Critical Path Segments Scheduling Technique

While the critical path method (CPM) has been useful for scheduling construction projects, years of practice and research have highlighted serious drawbacks that hinder its use as a decision support tool. This paper argues that many of CPM drawbacks stem from the rough level of detail at which the analysis is conducted, where activities’ durations are considered as continuous blocks of time. The paper thus proposes a new critical path segments (CPS) mechanism with a finer level of granularity by decomposing the duration of each activity into separate time segments. Three cases are used to prove the benefits of using separate time segments in avoiding complex network relationships, accurately identifying all critical path fluctuation, better allocation of limited resources, avoiding multiple-calendar problems, and accurate analysis of project delays. The paper discusses the proposed CPS mechanism and comments on several issues related to its calculation complexity, its impact on existing procedures, and future extensions. This research is more beneficial to researchers and has the potential to revolutionize scheduling computations to resolve CPM drawbacks.     

Evaluation of the Resource-Constrained Critical Path Method Algorithms

This study evaluates the resource-constrained critical path method (RCPM), which the writers have recently proposed. RCPM establishes a critical path method (CPM)-like, resource-constrained schedule by resource-dependent activity relationships (or resource links) that the five-step RCPM technique identifies. With its CPM-like feature, RCPM provides the critical path and float data that are not available in traditional resource-constrained scheduling techniques. In addition, RCPM provides more flexibility to the schedule through identified alternative schedules, which allow certain activities to be executed beyond their late finish times without delaying the project completion. This paper evaluates the RCPM’s performance by comparing it with five related previous studies. A brief review of each study is also included in this paper. This comparison shows that RCPM performs well in identifying resource links and alternative schedules, compared to other methods. This study is of interest to academics because it highlights the advantages and disadvantages of different algorithms that have attempted to overcome present problems in traditional resource-constrained scheduling techniques.     

Linear versus Network Scheduling: A Critical Path Comparison

Linear scheduling methods provide an alternative way of scheduling repetitive projects, to the commonly used network methods. Critical path identification is a major attribute for both methods; therefore, it is very important for practitioners to understand the function of the two methods in this area. The present paper compares the critical path of the recently developed Kallantzis-Lambropoulos repetitive project model against the network scheduling critical path method (CPM), aiming at delving into and pointing out the differences and similarities between them. Initially, the rules for transforming the linear project into an equivalent CPM network are proposed. Then, the rules are applied on a sample linear project. Due to the additional constraint for maintaining resource continuity that the linear method takes into account, the critical paths vary. The constraint is subsequently removed from selected activities and comparison is repeated; the critical paths then coincide. In order to validate the findings and ensure impartiality of results, a random linear project generator is developed. A group of twenty-five random linear projects and their equivalent networks is produced. Their critical paths are analyzed, compared and classified. Conclusions support that the proposed comparison could be beneficial to users of linear scheduling methods, while the random project generator can serve other related research.     

Phantom Float

This paper presents a resource-constrained critical path method (RCPM) technique that capitalizes on and improves the existing critical path method (CPM) and resource-constrained scheduling (RCS) techniques. A traditional CPM schedule is not realistic, because it assumes unlimited resources, some of which are highly limited in practice. Although traditional RCS techniques can consider resource limitations, they do not provide the correct floats and critical path, as the CPM does. The difference between the theoretical remaining total float and the real remaining total float is referred to as “phantom float” in this study. Work sequence in a resource-constrained schedule could also be considerably changed with a schedule update, resulting in high costs to reorganize it. This is because in addition to technological relationships, a resource-constrained schedule contains resource dependencies between activities that are neglected in traditional RCS techniques. This study proposes a step-by-step RCPM procedure to consider those resource-constrained relationships. Hence, the method can identify real floats and correct critical paths considering both technological and resource relationships, making late start and late finish times more meaningful. In addition, because of identified resource relationships, the RCPM also provides a certain level of stability with a schedule update.     

Resource-Activity Critical-Path Method for Construction Planning

In this paper, a practical method is developed in an attempt to address the fundamental matters and limitations of existing methods for critical-path method (CPM) based resource scheduling, which are identified by reviewing the prior research in resource-constrained CPM scheduling and repetitive scheduling. The proposed method is called the resource-activity critical-path method (RACPM), in which (1) the dimension of resource in addition to activity and time is highlighted in project scheduling to seamlessly synchronize activity planning and resource planning; (2) the start/finish times and the floats are defined as resource-activity attributes based on the resource-technology combined precedence relationships; and (3) the “resource critical” issue that has long baffled the construction industry is clarified. The RACPM is applied to an example problem taken from the literature for illustrating the algorithm and comparing it with the existing method. A sample application of the proposed RACPM for planning a footbridge construction project is also given to demonstrate that practitioners can readily interpret and utilize a RACPM schedule by relating the RACPM to the classic CPM. The RACPM provides schedulers with a convenient vehicle for seamlessly integrating the technology/process perspective with the resource use perspective in construction planning. The effect on the project duration and activity floats of varied resource availability can be studied through running RACPM on different scenarios of resources. This potentially leads to an integrated scheduling and cost estimating process that will produce realistic schedules, estimates, and control budgets for construction.     

