Duration Uncertainty Research Articles

Risk Analysis of Project Scheduling Using Microsoft Excel

Scheduling plays a very important role for the successful implementation of construction projects. One of the biggest risks in scheduling is in terms of project costs and duration uncertainty. To anticipate these uncertainties, scheduling methods have been developed using probabilistic duration, including PERT and Monte Carlo Simulation methods. In this research the simulation process was carried out using Microsoft Excel which was integrated with @Risk's add-ins. From the results of the analysis, the project duration obtained from the scheduling model with the CPM method, conventional PERT and Monte Carlo simulation produces an average value that is close to the same. The difference occurs in the standard deviation value, the conventional PERT method produces the smallest standard deviation, followed by a Monte Carlo simulation using the PERT distribution and the last is Monte Carlo simulation using the TRIANGULAR distribution. From the results of the sensitivity analysis, it was found that the dominant input variables that affect the duration of the project are the duration of activities that most often enter the critical path or those that have a great critical index. Meanwhile, project costs are influenced by a combination of the duration of activities on the critical path and activities that have a great direct cost.

Multi‐stage restoration strategy for service restoration in distribution systems considering outage duration uncertainty

This study proposes a multi-stage restoration strategy to solve the service restoration problem in distribution systems considering the uncertainty of outage duration. Furthermore, it also proposes a restoration index defined in terms of (i) priority of the load restored, (ii) number of switching operations, and (iii) estimated likelihood of the restoration solution to assist the utility in enhanced decision-making. Service restoration is formulated as a single objective optimisation problem considering the maximising of the restoration index as the only objective. A decentralised multi-agent system method is developed to solve the service restoration problem considering controlled islanding of distributed generators. The uncertainty of outage duration is estimated using the maximum entropy principle-based on the cause of the fault. Exhaustive case studies are implemented on a small 38 bus and a large 119 bus test distribution system to demonstrate the effectiveness of the proposed multi-stage restoration strategy to restore the system under outage duration uncertainty.

Important classes of reactions for the proactive and reactive resource-constrained project scheduling problem

The proactive and reactive resource-constrained project scheduling problem (PR-RCPSP), that has been introduced recently (Davari and Demeulemeester, 2017), deals with activity duration uncertainty in a very unique way. The optimal solution to an instance of the PR-RCPSP is a proactive and reactive policy (PR-policy) that is a combination of a baseline schedule and a set of required transitions (reactions). In this research, we introduce two interesting classes of reactions, namely the class of selection-based reactions and the class of buffer-based reactions, the latter in fact being a subset of the class of selection-based reactions. We also discuss the theoretical relevance of these two classes of reactions. We run some computational results and report the contributions of the selection-based reactions and the buffer-based reactions in the optimal solution. The results suggest that although both selection-based reactions and buffer-based reactions contribute largely in the construction of the optimal PR-policy, the contribution of the buffer-based reactions is of much greater importance. These results also indicate that the contributions of non-selection-based reactions (reactions that are not selection-based) and selection-but-not-buffer-based reactions (selection-based reactions that are not buffer-based) are very limited.

Quantifying multi-dimensional attributes of human activities at various geographic scales based on smartphone tracking

BackgroundAdvancement in location-aware technologies, and information and communication technology in the past decades has furthered our knowledge of the interaction between human activities and the built environment. An increasing number of studies have collected data regarding individual activities to better understand how the environment shapes human behavior. Despite this growing interest, some challenges exist in collecting and processing individual’s activity data, e.g., capturing people’s precise environmental contexts and analyzing data at multiple spatial scales.MethodsIn this study, we propose and implement an innovative system that integrates smartphone-based step tracking with an app and the sequential tile scan techniques to collect and process activity data. We apply the OpenStreetMap tile system to aggregate positioning points at various scales. We also propose duration, step and probability surfaces to quantify the multi-dimensional attributes of activities.ResultsResults show that, by running the app in the background, smartphones can measure multi-dimensional attributes of human activities, including space, duration, step, and location uncertainty at various spatial scales. By coordinating Global Positioning System (GPS) sensor with accelerometer sensor, this app can save battery which otherwise would be drained by GPS sensor quickly. Based on a test dataset, we were able to detect the recreational center and sports center as the space where the user was most active, among other places visited.ConclusionThe methods provide techniques to address key issues in analyzing human activity data. The system can support future studies on behavioral and health consequences related to individual’s environmental exposure.

