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.     

Survey of the Construction Industry Relative to the Use of CPM Scheduling for Construction Projects

While critical-path method (CPM) scheduling has been around since the 1950s, its application in the construction industry has still not received 100% acceptance or consistency in how it is used. Project controls, and CPM scheduling in particular, have gone unchanged in the standards arena with little focus for a common understanding and recognition of what is required for CPM schedule development, implementation, and use. In recent years, little research has been conducted relative to the use of CPM and its benefits. In order to determine how the industry views its applicability and usage, a survey was developed for the stakeholders in the construction industry. This paper summarizes extensive research that was performed of the construction industry relative to the use of CPM scheduling, its applicability and its acceptance in the execution of today’s constructed projects. The research obtained the stakeholders’ views on the use and effectiveness of CPM scheduling; the necessary qualifications of scheduling personnel; and opinions relative to whether standards and/or best practices are necessary. The paper discusses the different views of the stakeholders and recommendations as to how consistency can be obtained in the use of CPM scheduling in order to improve the construction industry.     

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.     

Comparison of Linear Scheduling Model (LSM) and Critical Path Method (CPM)

Due to an increasingly competitive environment, construction companies are becoming more sophisticated, narrowing their focus, and becoming specialists in certain types of construction. This specialization requires more focused scheduling tools that prove to be better for certain type of projects. The critical path method (CPM) is the most utilized scheduling tool in the construction industry. However, for certain types of projects, CPM's usefulness decreases, because it becomes complex and difficult to use and understand. Alternative scheduling tools designed to be used with specific types of projects can prove to be more practical than CPM solutions. This paper provides a comparison of the CPM and a specialized tool, the linear scheduling model, by identifying critical attributes needed by any scheduling tool both at the higher management level and at the project level. Two project examples are scheduled with each method, and differences are discussed. Conclusions support that specialization of scheduling tools could be beneficial for the project manager and the project.     

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.     

Network Creation and Development for Repetitive-Unit Projects

Network scheduling is typically performed in three phases—network creation, analysis, and development. Although the critical path method (CPM) constitutes a well-established logic in network analysis, human intuition and experience are required for the creation and development of the network. Because of this, a variety of alternative CPM networks can be created in scheduling the same project. The use of the most desirable network can lead to a considerable reduction in the duration of the projects. This can be achieved by accurately identifying activities and linking them in an appropriate manner. Many researchers insisted that network scheduling lacks efficiency in scheduling repetitive-unit projects. Because of this, many scheduling methods have been developed to model such types of projects. However, most are not network based and require a large amount of input data, although most leading scheduling software remains network based and field engineers desire networklike forms of the schedule. In an effort to overcome this limitation, this paper presents a procedure for creating and developing networks for repetitive-unit projects. This network-based model incorporates a two-dimensional arrangement of activities, resource-space coordinates, for ease in creating a network and optimizes the activity linkage, thus resulting in the most desirable results. The model is applied to a typical repetitive-unit project to illustrate the use and capabilities of the model. The model can serve as an aid for inexperienced schedulers in creating a network as well as its optimization. An experienced scheduler can also check the desirability of his or her own created network via the use of this model.     

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.     

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.     

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.     

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.     

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.     

Formalization of Construction Sequencing Rationale and Classification Mechanism to Support Rapid Generation of Sequencing Alternatives

Resequencing construction activities is a critical task for project planners for effective project control. Resequencing activities require planners to determine the impact or “role” an activity has on successor activities. They also need to determine the status of activities, i.e., which activities may or may not be delayed. Distinguishing the role and status of activities in turn requires planners to understand the rationale for activity sequences. The current critical path method (CPM) framework, however, represents sequencing rationale using precedence relationships and distinguishes activities only with respect to their time-criticality. Thus, planners find it difficult to keep track of individual sequencing logic, and manually inferring the role and status of activities becomes practically prohibitive in complex project schedules. The research presented in this paper addressed this limitation of the CPM framework by formalizing a constraint ontology and classification mechanism. The ontology allows planners to describe their rationale for activity sequences in a consistent and intuitive way, whereas the classification mechanism leverages the ontology to automatically infer the role and status of activities. The ontology and mechanisms were implemented in a prototype tool. With this tool, users can quickly verify which activities to delay to expedite critical milestone or bottleneck activities, thus making it possible to quickly evaluate and generate sequencing alternatives in CPM-based schedules.     

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 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.     

