Probability of Project Completion Using Stochastic Project Scheduling Simulation

This paper introduces a software, Stochastic Project Scheduling Simulation (SPSS), developed to measure the probability to complete a project in a certain time specified by the user. To deliver a project by a completion date committed to in a contract, a number of activities need to be carried out. The time that an entire project takes to complete and the activities that determine total project duration are always questionable because of the randomness and stochastic nature of the activities’ durations. Predicting a project completion probability is valuable, particularly at the time of bidding. The SPSS finds the longest path in a network and runs the network a number of times specified by the user and calculates the stochastic probability to complete the project in the specified time. The SPSS can be used by a contractor: (1) to predict the probability to deliver the project in a given time frame and (2) to assess its capabilities to meet the contractual requirement before bidding. The SPSS can also be used by a construction owner to quantify and analyze the risks involved in the schedule. The benefits of the tool to researchers are: (1) to solve program evaluation and review technique problems; (2) to complement Monte Carlo simulation by applying the concept of project network modeling and scheduling with probabilistic and stochastic activities via a web based Java Simulation which is operateable over the Internet, and (3) to open a way to compare a project network having different distribution functions.     

Automated Statistical Analysis in Stochastic Project Scheduling Simulation

This paper describes a stochastic simulation-based scheduling system (S3) that: (1) integrates the deterministic critical path method (CPM), the probabilistic program evaluation and review technique (PERT), and the stochastic discrete event simulation (DES) approaches into a single system and lets the scheduler make an informed decision as to which method is better suited to the company’s risk-taking culture; (2) automatically determines the minimum number of simulation runs in DES mode and therefore optimizes the simulation process; and (3) provides a terminal method that tests the statistical significance of the differences between simulations, hence eliminating outliers and therefore increasing the accuracy of the DES process. The system is based on an earlier version of the system called stochastic project scheduling simulation and makes use of all the capabilities of this system. The study is of value to practitioners because S3 produces a realistic prediction of the probability of completing a project in a specified time. The study is also of relevance to researchers in that it allows researchers to compare the outcome of CPM, PERT, and DES under different conditions such as different variability or skewness in the activity duration data, the configuration of the network, or the distribution of the activity durations.     

Analytical Approximation to the Probability Distribution of Electricity Marginal Production Costs

This paper proposes an analytical approximation to calculate the probability distribution of the marginal production cost of an electric power system. This information is expected to benefit both buyers and sellers of electricity in the upcoming deregulated environment. Since the exact computation of the probability distribution is prohibitive for large systems, we propose to use a combination of the Edgeworth expansion and the large deviation approximation. The results show that the Edgeworth expansion is accurate for computing probabilities at the center of the distribution and the large deviation approximation for computing tail probabilities. Monte Carlo simulation is used as a benchmark to verify and assess the performance of the approximation method in a large power system. In our stochastic model of the system marginal production cost, the load is represented by a normal distribution and the generating unit availability is characterized by its forced outage rate. It is found that the proposed approximation provides accurate estimates at a reasonable computational time.     

Extending Monte Carlo Simulations to Represent and Propagate Uncertainties in Presence of Incomplete Knowledge: Application to the Transfer of a Radionuclide in the Environment

This work is devoted to some recent developments in uncertainty analysis of environmental models in the presence of incomplete knowledge. The classical uncertainty methodology based on probabilistic modeling provides direct estimations of relevant statistical measures to quantify the uncertainty on the model responses thanks to a nice mixing between Monte Carlo simulations and the use of efficient statistical treatments. However, this approach may lead to unrealistic results when not enough information is available to specify the probability distribution functions (pdfs) of input parameters. For example, if a fixed (i.e., the pdf is a Dirac distribution) variable is unknown between a and b, the proper way to model this knowledge is to consider a set of δc distributions (a δc distribution means that the probability that the parameter is equal to c is 1 and 0 elsewhere), c belonging to [a,b]. This is quite different from assume an equidistribution. Thus, to respect the real state of knowledge in industrial applications, a new modeling based on the theory of evidence is introduced. It allows an extension of classical Monte Carlo simulations by relaxing assumptions related to the choice of probability distribution functions and possible dependencies between uncertain parameters. To illustrate the principle of our modeling, a comparison with the probabilistic modeling is given in the case of the transfer of a radionuclide in the environment.     

