Stochastic Construction Time-Cost Trade-Off Analysis

Traditional time-cost trade-off analysis assumes that the time and cost of an option within an activity are deterministic. However, in reality the time and cost are uncertain. Therefore, in analyzing the time-cost trade-off problem, uncertainties should be considered when minimizing project duration or cost. Simulation techniques are useful for analyzing stochastic effects, but a general strategy∕algorithm is needed to guide the analysis to obtain optimal solutions. This paper presents a hybrid approach that combines simulation techniques and genetic algorithms to solve the time-cost trade-off problem under uncertainty. The results show that genetic algorithms can be integrated with simulation techniques to provide an efficient and practical means of obtaining optimal project schedules while assessing the associated risks in terms of time and cost of a construction project. This new approach provides construction engineers with a new way of analyzing construction time∕cost decisions in a more realistic manner. Historical time∕cost data and available options to complete a project can be modeled, so that construction engineers can identify the best strategies to take to complete the project at minimum time and cost. Also, what-if scenarios can be explored to decide the desired∕optimal time and∕or cost in planning and executing project activities.     

Simplified Spreadsheet Solutions.?II: Overall Schedule Optimization

Overall schedule optimization, considering time, cost, and resource constraints is a difficult task due to the inherent complexity of projects, the difficulties associated with modeling all aspects combined, and the inability of traditional optimization tools to solve this large-size problem. In this paper, a practical approach is presented for the modeling and optimization of overall construction schedules. To simplify modeling, a spreadsheet-based model is developed to be easily usable by practitioners. The spreadsheet model integrates critical-path network scheduling with time-cost trade-off analysis, resource allocation, resource leveling, and cash flow management. The model uses the total project cost as the objective function to be minimized. To facilitate this large-size optimization, a nontraditional optimization technique, genetic algorithms, is used to locate the globally optimal solution, considering all aspects simultaneously. Details of the proposed model are described, and a hypothetical case study was used to experiment with it. Integration of the model with a simple information system is described to automate the development of optimal construction schedules.     

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.     

Optimizing Resource Utilization for Repetitive Construction Projects

Optimizing resource utilization can lead to significant reduction in the duration and cost of repetitive construction projects such as highways, high-rise buildings, and housing projects. This can be achieved by identifying an optimum crew size and interruption strategy for each activity in the project. Available dynamic programming formulations can be applied to provide solutions for this optimization problem; however, their application is limited, as they require planners to specify an arbitrary and an unbounded set of interruption options prior to scheduling. Such a requirement is not practical and may render the optimization problem infeasible. To circumvent the limitations of available formulations, this paper presents an automated and practical optimization model. The model utilizes dynamic programming formulation and incorporates a scheduling algorithm and an interruption algorithm so as to automate the generation of interruptions during scheduling. This transforms the consideration of interruption options, in optimizing resource utilization, from an unbounded and impractical problem to a bounded and feasible one. A numerical example from the literature is analyzed to illustrate the use and capabilities of the model.     

Applying a Genetic Algorithm-Based Multiobjective Approach for Time-Cost Optimization

Reducing both project cost and time (duration) is critical in a competitive environment. However, a trade-off between project time and cost is required. This in turn requires contracting organizations to carefully evaluate various approaches to attaining an optimal time-cost equilibrium. Although several analytical models have been developed for time-cost optimization (TCO), they mainly focus on projects where the contract duration is fixed. The optimization objective in those cases is therefore restricted to identifying the minimum total cost only. With the increasing popularity of alternative project delivery systems, clients and contractors are targeting the increased benefits and opportunities of seeking an earlier project completion. The multiobjective model for TCO proposed in this paper is powered by techniques using genetic algorithms (GAs). The proposed model integrates the adaptive weights derived from previous generations, and induces a search pressure toward an ideal point. The concept of the GA-based multiobjective TCO model is illustrated through a simple manual simulation, and the results indicate that the model could assist decision-makers in concurrently arriving at an optimal project duration and total cost.     