Operating room scheduling and surgeon assignment problem under surgery durations uncertainty.

Scientific management methods are urgently needed to balance the demand and supply of heath care services in Chinese hospitals. Operating theatre is the bottleneck and costliest department. Therefore, the surgery scheduling is crucial to hospital management. To increase the utilization and reduce the cost of operating theatre, and to improve surgeons' satisfaction in the meantime, a practical surgery scheduling which could assign the operating room (OR) and surgeon for the surgery and sequence surgeries in each OR was provided for hospital managers. Surgery durations were predicted by fitting the distributions. A two-step mixed integer programming model considering surgery duration uncertainty was proposed, and sample average approximation (SAA) method was applied to solve the model. Durations of various surgeries were log-normal distributed respectively. Numerical experiments showed the model and method could get good solutions with different sample sizes. Real-life constraints and duration uncertainty were considered in the study, and the model was also very applicable in practice. Average overtime of each OR was reducing and tending to be stable with the number of surgeons increasing, which is a discipline for OR management.

Drone flight scheduling under uncertainty on battery duration and air temperature

Abstract Commercial drones are expected to be widely used in the near future. They are generally powered by batteries to fly aerial areas. Flying time performance is known to change depending on air temperature. Hence, this paper proposes a robust optimization approach to find the optimal flight schedule (i.e., the number of drones and flight paths) in the flight network considering uncertain battery duration. A regression model is first developed to estimate battery duration as a function of air temperature. Three flight duration uncertainty sets (polyhedral, box, and ellipsoidal) are explored based on the regression model, and the robust optimization model is solved for each of the three sets. A decision tool is developed to analyze performance of the sets, and to help a decision maker select an appropriate uncertainty set that is most appropriate for a specific application of interest. The tool considers both minimizing the total operating cost and minimizing the probability of not completing the scheduled flights. Numerical results are presented to illustrate the proposed method.

Solving Robust Resource Constrained Scheduling Problem by Multi-objective Optimization Method based on Hybridization of EDA and GA

This paper proposes a robust scheduling method based on hybridization of EDA and GA, dealing with resource constrained scheduling problems with uncertainty of activity duration times. Two kinds of robust measures on time-based-robust and capacity-based-robust are introduced to evaluate the robustness of scheduling solutions, and the robust scheduling problem is formulated as bi-objective of minimizing makespan and maximizing time based robustness under a chance constraint of satisfying the threshold of capacity based robustness. By using scenario-based simulation, a stochastic multi-phased robust optimization method is proposed. In the first phase, with the average duration, the problem is solved as the deterministic multi-objective scheduling problem without considering duration uncertainty and chance constraints, and some candidate solutions are collected. In the second phase, the alternative solutions are checked by the chance constraints of capacity-based-robust measure and then, robustness measure is evaluated by using scenario-based simulation. Moreover, one problem-specific local search with considering both makespan and robustness is designed to increase the solution quality. Experiment results based on a benchmark (PSPLIB) and comparisons demonstrate that our approach is highly effective and tolerant of uncertainty.

Global Comprehensive Sensitivity Analysis of Arch Dam Construction Parameters Based on Orthogonal Experiment

The construction of arch dams exhibits high uncertainty. Sensitivity analysis of construction parameters is important for the design and optimization of dam construction duration. However, current research cannot fully consider the combined influences of multiple parameters on the total construction. To effectively analyze the duration of arch dam construction, this study proposes a global comprehensive sensitivity analysis method in view of the whole process of arch dam construction based on an orthogonal experiment. This method could comprehensively consider the influence of the construction parameters that may lead to the uncertainty of construction duration. In addition, this method is able to identify the key parameters that may have a significant effect on duration uncertainty and sums up the general rules of combined parameters’ interaction effect, which provides a scientific basis for reasonable optimization of the duration of dam construction.

