Optimization of Project Time-Cost Trade-Off Problem with Discounted Cash Flows

Traditional time-cost trade-off (TCTO) analysis assumes constant value of activities’ cost along the project time span. However, the value of money decreases with time and, therefore, discounted cash flows should be considered when solving TCTO optimization problem. Optimization problems in project management have been traditionally solved by two distinctive approaches: heuristic methods and optimization techniques. Although heuristic methods can handle large-size projects, they do not guarantee optimal solutions. A nonlinear mathematical optimization model for project TCTO problem is developed, which minimizes project direct cost and takes into account discounted cash flows. Costs of activities are assumed to be incurred at their finish times. The model guarantees the optimal solution, in which precise discrete activity time-cost function is used. The model input includes precedence relationship between project activities, discrete utility data for project activities, and discount rate. Details of model formulation are illustrated by an example project. The results show that selected activities’ durations and costs and consequently optimal project duration differ from traditional analysis if discounted cash flow is considered. The new approach provides project practitioners with a way for considering net present value in time-cost decisions so that the best option can be identified.     

Hybrid Time-Cost Optimization of Nonserial Repetitive Construction Projects

Time-cost trade-off analysis represents a challenging task because the activity duration and cost have uncertainty associated with them, which should be considered when performing schedule optimization. This study proposes a hybrid technique that combines genetic algorithms (GAs) with dynamic programming to solve construction projects time-cost trade-off problems under uncertainty. The technique is formulated to apply to project schedules with repetitive nonserial subprojects that are common in the construction industry such as multiunit housing projects and retail network development projects. A generalized mathematical model is derived to account for factors affecting cost and duration relationships at both the activity and project levels. First, a genetic algorithm is utilized to find optimum and near optimum solutions from the complicated hyperplane formed by the coding system. Then, a dynamic programming procedure is utilized to search the vicinity of each of the near optima found by the GA, and converges on the global optima. The entire optimization process is conducted using a custom developed computer code. The validation and implementation of the proposed techniques is done over three axes. Mathematical correctness is validated through function optimization of test functions with known optima. Applicability to scheduling problems is validated through optimization of a 14 activity miniproject found in the literature for results comparison. Finally implementation to a case study is done over a gas station development program to produce optimum schedules and corresponding trade-off curves. Results show that genetic algorithms can be integrated with dynamic programming techniques to provide an effective means of solving for optimal project schedules in an enhanced realistic approach.     

Project Time-Cost Trade-Off Optimization by Maximal Flow Theory

Time and cost are related on projects. Project managers are frequently required to make time-cost trade-offs. With the complexity of large projects and the schedule impact of time-cost modifications, decisions on time-cost optimization are usually done on a hit or miss basis. This technical note presents an innovative technique that can be used to automate and optimize the time-cost trade-off process. The technique is based on “maximum flow–minimal cut” theory. The method is an improvement over current practice.     

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.     

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.     

Applying Pareto Ranking and Niche Formation to Genetic Algorithm-Based Multiobjective Time–Cost Optimization

Time–cost optimization (TCO) is one of the greatest challenges in construction project planning and control, since the optimization of either time or cost, would usually be at the expense of the other. Although the TCO problem has been extensively examined, many research studies only focused on minimizing the total cost for an early completion. This does not necessarily convey any reward to the contractor. However, with the increasing popularity of alternative project delivery systems, clients and contractors are more concerned about the combined benefits and opportunities of early completion as well as cost savings. In this paper, a genetic algorithms (GAs)-driven multiobjective model for TCO is proposed. The model integrates the adaptive weight to balance the priority of each objective according to the performance of the previous “generation.” In addition, the model incorporates Pareto ranking as a selection criterion and the niche formation techniques to improve popularity diversity. Based on the proposed framework, a prototype system has been developed in Microsoft Project for testing with a medium-sized project. The results indicate that greater robustness can be attained by the introduction of adaptive weight approach, Pareto ranking, and niche formation to the GA-based multiobjective TCO model.     

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.     

Optimizing Resource Leveling in Construction Projects

Construction schedules, generated by network scheduling techniques, often cause undesirable resource fluctuations that are impractical, inefficient, and costly to implement on construction sites. This paper presents the development of two innovative resource leveling metrics to directly measure and minimize the negative impact of resource fluctuations on construction productivity and cost. The first metric quantifies the total amount of resources that need to be temporarily released during low demand periods and rehired at a later stage during high demand periods. The second measures the total number of idle and nonproductive resource days that are caused by undesirable resource fluctuations. The two new metrics are incorporated in a robust and practical optimization model that is capable of generating optimal and practical schedules that maximize the efficiency of resource utilization. An application example is analyzed to illustrate the use of the model and demonstrate its capabilities. The results of this analysis show that the present model and metrics are capable of outperforming existing metrics and eliminating undesirable resource fluctuations and resource idle time.     

