Stochastic Project Network Research Articles

Analysis of the impact of corrective actions for stochastic project networks

In project management, a project plan is constructed that assigns a planned start time to each project activity. Based on this plan, the total planned project duration and cost can be determined. However, during project execution, deviations from the plan are inevitable due to uncertainty and variability. When these deviations endanger the timely completion of projects, the project manager should take corrective actions to get the project back on track. In this study, corrective actions are modelled as modifications of the original activity duration distributions (i.e., reduced mean and/or standard deviation) to account for the uncertain nature of their impact. Further, an analytical procedure is developed to rank activities according to their expected impact on the project duration distribution when they are controlled by a corrective action. This activity ranking is used to determine the number of actions that should be taken and to select the set of activities that will be controlled. A computational experiment on a large set of project networks with varying network complexity and network structures has been conducted. These experiments have shown that taking actions on a relatively small subset of activities, rather than on the entire set of project activities, proves more efficient, when the subset of activities is carefully selected. More precisely, the efficiency of the corrective actions process depends on both the number of actions and the activity selection criterion (activity ranking).

Universal generating function -based narrow reliability bounds to evaluate reliability of project completion time

Project completion time is one of the important indicators for managing/scheduling construction projects. This paper proposes a method for evaluating the reliability of project completion time by using the Universal Generating Function technique. The proposed method is used to overcome the limitations of existing project reliability evaluation methods by providing accurate results while requiring low computational burden. Also, unlike many of the methods revealed in the literature, in the proposed method, the activity duration does not need to follow any specific distribution. Our methodology consists of five main parts: 1) determining the u-function of the activity durations 2) modeling the stochastic project network as a parallel-series multi-state system, 3) determining the u-function of the project network paths to determine the probability of failure in each path, 4) determining the probability of simultaneous failure of each pair of paths, and 5) computing reliability bounds for project completion time by integrating the NRB and UGF methods. Results of the proposed method were compared with those of the Monte Carlo simulation method indicating that the reliability level obtained from both methods are indifferent at 0.01 significance level, while the computation time of the proposed method is significantly lower.

Aleatory uncertainty quantification of project resources and its application to project scheduling

The extant literature offers little basis for uncertainty analysis of resource acquisition in project management. Within the spirit of reliability theory, the present paper attempts to fill this gap by taking a success-oriented view of acquiring the required resources for completing a project. In this context, the Reliability Block Diagram (RBD) is constructed to quantify the aleatory uncertainty in resource acquisition by taking into account the supply of and demand for every resource, as well as the probability that the resource is available when it is required. Further, this article generates a new schedule sensitivity index that accounts for uncertainty in both time duration and resource acquisition of project activity. This paper compares the effectiveness of the proposed index in evaluating the relative importance of activities in stochastic project networks. The new index proves better performance due to its ability to capture uncertainty in both time duration and resource acquisition of project activity.

Reliability interval for a stochastic project network constrained by budget and time

In a project, duration and cost of activities are stochastic in nature due to uncertainties (natural disaster and human factors). Thus, a project is commonly modeled as a stochastic project network (SPN). For a project manager, it is a duty to manage both efficiency and effectiveness of an SPN. To achieve this goal, this paper develops a procedure to derive project reliability interval for an SPN. The project reliability interval is a performance indicator to assess the probability of project completion under budget and time constraints. Such an indicator provides project manager a quantitative measurement and a qualitative implication to decide a reasonable completion time and budget for an SPN. Quantitative measurement shows the efficiency of budget and time consumption to complete a project; while qualitative implication provides the effectiveness after implementing a project. A practical project of disaster recovery system is utilized to demonstrate how the project reliability interval is applicable in the real life. Sensitivity analysis is further implemented to investigate the project reliability interval under various constraints of project time and budget.