Finance-Based Scheduling of Construction Projects Using Integer Programming

Construction scheduling is the process of devising schemes for sequencing activities. A realistic schedule fulfills the real concerns of users, thus minimizing the chances of schedule failure. The minimization of total project duration has been the concept underlying critical-path method/program evaluation and review technique (CPM/PERT) schedules. Subsequently, techniques including resource management and time-cost trade-off analysis were developed to customize CPM/PERT schedules in order to fulfill users’ concerns regarding project resources, cost, and time. However, financing construction activities throughout the course of the project is another crucial concern that must be properly treated otherwise, nonrealistic schedules are to be anticipated. Unless contractors manage to procure adequate cash to keep construction work running according to schedule, the pace of work will definitely be relaxed. Therefore, always keeping scheduled activities in balance with available cash is a potential contribution to producing realistic schedules. This paper introduces an integer-programming finance-based scheduling method to produce financially feasible schedules that balance the financing requirements of activities at any period with the cash available during that same period. The proposed method offers twofold benefits of minimizing total project duration and fulfilling finance availability constraints.     

Simplified CPM∕PERT Simulation Model

Formal stochastic simulation study has been recognized as a remedy for the shortcomings inherent to classic critical path method (CPM) project evaluation and review technique (PERT) analysis. An accurate and efficient method of identifying critical activities is essential for conducting PERT simulation. This paper discusses the derivation of a PERT simulation model, which incorporates the discrete event modeling approach and a simplified critical activity identification method. This has been done in an attempt to overcome the limitations and enhance the computing efficiency of classic CPM∕PERT analysis. A case study was conducted to validate the developed model and compare it to classic CPM∕PERT analysis. The developed model showed marked enhancement in analyzing the risk of project schedule overrun and determination of activity criticality. In addition, the beta distribution and its subjective fitting methods are discussed to complement the PERT simulation model. This new solution to CPM network analysis can provide project management with a convenient tool to assess alternative scenarios based on computer simulation and risk analysis.     

Probabilistic Duration Estimation Model for High-Rise Structural Work

The duration of a construction project is a key factor to consider before starting a new project, as it can determine project success or failure. Despite the high level of uncertainty and risk involved in construction, current construction planning relies on traditional deterministic scheduling methods that cannot clearly ascertain the level of uncertainty involved in a project. This, subsequently, can prolong a project’s duration, particularly when that project is high-rise structural work, which is not yet a common project type in Korea. Indeed, among construction processes, structural work is notable, as it is basically performed outdoors. Thus, no matter how precisely a schedule is developed, such projects can easily fail due to unexpected events that are beyond the planner’s control, such as changes in weather conditions. Therefore, in this study, to cope with the uncertainties involved in high-rise building projects, a probabilistic duration estimation model is developed in which both weather conditions and work cycle time for unit work are considered to predict structural work duration. According to the proposed estimation model, weather variables are divided into two types: weather conditions that result in nonworking days and weather conditions that result in work productivity rate (WPR) change. Obtained from actual previous data, the WPR is used with relevant nonworking day weather conditions to modify the actual number of working days per calendar days. Furthermore, on the basis of previous research results, the cycle time of the unit work area is assumed to follow the β probability distribution function. Thus, the probabilistic duration model is valid for 95% probability. Finally, a case study is conducted that confirms the model can be practically used to estimate more reliable and applicable probabilistic durations of structural work. Indeed, this model can assist schedulers and site workers by alerting them, at the beginning of a project, to project uncertainties that specifically pertain to structural work and the weather. Thus, the proposed model can enable personnel to easily amend, and increase the reliability of, the construction schedule at hand.     

Construction Project Network Evaluation with Correlated Schedule Risk Analysis Model

Schedules are the means of determining project duration accurately, controlling project progress, and allocating resources efficiently in managing construction projects. It is not sufficient in today’s conditions to evaluate the construction schedules that are affected widely by risks, uncertainties, unexpected situations, deviations, and surprises with well-known deterministic or probabilistic methods such as the critical path method, bar chart (Gantt chart), line of balance, or program evaluation and review technique. In this regard, this paper presents a new simulation-based model—the correlated schedule risk analysis model (CSRAM)—to evaluate construction activity networks under uncertainty when activity durations and risk factors are correlated. An example of a CSRAM application to a single-story house project is presented in the paper. The findings of this application show that CSRAM operates well and produces realistic results in capturing correlation indirectly between activity durations and risk factors regarding the extent of uncertainty inherent in the schedule.     

Float Consumption Impact on Cost and Schedule in the Construction Industry

Quantifying and minimizing the risks associated with delays in the construction industry are the main challenges for all parties involved. Float loss impact in noncritical activities is one of the complicated delays to assess on a project’s duration and cost. This is due to the fact that the deterministic critical path method cannot cope with such delays unless they exceed the total float values. Further, stochastic analysis, which is used in this research to assess the impact of such delays, is perceived by many planners to be complicated and time consuming. This paper presents a method to control the risks associated with float loss in construction projects. The method uses a recently developed multiple simulation analysis technique that combines the results of cost range estimates and stochastic scheduling, using Monte Carlo simulation. The proposed method quantifies the float loss impact on project duration and cost. Least-squares nonlinear regression is used to convert the stochastic results into a polynomial function that quantifies the float loss impact by relating directly the float loss value to project duration and cost at a specified confidence level.     