Optimizing Construction Time and Cost Using Ant Colony Optimization Approach

Time and cost are the most important factors to be considered in every construction project. In order to maximize the return, both the client and contractor would strive to optimize the project duration and cost concurrently. Over the years, many research studies have been conducted to model the time–cost relationships, and the modeling techniques range from the heuristic methods and mathematical approaches to genetic algorithms. Despite that, previous studies often assumed the time being constant leaving the analyses based purely on a single objective—cost. Acknowledging the significance of time–cost optimization, an evolutionary-based optimization algorithm known as ant colony optimization is applied to solve the multiobjective time–cost optimization problems. In this paper, the basic mechanism of the proposed model is unveiled. Having developed a program in the Visual Basic platform, tests are conducted to compare the performance of the proposed model against other analytical methods previously used for time–cost modeling. The results show that the ant colony system approach is able to generate better solutions without utilizing much computational resources which provides a useful means to support planners and managers in making better time–cost decisions efficiently.     

Profit Measures for Construction Projects

The basic issues related to profit measures of a construction project for the contractor are presented. Specifically, the problem of measuring gross operating profit and financing costs under fluctuating economic environments which has been heretofore inadequately treated in the literature of construction management is addressed. A framework for analyzing financing costs under different financial mechanisms, including the effects of overdraft and other borrowing arrangements, is presented. The general procedure is also applicable to the analysis of the effects of inflation and of work stoppages on profit. Finally, the cost of a project to the owner and the relationship between uncertainty and contract price from the views of both the owner and the contractor are considered.     

Optimization of Earthmoving Operations in Heavy Civil Engineering Projects

Large scale earthmoving operations require the use of heavy and costly construction equipment. Optimum utilization of equipment is a crucial task for the project management team. It can result in substantial savings in both time and cost of earthmoving operations. This paper presents optimization model for earthmoving operations in heavy civil engineering projects. The developed model is designed to assist general contractor in optimizing planning of earthmoving operations. The model utilizes genetic algorithm, linear programming, and geographic information systems to support its management functions. The model assists in planning earthmoving operations; taking into consideration: (1) availability of resources to contractors; (2) project budget and/or time constraints, if any; (3) scope of work; (4) construction site conditions; (5) soil type; (6) project indirect cost; and (7) equipment characteristics. The model also determines the quantities of earth to be moved from different borrow pits and those to be placed at different landfill sites to meet optimization objective set by the user and to meet project constraints. The model has been implemented in prototype software, using object-oriented programming. Two numerical example projects are presented to validate and demonstrate the use of the developed model in optimizing earthmoving operations.     

Estimating Performance Time for Construction Projects

The prediction of performance time for construction projects is a problem of interest to both researchers and practitioners. This research seeks to gain insight into the significant factors impacting construction duration by developing a regression model. Data were collected for 856 facility projects completed between 1988 and 2004. These data were analyzed using Bromilow’s time-cost (BTC) model (1969) as well as multiple linear regression. The multiple linear regression model was found to provide the most acceptable prediction. As in the BTC model and previous research reported in the literature, a significant correlation was found to exist between cost and duration. However, several other factors were also identified that resulted in significantly lower than average construction durations. These include projects completed within certain management groupings, managed by a certain construction agent, and designed by in-house personnel.     

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.     

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.     

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.     

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.     

Modeling Time-Constraints in Construction Operations through Simulation

Construction operations often face time constraints that influence the execution of activities, which are not addressed enough when modeling through general discrete-event simulation. This paper describes a simulation-based methodology to handle the time constraints including the cyclical break, preemption, and overtime use. In consideration of the variable number of breaks or variable break duration for different activities, an algorithm to determine the execution of the time-constrained activities is proposed, in which the concepts of time cycle and time window are introduced. The proposed algorithm is incorporated with an activity scanning simulation strategy to develop a construction simulation for modeling the time-constrained construction operations. Some examples are presented to illustrate and validate the algorithm, and highlight the effectiveness of the developed construction simulation. The study provides an alternative to improve construction simulation in modeling of the time-constrained construction operations and is expected to assist researchers or practitioners at analyzing or planning construction operations.     

Improving Cost Estimates of Construction Projects Using Phased Cost Factors

Central to cost-based competition is the capability to accurately predict the cost of delivering a project. Most literature on cost estimation focuses on specific estimation methods as generic techniques and little attention has been paid to the unique requirements at each project stage. This note attempts to identify the critical factors for effective estimation at various stages of typical construction projects. Drawing from organization control theory and cost estimating literature, this note develops a theoretical framework that identifies the critical factors for effective cost estimation during each project phase of a conventional construction project. The underlying logic is that as a cost estimating effort progresses, both task programmability and output measurability improve. As a result, control effort will shift from input-oriented control to a combination of output and behavior control.     

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.