The Proactive and Reactive Resource-Constrained Project Scheduling Problem: The Crucial Role of Buffer-Based Reactions

The proactive and reactive resource-constrained project scheduling problem (PR-RCPSP), that has been introduced recently (Davari and Demeulemeester, 2016a), deals with activity duration uncertainty in a very unique way. The optimal solution to an instance of the PR-RCPSP is a proactive and reactive policy (PR-policy) that is a combination of a baseline schedule and a set of required transitions (reactions). In this research, we introduce two interesting classes of reactions, namely the class of selection-based reactions and the class of buffer-based reactions. We also discuss the theoretical relevance of these two classes of reactions. We run some computational results and report the contributions of the selection-based reactions and the buffer-based reactions in the optimal solution. The results suggest that although both selection-based reactions and buffer-based reactions contribute largely in the construction of the optimal PR-policy, the contribution of the buffer-based reactions is of much greater importance.

A Sampling Based Approach for Proactive Project Scheduling with Time-Dependent Duration Uncertainty

Most of the existing proactive scheduling approaches assume the durations of activities can be described by independent random variables that have no relation with time. We deal with the more challenging problem where the duration uncertainty is related to the scheduled time period. We propose a sampling based approach by extending the Consensus method from stochastic optimization. Experimental results show the effectiveness of our approach in solution quality and stability.

Duration and Duration Uncertainty of Trade Agreements : The Case of Agoa

Duration and Duration Uncertainty of Trade Agreements : The Case of Agoa

Construction Cost and Duration Uncertainty Model: Application to High-Speed Rail Line Project

AbstractTransportation construction projects are often plagued by cost overruns and delays. Applying contingencies and estimating risks at the project level often do not capture the multiple uncertainties in the construction process of large transportation projects. Thus, there is a need for innovative approaches and tools to avoid large construction cost and duration overruns. To counteract such underestimations, a construction model and an uncertainty model are developed. In the construction model, the construction of the four main types of structures in rail lines (tunnels, viaducts, cuts, and embankments) is modeled bottom-up from the single activity to the entire rail line. In the uncertainty model, three sources of uncertainty (variability in the construction process, correlations between the costs of repeated activities, and disruptive events) are modeled jointly at the level of the single activity. In a Monte Carlo simulation environment, these uncertainties are propagated to the total constructio...

Robust Optimization for RCPSP Under Uncertainty

The aim of the present article is to optimize the robustness objective for the Resource-Constrained Project scheduling Problem (RCPSP) dealing with activity duration uncertainty. The studied robustness consists in minimizing the worst-case performance, referred to as the min-max robustness objective, among a set of initial scenarios. We propose an enhanced GRASP approach as a solution to the given scenario-based robust model. This approach is based on different priority rules in the construction phase and a forwardbackward heuristic in the improvement phase. We investigate two different benchmark data sets, the Patterson set and the PSPLIB J30 set. Experiments show that the proposed enhanced GRASP outperforms the basic procedure, and a based-evolutionary algorithm, in robustness optimization.

Minimizing the expected makespan of a project with stochastic activity durations under resource constraints

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. 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.

Improved Critical Chain Project Management Framework for Scheduling Construction Projects

AbstractConstruction projects are subject to a wide range of constraints, such as project complexity, resource scarcity, and duration uncertainty. The critical chain project management (CCPM) has emerged as a method for construction scheduling. This paper proposes an improved CCPM framework to enhance the implementation of CCPM in construction project management practices. The framework addresses two major challenges in CCPM-based construction scheduling, including buffer sizing and multiple resources leveling. Buffers play a key role in ensuring successful schedule management. However, buffers generated by the existing sizing methods are either unnecessarily large, which wastes resources, or insufficiently robust against various uncertainties. Resource leveling is another critical challenge in CCPM-based construction scheduling because it requires a fundamentally different approach from the resource leveling used in traditional scheduling methods. The proposed framework improves buffer sizing by integrat...

Train Scheduling Networks under Time Duration Uncertainty

In this paper, we consider a railway traffic scheduling problem. We aim to find a schedule for a train scheduling networks where time duration uncertainties are considered. This problem was intensively studied with mixed linear models where trains moving duration are deterministic. In this paper, we formulate the problem as a classical one with scenario-based stochastic programming taking expected values as objective functions. Then, a new criterion is proposed to quantify scheduling robustness in the face of uncertainty. Besides, additional constraints were introduced to make the model feasible when unexpected event occurs during scheduling execution.