Optimal Design with Probabilistic Objective and Constraints

Significant challenges are associated with solving optimal structural design problems involving the failure probability in the objective and constraint functions. In this paper, we develop gradient-based optimization algorithms for estimating the solution of three classes of such problems in the case of continuous design variables. Our approach is based on a sequence of approximating design problems, which is constructed and then solved by a semiinfinite optimization algorithm. The construction consists of two steps: First, the failure probability terms in the objective function are replaced by auxiliary variables resulting in a simplified objective function. The auxiliary variables are determined automatically by the optimization algorithm. Second, the failure probability constraints are replaced by a parametrized first-order approximation. The parameter values are determined in an adaptive manner based on separate estimations of the failure probability. Any computational reliability method, including first-order reliability and second-order reliability methods and Monte Carlo simulation, can be used for this purpose. After repeatedly solving the approximating problem, an approximate solution of the original design problem is found, which satisfies the failure probability constraints at a precision level corresponding to the selected reliability method. The approach is illustrated by a series of examples involving optimal design and maintenance planning of a reinforced concrete bridge girder.     

Optimal Planning and Scheduling for Repetitive Construction Projects

This paper presents a multiobjective optimization model for the planning and scheduling of repetitive construction projects. The model enables construction planners to generate and evaluate optimal construction plans that minimize project duration and maximize crew work continuity, simultaneously. The computations in the present model are organized in three major modules: scheduling, optimization, and ranking modules. First, the scheduling module uses a resource-driven scheduling algorithm to develop practical schedules for repetitive construction projects. Second, the optimization module utilizes multiobjective genetic algorithms to search for and identify feasible construction plans that establish optimal tradeoffs between project duration and crew work continuity. Third, the ranking module uses multiattribute utility theory to rank the generated plans in order to facilitate the selection and execution of the best overall plan for the project being considered. An application example is analyzed to illustrate the use of the model demonstrate its new capabilities in optimizing the planning and scheduling of repetitive construction projects.     

Prediction System for Change Management in Construction Project

Changes are the main causes of delays and cost overruns in construction projects. Various change management systems have been developed to minimize the impacts of changes and to facilitate good project management. This paper presents a change prediction system using activity-based dependency structure matrix (DSM) to facilitate change management. DSM is used to model the process that may occur as a result of changes. Consequently changes can be predicted by setting the change criteria for each activity in the form of rework scope. Furthermore, Monte Carlo simulation is introduced to analyze the change probability of activities involved in construction projects. The effectiveness of the prediction system is verified by applying this system to an office building project. This study provides a useful tool for project management teams to manage changes proactively and efficiently.     

Parallel Genetic Algorithms for Optimizing Resource Utilization in Large-Scale Construction Projects

This paper presents the development of a parallel multiobjective genetic algorithm framework to enable an efficient and effective optimization of resource utilization in large-scale construction projects. The framework incorporates a multiobjective optimization module, a global parallel genetic algorithm module, a coarse-grained parallel genetic algorithm module, and a performance evaluation module. The framework is implemented on a cluster of 50 parallel processors and its performance was evaluated using 183 experiments that tested various combinations of construction project sizes, numbers of parallel processors and genetic algorithm setups. The results of these experiments illustrate the new and unique capabilities of the developed parallel genetic algorithm framework in: (1) Enabling an efficient and effective optimization of large-scale construction projects; (2) achieving significant computational time savings by distributing the genetic algorithm computations over a cluster of parallel processors; and (3) requiring a limited and feasible number of parallel processors/computers that can be readily available in construction engineering and management offices.     

Neural Network Embedded Monte Carlo Approach for Water Quality Modeling under Input Information Uncertainty

This paper proposes a neural network embedded Monte Carlo (NNMC) approach to account for uncertainty in water quality modeling. The framework of the proposed method has three major parts: a numerical water quality model, a neural network technique, and Monte Carlo simulation. The numerical model is used to generate desirable output for training and testing sets, and the neural network is used as a universal functional mapping tool to approximate the input-output response of the numerical model. The Monte Carlo simulation then uses the neural network to generate numerical realizations based on a probabilistic distribution of parameters, thus obtaining a probabilistic distribution of the simulated state variables. By embedding a neural network into the conventional Monte Carlo simulation, the proposed approach significantly improves upon the conventional method in computational efficiency. The proposed approach has been applied to uncertainty and risk analyses of a phosphorus model for Triadelphia Reservoir in Maryland. The results of this research show that the NNMC approach has potential for efficient uncertainty analysis of water quality modeling.     