Project Reliability Interval for a Stochastic Project Network Subject to Time and Budget Constraints

Completion time and cost in a project are affected by uncertainties, such as weather, human resources availability, equipment efficiency, etc. The activity durations of the project, thus, should be regarded as stochastic. Such a project is usually modeled as a stochastic project network (SPN). The SPN can be represented in the form of an activity-on-arc diagram, in which each activity has several possible durations and different costs. Every activity duration possesses a corresponding cost and probability. Based on the concept of minimal paths, two algorithms are utilized to find the upper and lower duration vectors under both time and budget constraints. For an SPN, the project reliability is defined as the probability that the project can be completed under both time and budget thresholds. Theoretically, it is difficult to compute project reliability using the upper and lower duration vectors directly because of the domination property among the duration vectors. Therefore, this paper proposes the derivation of project reliability interval depending on the relationships among the upper and lower duration vectors. The exact project reliability is proved to be contained within the interval. Two examples, including a practical case of disaster recovery system construction, are presented to demonstrate the scalability and practicability of the proposed solution procedure.

On path floats in a stochastic project network

In a deterministic project network, all the activity times are fixed values and the path float can be found by computing the difference between the project duration and the path length. This is not possible in its stochastic counterpart, where the path lengths and the project duration change constantly since each activity time is a random variable. In the current literature, several methods have been proposed to define the float of a path in this case but all of them are fundamentally flawed. This paper aims to suggest an improved definition of path float in a stochastic project network and show how to compute it through the use of an approximation algorithm for estimating the mean and variance of the project duration under some reasonable assumptions. A numerical example will be provided to demonstrate the superiority of the new approach to the existing ones.

Scheduling Critical Activities of Stochastic Projects Management

In this paper, we consider the problem of stochastic project network when some or all activities are interrupted. An approach has been built to schedule the critical activities, by constructing some expressions based on the project lateness costs due to the interruption activities. Two simple example are presented to validate our approach.
 Key words: Project Management, Project scheduling, Stochastic activity duration, Stochastic PERT. 
 Introduction
 Recently, Projects planning and optimal timing, under uncertainty are extremely critical for many organizations, see [19]. Having an effective mathematical model will give project managers a significant tool for replanning projects allocation decisions in response events and outcomes. As a result, the uncertainty associated with such risky projects should be reduced. 
 No one factor can account for, or prevent, failure in a project. It is common practice for a project team to develop a comprehensive risk assessment and risk management plan. Identifying the most critical activities with regard to schedule risk is a problem faced by all project managers.
 The problem of identifying critical activities (CA) in a deterministic network is well understood, by standard Critical Path Method (CPM) known as Program Evaluation and Review Technique (PERT). Since a project could be delayed if these activities were not completed in the scheduled time. The classical PERT method is the probably is the best-known mechanism for considering the stochastic nature of activity durations, in which it is possible to develop estimates of the uncertainty of the project make span. For more details see [8] & [10 ].

On Calculating Activity Slack in Stochastic Project Networks

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.

An Optimization Model for Stochastic Project Networks with Cash Flows

Project networks – or PERT networks – can be characterized by random completion times of activities and positive or negative cash flows throughout the project. In these cases the decision maker’s problem consists of determining a feasible activities schedule, to maximize the project financial value, where the financial value is measured by the net present value (npv) of cash flows.

A surrogate indicator of criticality for stochastic project networks

AbstractThe study of the delay that can be caused by any activity of a stochastic project network is a key topic because of the increasing importance of risk and time control in project management. The main concept adopted for this purpose has been the notion of critical activity developed for deterministic project networks but, in this paper, the inadequacy of the concept critical activity for stochastic project networks is shown and a new surrogate indicator of criticality (SIC) is built, using a regression model applied to a large set of generated project networks. This new indicator explains more than 90% of the initial variance estimated for more than 80,000 activities belonging to a wide range of project networks (580 nets), with very different morphological types.

A Computational Study on Bounding the Makespan Distribution in Stochastic Project Networks

Due to the practical importance of stochastic project networks (PERT-networks), many methods have been developed over the past decades in order to obtain information about the random project completion time. Of particular interest are methods that provide (lower and upper) bounds for its distribution, since these aim at balancing efficiency of calculation with accuracy of the obtained information.