Models for Accurate Computation of Earliest and Latest Start Times and Optimal Compression in Project Networks

Operations research techniques, especially linear and integer programming, have been suggested for use in project management. Most frequently these techniques are applied to finding critical path(s) in project networks and for compressing activities for an early project completion. The simplest of these models are usually found in introductory operations research/management science textbooks and they often suffer from a common deficiency: when they employ earliest start times (ES) as variables in the model, ES of activities that are not on the critical path may be computed incorrectly. This may lead to inefficient resource reallocation and leveling. Furthermore, activities outside the critical path may be compressed unnecessarily, as will be demonstrated in this paper. We present a zero–one mixed integer programming model to correctly compute earliest and latest start times of all activities and determine the optimal compression schedule. Several extensions to the model are offered to provide different perspectives of the project and enable a project manager to answer “what if” type questions. A small example is used to demonstrate the effectiveness of the models.     

Transform Schemes Applied on Non-Finish-to-Start Logical Relationships in Project Network Diagrams

Critical path analysis on a project network having non-finish-to-start (FS) logical relationships with lags is generally referred to as precedence diagram method (PDM). A PDM-based scheduling analysis is facilitated by mainstream project scheduling software (such as P3). However, PDM compounds total float determination and interpretation, potentially causing anomalous effects on critical path identification. In the present research, we generalize those particular circumstances that entail applying non-FS logical relationships on construction projects. We then propose generic transform schemes such that non-FS relationships in a PDM network can be detected and transformed—automatically—into equivalent FS. Moreover, we provide analytical proofs for the transform schemes being proposed to justify the logical equivalency between the original PDM network and the transformed activity-on-node (AON) network only having FS logical relationships. A PDM network example demonstrates that confusions would arise in interpreting P3’s critical path analysis results, but not in the case of the transformed AON counterpart. In conclusion, the transform schemes being proposed lead to better understanding of the scheduling results when critical path analysis is performed on a PDM network. This also paves the way for conducting further sophisticated scheduling analysis (such as resource loading or Monte Carlo simulation) on a PDM network.     

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.     

Network Scheduling Variations for Repetitive Work

Observant CPM schedulers in the early years of CPM application, the 1960s, noted that there were often familiar steps inherent in scheduling similar projects. This similarity occurred in the development of housing neighborhoods, such as New Town of Columbia, Maryland; schools, as in the Philadelphia School District Program involving 200 schools; and in the review process for projects during the preconstruction phase in large cities, namely Philadelphia and New York. In these situations, the development of a prototypical network provided a cost‐effective method of applying network scheduling to major programs. These applications are described in the form of case studies, and a recent application to the King Khalid Military City Housing Program is noted. An alternate manual approach to repetitive scheduling in highrise construction, the vertical production method developed in the 1970s, is also described.     

Critical Space Analysis

The construction space scheduling problem has received relatively little attention from researchers and practitioners. We now have sophisticated methods of planning and analyzing the sequence of tasks within the work breakdown structure through time, but the problem of planning where on site those tasks are to be executed is not well-supported especially as those spaces are dynamic as the project progresses. We know that congestion on site reduces output and generates hazards, yet construction planners presently have to rely upon experience and intuition. The research reported here presents a decision support tool for construction project planners to help them address the space scheduling problem. After a review of recent developments in construction space scheduling, the concept of critical space analysis is presented. This forms the basis of decision support tools presented for marking up available space, allocating tasks to spaces, and analyzing and optimizing space loading in relation to the critical path—what we call space-time broking. Requirements capture and evaluation reports from construction planners suggest that the tools presented here have immediate practical relevance. The paper will, therefore, be of interest to both practitioners and researchers.     

Float Types in Linear Schedule Analysis with Singularity Functions

This paper describes how float can be calculated exactly for linear schedules by using singularity functions. These functions originate in structural engineering and are newly applied to scheduling. They capture the behavior of an activity or buffer and the range over which it applies and are extensible to an infinite number of change terms. This paper builds upon the critical path analysis for linear schedules, which takes differences between singularity functions and differentiates them. It makes several important case distinctions that extend the earlier concept of rate float. Time and location buffers act along different axis directions. Together with different productivities between and within activities, this can create a complex pattern of critical and noncritical segments. Depending on starts and finishes, areas of float precede or follow these noncritical segments. The schedule of a small project is reanalyzed with case distinctions to demonstrate in detail what float types are generated.     