Stochastic Network Model for Planning Scheduling

A stochastic network model consisting of dependent and independent random variables is developed for construction scheduling. The network model is based on Monte‐Carlo simulation. Data for each network activity consist of a time distribution for the activity under optimal conditions and a series of time distributions for various problems that may lengthen the activity completion time. Dependencies between network activities may be modelled; also, time dependencies for a network activity may be modelled. The implementation of the model is discussed.     

Time-Profit Trade-Off Analysis for Construction Projects

This paper presents a multiobjective optimization model that provides new and unique capabilities including generating and evaluating optimal/near-optimal construction resource utilization and scheduling plans that simultaneously minimize the time and maximize the profit of construction projects. The computations in the present model are organized in three major modules: (1) a scheduling module that develops practical schedules for construction projects; (2) a profit module that computes the project profit; and (3) a multiobjective module that searches for and identifies optimal/near optimal trade-offs between project time and profit. A large-scale construction project is analyzed to illustrate the use of the model and to demonstrate its capabilities in generating and visualizing optimal trade-offs between construction time and profit.     

New Method for Calculating Path Float in Program Evaluation and Review Technique (PERT)

The path float use in the network is an effective method used to cope with various uncertainties existing within the construction. However, the current path float calculating method may bring misleading information to the managers on site and then cause project duration risk in the construction. The purpose of this paper is to present a new method, which calculates the noncritical path float in the program evaluation and review technique (PERT), to copy with the uncertainties within the network implementation, and to reduce the misleading information. An example network was analyzed with the new method, the results showed the consistent path float under required completion probability and required duration. The new path float concept will bring useful planning information to the managers and the planners in the construction.     

Multiple Simulation Analysis for Probabilistic Cost and Schedule Integration

One of the major goals of the construction industry today is the quantification and minimization of the risk associated with construction engineering performance. When specifically considering the planning of construction projects, one way to control risk is through the development of reliable project cost estimates and schedules. Two techniques available for achieving this goal are range estimating and probabilistic scheduling. This paper looks at the integration of these techniques as a means of further controlling the risk inherent in the undertaking of construction projects. Least-squares linear regression is first considered as a means of relating the data obtained from the application of these techniques. However, because of various limitations, the application of linear regression was not considered the most appropriate means of relating the results of range estimating and probabilistic scheduling. Integration of these techniques was, therefore, achieved through the development of a new procedure called the multiple simulation analysis technique. This new procedure combines the results of range estimating and probabilistic scheduling in order to quantify the relationship existing between them. Having the ability to accurately quantify this relationship enables the selection of high percentile level values for the project cost estimate and schedule simultaneously.     

Quasi-Monte Carlo Simulation with Low-Discrepancy Sequence for Reinforced Soil Slopes

This paper describes a precise numerical technique to compute the limit state exceedance probability of geosynthetic reinforced soil (GRS) slopes with normally distributed backfill and foundation soils by using the low-discrepancy sequence Monte Carlo (LDSMC) and importance sampling with LDSMC (ISLDSMC) methods. The LDSMC and ISLDSMC methods can effectively compute an accurate limit state exceedance probability of GRS slopes with a limited number of simulations. By using importance sampling, random variables can be generated in an expected failure region, thereby enabling enumeration by the Monte Carlo simulation. The failure region can be searched by the conventional first-order reliability method. To increase the computational efficiency, a low-discrepancy sequence, which is a sequence of quasi-random numbers with uniform distribution, is adopted in this study. The numerical simulation in this study revealed that the LDSMC and ISLDSMC methods can effectively compute an accurate limit state exceedance probability of GRS slopes by performing comparatively fewer simulations than the conventional crude Monte Carlo simulation.     

Probabilistic Approach for Budgeting in Portfolio of Projects

This paper presents a mathematical model for calculating the budgetary impact of increasing the required confidence level in a probabilistic risk assessment for a portfolio of projects. The model provides a rational approach for establishing a probabilistic budget for an individual project in such a way that the budget for a portfolio of projects will meet a required confidence level. The use of probabilistic risk assessment in major infrastructure projects is increasing to cope with major cost overruns and schedule delays. The outcome of the probabilistic risk assessment is often a distribution for project costs. The question is at what level of confidence (i.e., the probability that budget would be sufficient given the cost distribution) should be used for establishing the budget. The proposed method looks at a portfolio of such projects being funded by the same owner. The owner can establish a target probability with respect to its annual budget. The model can help the owner establish confidence level for individual projects and also examine the effect of changing the confidence level of the portfolio budget on the budget and the confidence level of individual projects. The paper is relevant to practitioners because it provides a methodology for establishing confidence levels by the owner agencies in the emerging field of cost risk assessment for infrastructure projects. A numerical example is provided using actual transit project data to demonstrate the model application.