Project network models with discounted cash flows a guided tour through recent developments

The vast majority of the project scheduling methodologies presented in the literature have been developed with the objective of minimizing the project duration subject to precedence and other constraints. In doing so, the financial aspects of project management are largely ignored. Recent efforts have taken into account discounted cash flows and have focused on the maximization of the net present value ( npv) of the project as the more appropriate objective. In this paper we offer a guided tour through the important recent developments in the expanding field of research on deterministic and stochastic project network models with discounted cash flows. Subsequent to a close examination of the rationale behind the npv objective, we offer a taxonomy of the problems studied in the literature and critically review the major contributions. Proper attention is given to npv maximization models for the unconstrained scheduling problem with known cash flows, optimal and suboptimal scheduling procedures with various types of resource constraints, and the problem of determining both the timing and amount of payments.

Activity Delay in Stochastic Project Networks

In this paper we deal with a stochastic project network and consider the impact of activity delay to maximize the expected present value of a project. It is shown that in certain situations, delaying the onset of an activity from its earliest start time can indeed increase the present value of a project due to the postponing of associated negative cash flows. Furthermore, a project that could otherwise be rejected (negative expected present value) may become profitable (positive expected present value) due to delay. We demonstrate that even activities on the critical path, as determined by each activity's expected duration, may be profitably delayed. Optimal and approximate procedures are developed to determine the amount of delay of the various activities.

Identifying critical activities in stochastic resource constrained networks

The analysis of the stochastic project network can provide indications of both the magnitude of temporal risk and the sources of that risk. In a project dominated by technological dependencies rather than resource constraints, the sources of risk can be identified by examining the probabilities of each activity lying on a critical path. Similar criticality probabilities can also be derived for resource constrained stochastic networks if the definition of the critical path is revised. The use of this revised criticality probability is illustrated in an analysis of an example project and other possible measures of identifying the important activities are considered. A quantitative test of the value of the information provided by the criticality probability is developed and applied to a set of 100 randomly generated project networks, comparing the possible measures. This test indicates that the criticality probability provides valuable management information, extending the familiar concept of the critical path to the resource constrained stochastic network.

Weather Risk in Offshore Projects

Risk analysis tools have been used to help manage various projects. This paper describes a case study in which an extension to the stochastic project network model was developed for a risk analysis of an oil platform installation, quantifying the possible impact of the weather on the project's schedule. Examination of the weather data suggested the use of a Markov weather model combined with a separate residence time distribution for key states. The weather model was incorporated into the stochastic project network allowing the interactions of the various project uncertainties to be examined. While the weather introduced a significant additional risk to the project, analysis of management's options indicated that much of the risk might be avoided. In particular, the analysis quantified the benefits of scheduling the project start to take advantage of the seasonal variations and hiring heavy duty equipment to operate in more arduous conditions.

Computing the probability distribution of project duration in a PERT network

AbstractThe algorithm presented here makes exact computations of characteristics of the probability distribution of project duration for a stochastic project network. Given discrete independent probability distributions for task durations, the algorithm will compute either moments of the project duration distribution or values of the cumulative distribution function of project duration. The algorithm can be used for sensitivity analysis on probability weights since several task duration distributions having the same range can be handled simultaneously with no great increase in computation time requirements.

Preselective strategies for the optimization of stochastic project networks under resource constraints

AbstractThis article deals with a stochastic version of the optimization problem for project networks under resource constraints. In this, activity durations are assumed to be realized according to some joint probability distribution and the aim of optimization is to minimize the expected overall project cost (monotonically increasing with project duration). Certain strategies are known that constitute feasible solutions to this problem, the best studied of which are the so‐called ES strategies (“earliest start” with regard to fixed project structures). In this paper, a considerably broader class of strategies is introduced, namely preselective strategies. It is shown that this generalization, for which an algorithmic approach remains possible, preserves almost all the desirable behavior known for ES strategies. In particular, the number of “essential” strategies remains finite and even minimal optimum‐determining sets of such strategies can, in general, be characterized. Also, the analytic behavior is still proper and there is considerable “stability” to weak convergence of the joint distribution of activity durations as well as to a. e. convergence of the cost function. Last but not least, possible generalization to arbitrary regular cost functions is again imminent.