Nondominated Archiving Multicolony Ant Algorithm in Time–Cost Trade-Off Optimization

Time–cost trade-off analysis is addressed as an important aspect of any construction project planning and control. Nonexistence of a unique solution makes the time–cost trade-off problems very difficult to tackle. As a combinatorial optimization problem one may apply heuristics or mathematical programming techniques to solve time–cost trade-off problems. In this paper, a new multicolony ant algorithm is developed and used to solve the time–cost multiobjective optimization problem. Pareto archiving together with innovative solution exchange strategy are introduced which are highly efficient in developing the Pareto front and set of nondominated solutions in a time–cost optimization problem. An 18-activity time–cost problem is used to evaluate the performance of the proposed algorithm. Results show that the proposed algorithm outperforms the well-known weighted method to develop the nondominated solutions in a combinatorial optimization problem. The paper is more relevant to researchers who are interested in developing new quantitative methods and/or algorithms for managing construction projects.     

Cost Optimization in Projects with Repetitive Nonserial Activities

A practical model for scheduling and cost optimization of repetitive projects is proposed in this paper. The model objective is to minimize total construction cost comprising direct cost, indirect cost, interruption cost, as well as incentives and liquidated damages. The novelty of this model stems from four main aspects: (1) it is based on full integration of the critical path and the line of balance methodologies, thus considering crew synchronization and work continuity among nonserial activities; (2) it performs time-cost trade-off analysis considering a specified deadline and alternative construction methods with associated time, cost, and crew options; (3) it is developed as a spreadsheet template that is transparent and easy to use; and (4) it utilizes a nontraditional optimization technique, genetic algorithms, to determine the optimum combination of construction methods, number of crews, and interruptions for each repetitive activity. To automate the model, macroprograms were developed to integrate it with commercial scheduling software. Details of the model are presented, and an example project is used to demonstrate its benefits.     

Optimal Planning and Scheduling for Repetitive Construction Projects

This paper presents a multiobjective optimization model for the planning and scheduling of repetitive construction projects. The model enables construction planners to generate and evaluate optimal construction plans that minimize project duration and maximize crew work continuity, simultaneously. The computations in the present model are organized in three major modules: scheduling, optimization, and ranking modules. First, the scheduling module uses a resource-driven scheduling algorithm to develop practical schedules for repetitive construction projects. Second, the optimization module utilizes multiobjective genetic algorithms to search for and identify feasible construction plans that establish optimal tradeoffs between project duration and crew work continuity. Third, the ranking module uses multiattribute utility theory to rank the generated plans in order to facilitate the selection and execution of the best overall plan for the project being considered. An application example is analyzed to illustrate the use of the model demonstrate its new capabilities in optimizing the planning and scheduling of repetitive construction projects.     

Optimized Scheduling of Linear Projects

This paper presents a model, designed to optimize scheduling of linear projects. The model employs a two-state-variable, N-stage, dynamic programming formulation, coupled with a set of heuristic rules. The model is resource-driven, and incorporates both repetitive and nonrepetitive activities in the optimization process to generate practical and near-optimal schedules. The model optimizes either project construction duration, total cost, or their combined impact for what is known as cost-plus-time bidding, also referred to as A+B bidding. The model has a number of interesting and practical features. It supports multiple crews to work simultaneously on any activity, while accounting for: (1) multiple successors and predecessors with specified lead and lag times; (2) the impact of transverse obstructions, such as rivers and creeks, on crew assignments and associated time and cost; (3) the effect of inclement weather and learning curve on crew productivity; and (4) variations in quantities of work in repetitive activities from one unit to another. The model is implemented in a prototype software that operates in Windows? environment. It is developed utilizing object-oriented programming, and provides for automated data entry. Several graphical and tabular output reports can be generated. An example project, drawn from the literature, is analyzed to demonstrate the features of the developed model.     

Optimum Planning of Highway Construction under A + B Bidding Method

In recent years, many departments of transportation in the United States have started to apply the A + B bidding method in highway projects in order to reduce construction time and minimize its associated traffic congestion and adverse impact on local economies. The application of this method places an increased pressure on contractors to minimize both the time and cost of highway construction. This paper presents a practical model for optimizing resource utilization in highway projects that utilize the A + B bidding method. The model is designed to minimize the total combined bid by identifying the optimum crew formation and the optimum level of crew work continuity for each activity in the project. The model is developed using a dynamic programming formulation and is incorporated in a Windows application that provides a user-friendly interface to facilitate the optimization analysis. An application example of a highway project is analyzed to illustrate the use of the model and to demonstrate its capabilities.     

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.     

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.     

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.     

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.     