Delay Analysis under Multiple Baseline Updates

Windows delay analysis has been recognized as one of the most credible techniques for analyzing construction delays. To overcome some of the drawbacks of windows delay analysis, this paper introduces improvements to a computerized schedule analysis model so that it will produce accurate and repeatable results. The model considers multiple baseline updates due to changes in the durations of the activities and the logical relationships among them, as well as the impact of resource overallocation. The model uses a daily window size in order to consider all fluctuations in the critical path(s) and uses a legible representation of progress information to accurately apportion delays and accelerations among project parties. A simple case study has been implemented to demonstrate the accuracy and usefulness of the proposed delay analysis model. This research is useful for both researchers and practitioners and allows detailed and repeatable analysis of the progress of a construction project in order to facilitate corrective actions and claim analysis.     

Non-Unit-Based Planning and Scheduling of Repetitive Construction Projects

Repetitive scheduling methods are more effective than traditional critical path methods in the planning and scheduling of repetitive construction projects. Nevertheless, almost all the repetitive scheduling methods developed so far have been based on the premise that a repetitive project is comprised of many identical production units. In this research a non-unit-based algorithm for the planning and scheduling of repetitive projects is developed. Instead of repetitive production units, repetitive or similar activity groups are identified and employed for scheduling. The algorithm takes into consideration: (1) the logical relationship of activity groups in a repetitive project; (2) the usage of various resource crews in an activity group; (3) the maintaining of resource continuity; and (4) the time and cost for the routing of resource crews. A sample case study and a case study of a sewer system project are conducted to validate the algorithm, as well as to demonstrate its application. Results and findings are reported.     

Critical path method: an important tool for coordinating clinical care

BACKGROUND: In May 1991 Mount Clemens General Hospital (MCGH) began investigating the critical path method (CPM) as a tool for extending total quality management in clinical areas. In its search for guidelines on how to develop a critical path program, it found that other hospitals used a variety of approaches. These included employing case managers or outside consultants to develop programs or implementing prepurchased paths. Because these approaches often are difficult to customize for a specific institution and because MCGH wanted to use an internal team, none of these options seemed appropriate. With no definitive guidelines to follow, MCGH developed and implemented its own CPM. METHODS: The developmental process was composed of activities in nine primary categories: literature search, steering group, targeting strategy, paperwork design, gaining consensus, pilot program, preliminary findings, refine program, and full implementation. RESULTS: A pilot was performed to assess if the CPM would be beneficial. Six months into the pilot a preliminary review of coronary artery bypass graft paths was conducted. There were 44 patients in the study group (35 men, 9 women). Twenty-four patients were cared for before the critical path form was available. Preliminary findings indicated a lower rate of complications in patients cared for with the critical path form. The data revealed a 5% complication rate with the critical path compared to a 16.6% rate for those whose care was not guided by the form. In addition, patients with the path on their clipboards had an overall shorter length of stay than patients without the path. It is important to remember that these early data are based on the six-month pilot; they are not considered a conclusive research finding. NEXT STEPS: The next step in the CPM process is to examine other diagnoses that might benefit from a critical path approach. A steering committee composed of representatives from hospital administration, nursing, medical staff, quality assurance and risk management, and total quality management will act as the approval body for investigating and sanctioning other paths for development. CONCLUSION: The primary lesson learned at MCGH is that the CPM is most effective in an environment of communication and commitment. This approach allows clinic and nonclinic staff to talk about how their work influences each other's. CPM provides all caregivers with a common language and encourages everyone to look at the whole patient and the entire care process. The key message of success is: Get a group of people together who are motivated and empowered to move this exciting tool of the future through the necessary steps.     

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.     

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.     

Multiobjective Linear Programming Model for Scheduling Linear Repetitive Projects

Linear repetitive construction projects require large amounts of resources which are used in a sequential manner and therefore effective resource management is very important both in terms of project cost and duration. Existing methodologies such as the critical path method and the repetitive scheduling method optimize the schedule with respect to a single factor, to achieve minimum duration or minimize resource work breaks, respectively. However real life scheduling decisions are more complicated and project managers must make decisions that address the various cost elements in a holistic way. To respond to this need, new methodologies that can be applied through the use of decision support systems should be developed. This paper introduces a multiobjective linear programming model for scheduling linear repetitive projects, which takes into consideration cost elements regarding the project’s duration, the idle time of resources, and the delivery time of the project’s units. The proposed model can be used to generate alternative schedules based on the relative magnitude and importance of the different cost elements. In this sense, it provides managers with the capability to consider alternative schedules besides those defined by minimum duration or maximizing work continuity of resources. The application of the model to a well known example in the literature demonstrates its use in providing explicatory analysis of the results.