Finance-Based Scheduling: Tool to Maximize Project Profit Using Improved Genetic Algorithms

Contractor’s ability to procure cash to carry out construction operations represents a crucial factor to run profitable business. Bank overdrafts have always been the major source to finance construction projects. However, it is not uncommon that bankers set a limit on the credit allocated to an established overdraft. Bankers’ interest rates and consequently contractors’ financing costs are basically determined based on the allocated credit limits. Furthermore, project indirect costs are directly proportional to the project duration which is affected by the allocated credit limit. Thus, the credit limit affects project financing costs and indirect costs which in turn affect project profit. However, finance-based scheduling produces financially executable schedules at specified credit limits while maintaining the demand of time minimization. Thus, finance-based scheduling provides a tool to control the credit requirements. This control enables contractors to negotiate lower interest rates which reduce financing costs. Thus, finance-based scheduling enables contractors to reduce project indirect costs and financing costs. This paper utilizes genetic algorithm’s technique to devise finance-based schedules that maximize project profit through minimizing financing costs and indirect costs.     

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.     

Time-Cost Optimization of Construction Projects with Generalized Activity Constraints

Time-cost analysis is an important element of project scheduling, especially for lengthy and costly construction projects, as it evaluates alternative schedules and establishes an optimum one considering any project completion deadline. Existing methods for time-cost analysis have not adequately considered typical activity and project characteristics, such as generalized precedence relationships between activities, external time constraints, activity planning constraints, and bonuses/penalties for early/delayed project completion that would provide a more realistic representation of actual construction projects. The present work aims to incorporate such characteristics in the analysis and has developed two solution methods, an exact and an approximate one. The exact method utilizes a linear/integer programming model to provide the optimal project time-cost curve and the minimum cost schedule considering all activity time-cost alternatives together. The approximate method performs a progressive project length reduction providing a near-optimal project time-cost curve but it is faster than the exact method as it examines only certain activities at each stage. In addition, it can be easily incorporated in project scheduling software. Evaluation results indicate that both methods can effectively simulate the structure of construction projects, and their application is expected to provide time and cost savings.     

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.     

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.     

Scheduling∕Cost Optimization and Neural Dynamics Model for Construction

A general mathematical formulation is presented for the scheduling of construction projects and is applied to the problem of highway construction scheduling. Repetitive and nonrepetitive tasks, work continuity constraints, multiple-crew strategies, and the effects of varying job conditions on the performance of a crew can be modeled. An optimization formulation is presented for the construction project scheduling problem, with the goal of minimizing the direct construction cost. The nonlinear optimization is then solved by the neural dynamics model developed recently by Adeli and Park. For any given construction duration, the model yields the optimum construction schedule for minimum construction cost automatically. By varying the construction duration, one can solve the cost-duration trade-off problem and obtain the global optimum schedule and the corresponding minimum construction cost. The new construction scheduling model provides the capabilities of both the critical path method (CPM) and linear scheduling method (LSM) approaches. In addition, it provides features desirable for repetitive projects, such as highway construction, and allows schedulers greater flexibility. It is particularly suitable for studying the effects of change order on the construction cost. This research provides the mathematical foundation for development of a new generation of more general, flexible, and accurate construction scheduling systems.     

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.     

Expanding Finance-Based Scheduling to Devise Overall-Optimized Project Schedules

Construction contractors often finance projects using bank credit lines that allow contractors to withdraw money up to certain credit limits. Finance-based scheduling provides schedules that ensure that the contractor’s indebtedness at any time during the construction stage does not exceed the credit limit. Generally, constricted credit limits tend to yield prolonged schedules. Provided that credit limits can be adequately relaxed, compressed schedules of compressed-duration activities can be attained. Devising a compressed schedule calls for the incorporation of time-cost trade-off (TCT) analysis to strike a balance between the decreased overhead costs and the increased direct costs of the activities. Since employing TCT analysis usually causes great fluctuations in the daily resource requirements by mixing compressed-duration activities of high resource demand with others of low resource demand, therefore, the need for resource management techniques becomes inevitable to ensure efficient utilization of resources. This note used genetic algorithms to expand finance-based scheduling to devise schedules for relaxed credit limits. A prototype system was developed and coded using VISUAL BASIC, then demonstrated using a five-activity example project. The prototype was validated by comparing the results with those obtained by using the integer programming. Expanding finance-based scheduling to handle the whole spectrum of credit limits helps devise overall-optimized schedules that consider cash, time, cost, and resources.     