New Aspects in Time-Cost Tradeoff Analysis

AbstractThis paper presents a linear programming model for solution of the time-cost tradeoff problem. Although several analytical models have been developed for time-cost optimization (TCO), many of them mainly focused on projects where the contract duration is fixed. The optimization objective is therefore restricted to identify the minimum total cost only. Another group has primarily focused on project duration minimization. The model presented here considers scheduling characteristics that were ignored in prior research. In the new formulation, variability of funding and uncertainty of project duration are considered together. A chance-constrained programming is used to incorporate the variability of funding, which is quantified by the coefficient of variation. Financial feasibility is expressed as a stochastic constraint, which is transformed into a deterministic equivalent at a prespecified confidence level. Also, project duration uncertainty is incorporated into the model by applying the program ev...

Robust Scheduling of Task Graphs under Execution Time Uncertainty

Effective multicore computing requires to make efficient usage of the computational resources on a chip. Offline mapping and scheduling can be applied to improve the performance, but classical approaches require considerable a priori knowledge of the target application. In a practical setting, precise information is often unavailable; one can then resort to approximate time and resource usage figures, but this usually requires to make conservative assumptions. The issue is further stressed if real-time guarantees must be provided. We tackle predictable and efficient nonpreemptive scheduling of multitask applications in the presence of duration uncertainty. Hard real-time guarantees are provided with limited idle time insertion, by exploiting a hybrid offline/online technique known as Precedence Constraint Posting (PCP). Our approach does not require probability distributions to be specified, relying instead on simple and cheaper-to-obtain information (bounds, average values). The method has been tested on synthetic applications/platforms and compared with an offline optimized Fixed Priority Scheduling (FPS) approach and a pure online FIFO scheduler; the results are very promising, as the PCP schedules exhibit good stability and improved average execution time (14 percent on average, up to 30 percent versus FPS and up to 40 percent versus the FIFO scheduler).

Time–cost tradeoff analysis considering funding variability and time uncertainty

This paper presents a linear programming model for solution of the time–cost tradeoff problem. Although several analytical models have been developed for time–cost optimization (TCO), some of them mainly focused on projects where the contract duration is fixed. The optimization objective is therefore restricted to identify the minimum total cost only. Another group have primarily focused on project duration minimization. The model presented here considers scheduling characteristics that were ignored simultaneously in prior research. In the new formulation, variability of funding and uncertainty of project duration are considered simultaneously. A chance-constrained programming is used to incorporate the variability of funding, which is quantified by the coefficient of variation. The financial feasibility expressed as a stochastic constraint, which transformed into a deterministic equivalent at a pre-specified confidence level. Also, the project duration uncertainty incorporated into the model by applying PERT in scheduling and then the uncertainty is quantified by the coefficient of variation at a pre-specified confidence level. A system of objective function, which is minimizing direct cost and the group of constraints are solved by means of Lindo software. Two examples are conducted to demonstrate the model performance and its contributions. Four scenarios were adopted in solving the example problems to reflect the effect of each of funding variability and time uncertainty on project cost and duration. The results revealed that with 95% confidence level: 10% variability in funding versus neglecting it, would increase direct cost with 20% approximately for a pre-specified project deadline. Also, 10% variability in time versus neglecting it, would increase duration in range from 16.5% to 30% approximately, for a pre-specified direct cost. Also, considering 10% variability in funding and time would increase direct cost with more than 25% for a pre-specified project deadline. In parallel, an increase in project duration, more than 30% will occur for a pre-specified direct cost.

Duration and Duration Uncertainty of Trade Agreements: The Case of AGOA

In this paper, we tried to highlight all the kinds of temporal uncertainties that AGOA creates on the eligible countries. With a dynamic model in presence of technologic transfers and irreversibility of investments, we found that long run uncertainty has a negative impact not only on investment decisions but also on wages and on others sides of economy. In addition, when we coupled short run and long run uncertainties, we found that these effects are more horrendous. After running our simulations, we have put forward the following hypothesis, a suppression of short run uncertainty is the optimal framework to enhance the efficiency of AGOA on the eligible countries.