Productivity Scheduling Method Compared to Linear and Repetitive Project Scheduling Methods

The analysis of project schedules is among the central tasks of construction managers. Parallel to the well-known critical path method, linear scheduling techniques have been researched. The two most fully developed existing methods, the linear scheduling model and the repetitive scheduling method, are reviewed. Based on a discussion of a published example, the new mathematical analysis method for linear and repetitive schedules is introduced. The productivity scheduling method is based on singularity functions that provide a flexible and powerful mathematical model for construction activities and their buffers that are characterized by their linear or repetitive nature. The steps of formulating initial equations, stacking and consolidating them, and deriving information about their criticality are described in detail. The mathematical approach of the new method allows an integrated treatment of activities regardless of the number of changes in productivity within them and does not depend on the graphical representation of the schedule.     

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.     

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.     

Challenges in Line-of-Balance Scheduling

The line-of-balance (LOB) method of scheduling is well suited to projects that are composed of activities of a linear and repetitive nature. The objective of this study is to set down the basic principles that can be used in the development of a computerized LOB scheduling system that overcomes the problems associated with existing systems and creates solutions to problems encountered in the implementation of repetitive-unit construction. The challenges associated with LOB scheduling include developing an algorithm that handles project acceleration efficiently and accurately, recognizing time and space dependencies, calculating LOB quantities, dealing with resource and milestone constraints, incorporating the occasional nonlinear and discrete activities, defining a radically new concept of criticalness, including the effect of the learning curve, developing an optimal strategy to reduce project duration by increasing the rate of production of selected activities, performing cost optimization, and improving the visual presentation of LOB diagrams.     

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.     

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.     

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.     

Precedence-Preserving GAs Operators for Scheduling Problems with Activities’ Start Times Encoding

Precedence-preserving crossover and mutation operators for scheduling problems with activities’ start times encoding are proposed and employed in this paper. The objective is to tackle the incapability of the genetic algorithms (GAs) operators to preserve the precedence relationships among activities and generate feasible solutions in scheduling problems. The proposed operators employ an embedded precedence-preserving algorithm that determines the activities’ forward free float and backward free float and utilize them in randomly selected backward and forward paths, respectively. The proposed operators were evaluated using finance-based scheduling problems for large-scale projects of 120 repetitive activities. Moreover, the proposed operators were validated by comparing the results with the optimum results of a resource-constrained scheduling problem reported in the literature. The results exhibited the robustness of the proposed operators to reduce the computational costs. In addition, the results demonstrated the high potential and effectiveness of the proposed operators to capture the optimal solutions of the problems considered.     

Object-Oriented Scheduling for Repetitive Projects with Soft Logics

The application of network techniques of project scheduling to repetitive projects has been criticized for the inability of network techniques to help maintain work continuity. Moreover, current network techniques require a large number of activities to represent a repetitive project and presume that there is only one logical sequence. This makes schedules time consuming to develop as well as maintain. Further, the logic chosen by the planner might be far from the shortest possible duration. This paper, utilizing the soft logic sequencing principles developed by Fan et al., develops a system which provides an easy input module in addition to scheduling and work-continuity-maintenance modules. The system eases the network generation and update processes, which in turn provides the shortest possible duration logics and the start and finish dates required to maintain work continuity.     

Decision Support System for Scheduling Steel Fabrication Projects

One of the most important and difficult problems faced by the steel fabrication industry is the planning and scheduling of shop activities. Competitive pressures force fabricators to disrupt schedules in progress to accommodate frequent requests from key customers for changes in design and/or delivery schedules. Capacity management is a complex problem and is key to proper management of manufacturing/fabrication activities. This paper presents a decision support system for planning and scheduling of steel fabrication projects. Although the immediate application of this approach is steel fabrication, its fundamental heuristic approach can be applied to any construction job shop scheduling exercise. Its main advantage over techniques such as CPM is that it is resource driven; its advantages over simulation techniques are its simplicity and overall schedule development time.     

Algorithm for Scheduling with Multiskilled Constrained Resources

Scheduling with constrained resources, particularly skilled labor, is a major challenge for almost all construction projects. In the literature, various techniques have been developed to reduce consequent project delay of constrained resources. Most of these techniques assume single-skilled resources and use heuristic rules to decide which activity will receive the resource first and which ones to delay. To improve existing solutions, this paper introduces some modifications to heuristic resource-scheduling solutions, considering multiskilled resources. The proposed approach stores and utilizes information about the resource(s) that can be substituted when there is a shortage in another one. Using this information, less utilized resources can be combined to substitute the shortages in constrained resources during the shortage period, taking into consideration the loss in work productivity. To automate the proposed algorithm, a macroprogram has been written on a commercial scheduling software. An example application is presented to show the improved results of the proposed approach over existing heuristics. The use of the proposed approach as a better resource management tool within the construction industry is then discussed.     