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.     

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.     

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.     

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.     

Construction Project Network Evaluation with Correlated Schedule Risk Analysis Model

Schedules are the means of determining project duration accurately, controlling project progress, and allocating resources efficiently in managing construction projects. It is not sufficient in today’s conditions to evaluate the construction schedules that are affected widely by risks, uncertainties, unexpected situations, deviations, and surprises with well-known deterministic or probabilistic methods such as the critical path method, bar chart (Gantt chart), line of balance, or program evaluation and review technique. In this regard, this paper presents a new simulation-based model—the correlated schedule risk analysis model (CSRAM)—to evaluate construction activity networks under uncertainty when activity durations and risk factors are correlated. An example of a CSRAM application to a single-story house project is presented in the paper. The findings of this application show that CSRAM operates well and produces realistic results in capturing correlation indirectly between activity durations and risk factors regarding the extent of uncertainty inherent in the schedule.     

Application of Linear Scheduling

Many projects, such as the construction of roadways, pipelines, and high‐rise buildings, involve repetitive activities. A method for scheduling such work, the Linear Scheduling Method (LSM) is presented. In an LSM schedule, the repetitive activities are plotted as lines of constant or varying slopes on two axes, distance versus time. Discrete activities may be shown at their appropriate times and locations and then referenced to a network schedule for additional detail. The Linear Scheduling Method is illustrated by applying it to an actual roadway construction project. The simplicity of the system and advantages for certain types of projects are revealed. A sample schedule is used to derive information that is comparable to what may be obtained from an equivalent CPM network.     

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.     

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.     

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.     

Accuracy of Highway Contractor’s Schedules

Contractors are required by the Michigan Department of Transportation (MDOT) to submit a progress schedule identifying the controlling path of activities for a construction project. During the 2000 construction season, MDOT allowed contractors to submit a progress schedule with overlapping or concurrent controlling operations. Prior to this, only one activity at a time could be controlling on the progress schedule. This paper reports on the results of a research project where the focus was to examine the accuracy of the progress schedules, which only list controlling items. Eight construction projects were studied and a determination of progress schedule accuracy was made. This was done to determine if there was an increase in accuracy of the schedules when concurrent controlling operations were used. Included in the eight projects were four without concurrent controlling activities and four with concurrent controlling activities. A comparison based upon similar projects with and without concurrent activities was made. Additionally, 22 projects were analyzed, all without concurrent controlling activities, to determine the accuracy of progress schedules for two types of projects. The comparison revealed that, in three of the four cases, the accuracy of progress schedules increased with the allowance of concurrent controlling activities. The 22 projects revealed that the accuracy of progress schedules varied considerably. It was also determined that contractors overestimated the duration of activities included in progress schedules.     

Particle Swarm Optimization for Preemptive Scheduling under Break and Resource-Constraints

This paper introduces a particle swarm optimization (PSO)-based methodology to implement preemptive scheduling under break and resource-constraints (PSBRC) for construction projects. The PSBRC under study allows the preemptive activities to be interrupted in off-working time and not to resume immediately in the next working period because all the limited resources are to be reallocated during a break. The potential solution to the PSBRC, i.e., a set of priorities deciding the order to start the activities or restart the interrupted activities, is represented by the multidimensional particle position. Hence PSO is applied to search for the optimal schedule for the PSBRC, in which a parallel scheme is adopted to transform the particle-represented priorities to a schedule. Computational analyses are presented to verify the effectiveness of the proposed methodology. This paper provides an attempt to make use of preemption and break for the resource-constrained construction project with the objective of minimizing project duration.     

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.