Minimizing Cutting Wastes of Reinforcement Steel Bars Using Genetic Algorithms and Integer Programming Models

Materials that are in the form of one-dimensional stocks such as steel rebars, structural steel sections, and dimensional lumber generate a major fraction of the generated construction waste. Cutting one-dimensional stocks to suit the construction project requirements result in trim or cutting losses, which is the major cause of the one-dimensional construction waste. The optimization problem of minimizing the trim losses is known as the cutting stock problem (CSP). In this paper, three approaches for solving the one-dimensional cutting stock problem are presented. A genetic algorithm (GA) model, a linear programming (LP) model, and an integer programming (IP) model were developed to solve the one-dimensional CSP. Three real life case studies from a steel workshop have been studied. The generated cutting schedules using the GA, LP, and IP approaches are presented and compared to the actual workshop’s cutting schedules. The comparison shows a high potential of savings that could be achieved using such techniques. Additionally, a user friendly Visual Basic computer program that utilizes genetic algorithms for solving the one-dimensional CSP is presented.     

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.     

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.     

Stochastic Time-Cost-Resource Utilization Optimization Using Nondominated Sorting Genetic Algorithm and Discrete Fuzzy Sets

In a construction project, the cost and duration of activities could change due to different uncertain variables such as weather, resource availability, etc. Resource leveling and allocation strategies also influence total time and costs of projects. In this paper, two concepts of time-cost trade-off and resource leveling and allocation have been embedded in a stochastic multiobjective optimization model which minimizes the total project time, cost, and resource moments. In the proposed time-cost-resource utilization optimization (TCRO) model, time and cost variables are considered to be fuzzy, to increase the flexibility for decision makers when using the model outputs. Application of fuzzy set theory in this study helps managers/planners to take these uncertainties into account and provide an optimal balance of time, cost, and resource utilization during the project execution. The fuzzy variables are discretized to represent different options for each activity. Nondominated sorting genetic algorithm (NSGA-II) has been used to solve the optimization problem. Results of the TCRO model for two different case studies of construction projects are presented in the paper. Total time and costs of the two case studies in the Pareto front solutions of the TCRO model cover more than 85% of the ranges of total time and costs of solutions of the biobjective time-cost optimization (TCO) model. The results show that adding the resource leveling capability to the previously developed TCO models provides more practical solutions in terms of resource allocation and utilization, which makes this research relevant to both industry practitioners and researchers.     

Construction Planning Method Using Case-Based Reasoning (CONPLA-CBR)

During the construction process, there occur many unexpected events that hinder timely completion of a project. One plausible solution in formulating a robust plan against such uncertainties is to provide the proper construction duration by utilizing as-built schedules in which past events are stored for similar future projects. Many schedulers thus develop schedules based on similar past schedules, taking into consideration the dynamic construction environment. As a result, construction schedulers normally refer to similar past schedules for their current projects. Few studies on the reuse of past schedules using case-based reasoning (CBR) have been conducted, and those that are available are limited to specific areas of construction such as apartment-building construction and boiler manufacturing. This research has an emphasis on developing a CBR-based general planning tool with higher applicability, which consists of generic attributes with the capability to be customized to the given project. To address this issue, construction planning by CBR (CONPLA-CBR) is presented as a generic planning tool for various types of construction projects. CONPLA-CBR, with the dynamic case approach and construction schedule data mart, also developed in this research, helps schedulers to utilize past schedules. CONPLA-CBR was not only verified to be of practical utility by experts, but also, because it uses past cases to which the successor relationships pertain, it does not require users to input all relationships. Whereas the proposed CONPLA-CBR generates master schedules at the preconstruction stage, its concept can also be applied to the construction stages to generate more detailed, for example, weekly or monthly, schedules. Thereby, CONPLA-CBR would enhance construction performance through the increased application of CBR in construction.     

Time-Profit Trade-Off Analysis for Construction Projects

This paper presents a multiobjective optimization model that provides new and unique capabilities including generating and evaluating optimal/near-optimal construction resource utilization and scheduling plans that simultaneously minimize the time and maximize the profit of construction projects. The computations in the present model are organized in three major modules: (1) a scheduling module that develops practical schedules for construction projects; (2) a profit module that computes the project profit; and (3) a multiobjective module that searches for and identifies optimal/near optimal trade-offs between project time and profit. A large-scale construction project is analyzed to illustrate the use of the model and to demonstrate its capabilities in generating and visualizing optimal trade-offs between construction time and profit.