Object-Oriented Model for Repetitive Construction Scheduling

This paper presents the development of an object-oriented model for scheduling of repetitive construction projects such as high-rise buildings, housing projects, highways, pipeline networks, bridges, tunnels, railways, airport runways, and water and sewer mains. The paper provides an overview of the analysis, design, and implementation stages of the developed object-oriented model. These stages are designed to provide an effective model for scheduling repetitive construction projects and to satisfy practical scheduling requirements. The model incorporates newly developed procedures for resource-driven scheduling of repetitive activities, optimization of repetitive construction scheduling, and integration of repetitive and nonrepetitive scheduling techniques. The model is named LSCHEDULER and is implemented as a windows application that supports user-friendly interface including menus, dialogue boxes, and windows. LSCHEDULER can be applied to perform regular scheduling as well as optimized scheduling. In optimized scheduling, the model can assist in identifying an optimum crew utilization option for each repetitive activity in the project that provides a minimum duration or cost for the scheduled repetitive construction project.     

Resource Scheduling Using Neural Dynamics Model of Adeli and Park

This paper presents a mathematical model for resource scheduling considering project scheduling characteristics generally ignored in prior research, including precedence relationships, multiple crew-strategies, and time cost trade-off. Previous resource scheduling formulations have traditionally focused on project duration minimization. The proposed model considers the total project cost minimization. Furthermore, resource leveling and resource-constrained scheduling have traditionally been solved independently. In the new formulation, resource leveling and resource-constrained scheduling are performed simultaneously. The proposed model is solved using the patented neural dynamics model of Adeli and Park. A case study is presented to demonstrate the performance of the method under various resource availability profiles.     

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.     

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.     

Linear Scheduling Model with Varying Production Rates

Activity production rates drive the development and accuracy of linear schedules. The nature of linear projects dictates an assortment of variables that affect each activity’s production rate. The purpose of this research was to expand the capabilities of linear scheduling to account for variance in production rates when and where the variance occurs and to enhance the visual capabilities of linear scheduling. This new linear scheduling model, a linear scheduling model with varying production rates (LSMVPR), has two objectives. The first is to outline a framework to apply changes in production rates when and where they occur along the horizontal alignment of the project. The second objective is to illustrate the difficulty or ease of construction through the time-location chart. This research showed that the changes in production rates because of time and location can be modeled for use in predicting future construction projects. Using the concept of working windows, LSMVPR allows the scheduler to develop schedule durations on the basis of minimal project information. The model also allows the scheduler to analyze the impact of various routes or start dates for construction and the corresponding impact on the schedule. The graphical format allows the construction team to visualize the obstacles in the project when and where they occur by using a new feature called the activity performance index (API). This index is used to shade the linear scheduling chart by time and location with the variation in color indicating the variance in predicted production rate from the desired production rate.     

Improvement Algorithm for Limited Space Scheduling

Selecting construction methods, scheduling activities, and planning the use of site space are key to constructing a project efficiently. Site layout and activity scheduling have been tackled as independent problems. Their interdependence is often ignored at the planning stage and may be dealt with—if at all—when construction is underway. Problems that may have had easy solutions if dealt with earlier, may then be expensive to remedy. This paper addresses the combined problem termed “space scheduling” and presents an algorithmic time-space trade-off model for adjusting activity durations and start dates to decrease the need for space over congested time periods. The model characterizes resource space requirements over time and establishes a time-space relationship for each activity in the schedule, based on alternative resource levels. An example illustrates the presented algorithm that generates a feasible space schedule.     

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.     

Use of Genetic Algorithms in Resource Scheduling of Construction Projects

This paper presents an augmented Lagrangian genetic algorithm model for resource scheduling. The algorithm considers scheduling characteristics that were ignored in prior research. Previous resource scheduling formulations have primarily focused on project duration minimization. Furthermore, resource leveling and resource-constrained scheduling have traditionally been solved independently. The model presented here considers all precedence relationships, multiple crew strategies, total project cost minimization, and time-cost trade-off. In the new formulation, resource leveling and resource-constrained scheduling are performed simultaneously. The model presented uses the quadratic penalty function to transform the resource-scheduling problem to an unconstrained one. The algorithm is general and can be applied to a broad class of optimization problems. An illustrative example is presented to demonstrate the performance of the proposed method.     

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.