Risk Planning and Management for the Panama Canal Expansion Program

In April 2006, the Panama Canal Authority formally proposed a major expansion of the canal to increase its capacity and make it more productive, safe, and efficient. This proposal included cost and schedule estimates for completing the expansion and was supported overwhelmingly by the citizens of Panama in an October 2006 public referendum. Given the conceptual level of design at the time of the proposal and the inherent uncertainty in a project of this magnitude at the early stages of engineering, a comprehensive risk analysis was performed to develop a contingency model for the total expansion program cost and schedule. This contingency model is based on a Monte Carlo simulation of the cost and schedule estimates, taking into account the most significant risks identified for the project. The resulting model provides contingency assessments for duration and total cost and sensitivity analysis of the risks; it also allows for multiple scenario planning and ultimately supports overall risk management. This paper presents a project case study that focuses on the contingency model development and the resulting risk management and contingency resolution processes.     

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.     

Exact Algorithm for Solving Project Scheduling Problems under Multiple Resource Constraints

This paper presents a new algorithm, called the enumerative branch-and-cut procedure (EBAC), for minimizing the total project duration of a construction project under multiple resource constraints based on an enumeration tree. The EBAC generates new branches to the tree corresponding to “better” feasible alternatives. It starts with all of the feasible schedule alternatives as the trial schedule alternatives at any node. The trial schedule alternatives are then evaluated to determine whether they are “worse” than any existing partial schedules in the tree by using the presented cut rules, and a worse alternative will be eliminated from the enumeration tree. In other words, the tree will contain only better feasible schedules. The presented algorithm has been coded in the VB6.0 language on a personal computer. It has been tested with the 110 scheduling problems, which have been widely used for validating a variety of schedule algorithms over the last 20?years. The EBAC can obtain the shortest project durations for all of the 110 problems.     

The Federal Government and the Critical Path

The critical path method has been increasingly used as an administrative and legal tool rather than as a planning instrument. The writer claims that this evolution has made its planning function of little use to the contractor, using the contract clause of the Federal Government regarding the method of determining allowable contract delay as an illustration. It is asserted that this clause greatly increases the contractors' responsibilities for planning, at the expense of efficient construction management.     

Criticism of CPM for Project Planning Analysis

Published criticism in recent years concerning the inadequacy of Critical Path Method (CPM) as a project planning tool is identified and grouped under six major headings with reference to the publications in which the criticism were contained. These are answered from the writer's field experience and from experiences published by other authors. The object of the analysis is to see whether or not CPM as a project planning tool can meet the required functions of planning in construction, including consideration of legal and contractual framework and the complex and interdisciplinary nature of the project environment. The analysis reveals that, despite numerous criticism, project and construction planning should be done using CPM scheduling. Main factors affecting successful planning are realistic estimation of the productivity of crews in the context of expected job‐management efficiency conditions, and inclusion of sufficient time buffers between dissimilar trades. CPM is found to be equally useful as a planning tool for linear or repetitive projects. The limitations of this technique are identified in terms of the defined planning functions in the engineering phase of capital projects. A broad model for management of the engineering phase in revenue‐generating projects is suggested.     

Integrated Framework for Quantifying and Predicting Weather-Related Highway Construction Delays

Constant exposure to the environment makes highway construction highly dependent on weather. However, highway construction contracts are often unclear about the potential influence of weather-related delays on highway construction project schedules. There is a need to discourage litigation arising from weather-related delays by including in contracts a reasonable number of nonwork days as a consequence of adverse weather and providing an equitable criteria for the course of action when the predictions in the contracts turn out to be inaccurate. To address this need, an integrated framework consisting of the following two key components is proposed: (1) identification of attributes of weather that cause construction delays and (2) generation of synthetic weather sequences using a stochastic weather generator to quantify and provide probabilistic forecasts of weather threshold values. The utility of this framework is demonstrated through its application to construction work on a project in Texas. The use of probabilistic forecast of construction delay attributes provided by a semiparametric weather generator in this research is an example of interdisciplinary study to help address this problem. The result of the research is better decision support for agencies who wish to author contracts that more equitably allow for the influence of weather during construction.     

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.     

Critical Path Scheduling under Resource Calendar Constraints

Resource calendars specify nonworking days of driving resources involved in construction projects. As part of the resource availability constraints in critical path method (CPM) scheduling, resource calendars may postpone activity start time, extend activity duration, and hence prolong the total project duration. Ultimately, resource calendars bring about changes to the critical path identification. Research has yet to address how to incorporate the effects of multiple resource calendars on the total float determination. In this research, the popular P3 software is used as a tool for investigating the current practice of CPM scheduling under resource limit and calendar constraints. We assess P3’s advanced resource scheduling functions (including resource leveling and resource calendars) and identify P3’s potential errors in total float determination. Further, we propose a new method based on the forward pass analysis alone for accurately evaluating activity total float subject to resource calendar constraints. The application of the new method is illustrated with an activity-on-node case and a precedence-diagram-method case, with the results compared against those produced from P3. Our research has elucidated on some critical issues of resource-constrained scheduling in the application domain of construction project management. The findings will provide useful input for the vendors and users of the CPM software—which is not limited to P3—to improve the scheduling methodology as well as the accuracy of the resulting project schedules.