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.     

Critical Path Method with Multiple Calendars

This paper presents the critical path method forward and backward passes with multiple calendars. Multiple calendars are required in many construction projects to effectively represent various project conditions such as work properties, resource availabilities, weather conditions, etc. For this reason, major project management software packages such as P3 and MS-Project provide functions to handle multiple calendars. However, the background theory of handling multiple calendars has not been disclosed, so users of those software packages simply assume without clear knowledge that the time data generated by them are correct. This paper provides how multiple calendars should be handled in scheduling. Applying the theory presented herein, it has been noticed that the P3 operations with two calendars may generate a wrong answer for a start-to-finish with zero lag and inconsistent results in all negative lags when nonworking days are involved. The theory covers all four relationships in the precedence diagramming method with lags of zero, positive, and negative values. This study should be of considerable benefit to the construction industry and academics because it details and advances the theory for scheduling with multiple calendars, which is real scheduling in practice.     

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.     

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.     

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.     

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.     

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.     

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.     

Productivity Scheduling Method: Linear Schedule Analysis with Singularity Functions

This paper describes a new integrated method of linear schedule analysis using singularity functions. These functions have previously been used for structural analysis and are newly applied to scheduling. Linear schedules combine information on time and amount of work for each activity. A general model is presented with which activities and their buffers can be mathematically described in detail. The algorithm of the new method forms the body of the paper, including the steps of setting up initial equations, calculating pairwise differences between them, differentiating these to obtain the location of any minima, and deriving the final equations. The algorithm consolidates the linear schedule under consideration of all constraints and, thus, automatically generates the minimum overall project duration. The model distinguishes time and amount buffers, which bears implications for the definition and derivation of the critical path. Future research work will address float and resource analysis using the new model.     

Construction Scheduling and Progress Control Using Geographical Information Systems

Traditional scheduling and progress control techniques such as bar charts and the critical path method (CPM) fail to provide information pertaining to the spatial aspects of a construction project. A system called PMS-GIS (Progress Monitoring System with Geographical Information Systems) was developed to represent construction progress not only in terms of a CPM schedule but also in terms of a graphical representation of the construction that is synchronized with the work schedule. In PMS-GIS, the architectural design is executed using a computer-aided drafting (CAD) program (AutoCAD), the work schedule is generated using a project management software (P3), the design and schedule information (including percent complete information) are plugged into a GIS package (ArcViewGIS), and for every update, the system produces a CPM-generated bar chart alongside a 3D rendering of the project marked for progress. The GIS-based system developed in this study helps to effectively communicate the schedule∕progress information to the parties involved in the project, because they will be able to see in detail the spatial aspects of the project alongside the schedule.     

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.     

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.     

Linear Scheduling Model: Float Characteristics

By definition, any activity not on the critical path must have float. The concept of float in the critical path method relates to how long an activity can be delayed before it becomes a critical activity. For linear construction activities, however, the concept of float is somewhat different from that of traditional scheduling techniques. Rather than start time and duration being the main attributes of float, production rate is a more fundamental attribute of a linear activity. As such, for float to be meaningful for a linear activity, it must be reflective of the activity's major characteristic. Rate float captures this characteristic and presents information to construction planners and managers in terms that are meaningful for linear projects. This paper describes rate float as it applies to the linear scheduling model developed by Harmelink and Rowings in 1998.     

Algorithm for Determining Controlling Path Considering Resource Continuity

Scheduling of construction projects that have multiple units, wherein activities repeat from one unit to another, always represent a major challenge to project managers. These projects require schedules that ensure the uninterrupted usage of resources from an activity in one unit to the similar activity in the next unit and maintaining logic constraints at the same time. The scheduling method presented in this paper considers both logic and resource continuity constraints. The method utilizes the critical path method network of a single unit. Start-to-start and finish-to-finish relationships are used. Constant activity production rate is assumed. The proposed approach determines the controlling path (logically and resource critical units) in a simplified way. To automate the proposed algorithm, a macroprogram has been written on commercial scheduling software. Details of the model development and implementation are described, and an example application is presented to validate the proposed approach. The advantages, limitations, and future extensions of the proposed approach are then discussed.     

Construction Project Scheduling with Time, Cost, and Material Restrictions Using Fuzzy Mathematical Models and Critical Path Method

This article evaluates the viability of using fuzzy mathematical models for determining construction schedules and for evaluating the contingencies created by schedule compression and delays due to unforeseen material shortages. Networks were analyzed using three methods: manual critical path method scheduling calculations, Primavera Project Management software (P5), and mathematical models using the Optimization Programming Language software. Fuzzy mathematical models that allow the multiobjective optimization of project schedules considering constraints such as time, cost, and unexpected materials shortages were used to verify commonly used methodologies for finding the minimum completion time for projects. The research also used a heuristic procedure for material allocation and sensitivity analysis to test five cases of material shortage, which increase the cost of construction and delay the completion time of projects. From the results obtained during the research investigation, it was determined that it is not just whether there is a shortage of a material but rather the way materials are allocated to different activities that affect project durations. It is important to give higher priority to activities that have minimum float values, instead of merely allocating materials to activities that are immediately ready to start.     

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.     

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.     

Work Continuity Constraints in Project Scheduling

Repetitive projects involve the repetition of activities along the stages of the project. Since the resources required to perform these activities move from one stage to the other, a main objective of scheduling these projects is to maintain the continuity of work of these resources so as to minimize the idle time of resources. This requirement, often referred to as work continuity constraints, involves a tradeoff between total project duration and the resource idle time. The contribution of this paper is threefold. First, we provide an extensive literature summary of the topic under study. Although most research papers deal with the scheduling of construction projects, we show that this can be extended to many other environments. Second, we propose an exact search procedure for scheduling repetitive projects with work continuity constraints. This algorithm iteratively shifts repeating activities further in time in order to decrease the resource idle time. We have embedded this recursive search procedure in a horizon-varying algorithm in order to detect the complete tradeoff profile between resource idle time and project duration. The procedure has been coded in Visual C++ and has been validated on a randomly generated problem set. Finally, we illustrate the concepts on three examples. First, the use of our new algorithm is illustrated on a small fictive problem example from literature. In a second example, we show that work continuity constraints involve a tradeoff between total project duration and the resource idle time. A last example describes the scheduling of a well-known real-life project that aims at the construction of a tunnel at the Westerschelde in The Netherlands.     

Application of Innovative Critical Chain Method for Project Planning and Control under Resource Constraints and Uncertainty

This research proposes an innovative critical chain method (ICCM) for project planning and control under resource constraints and uncertainty. An improved genetic algorithm is developed to identify the critical chain and to obtain the optimal start time of each activity under the most optimistic duration of each activity and resource constraints. Furthermore, a feeding buffer is added in an insert point in order to deal with uncertainties. The benefits of applying this ICCM are demonstrated in an example project.