the best fit PDF of project completion times (PCTs). AS4 improves the reliability of simulation-based scheduling by effectively dealing with the uncertainties of the activities' durations, increases the usability of the schedule data obtained from commercial CPM software, and effectively handles the variability of the PCTs by finding the best fit PDF of PCTs. It is designed as an easy-to-use computer tool programmed in MATLAB. AS4 encourages the use of simulation-based scheduling because it is simple to use, it simplifies the tedious and burdensome process involved in finding the PDFs of the many activities' durations and in assigning the PDFs to the many activities of a new network under modeling, and it does away with the normality assumptions used by most simulation-based scheduling systems in modeling PCTs.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1991.10a
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• pp.147-159
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• 1991

Stochastic convexity(concvity) of a stochastic process is a very useful concept for various stochastic optimization problems. In this study we first establish stochastic convexity of a certain class of Markov additive processes through the probabilistic construction based on the sample path approach. A Markov additive process is obtained by integrating a functional of the underlying Markov process with respect to time, and its stochastic convexity can be utilized to provide efficient methods for optimal design or for optimal operation schedule of a wide range of stochastic systems. We also clarify the conditions for stochatic monotonicity of the Markov process, which is required for stochatic convexity of the Markov additive process. This result shows that stochastic convexity can be used for the analysis of probabilistic models based on birth and death processes, which have very wide application area. Finally we demonstrate the validity and usefulness of the theoretical results by developing efficient methods for the optimal replacement scheduling based on the stochastic convexity property.