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.     

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.     

Using Elitist Particle Swarm Optimization to Facilitate Bicriterion Time-Cost Trade-Off Analysis

The present study develops a new optimization algorithm to find the complete time-cost profile (Pareto front) over a set of feasible project durations, i.e., it solves the time-cost trade-off problem. To improve existing methods, the proposed algorithm aims to achieve three goals: (1) to obtain the entire Pareto front in a single run; (2) to be insensitive to the scales of time and cost; and (3) to treat all existing types of activity time-cost functions, such as linear, nonlinear, discrete, discontinuous, and a hybrid of the above. The proposed algorithm modifies a population-based search procedure, particle swarm optimization, by adopting an elite archiving scheme to store nondominated solutions and by aptly using members of the archive to direct further search. Through a fast food outlet example, the proposed algorithm is shown effective and efficient in conducting advanced bicriterion time-cost analysis. Future applications of the proposed algorithm are suggested in the conclusion.     

Optimizing Cash Flows for Linear Schedules Modeled with Singularity Functions by Simulated Annealing

The ability of construction contractors to plan and manage cash flow is critical for their economic success. The cumulative interaction of outflows (labor, materials, and equipment costs) and inflows (progress payments less retainage) creates a profile with a complex zigzag shape. This could only be modeled by simplification, e.g., as values tabulated at discrete times; averaged S-curves without peaks; or envelopes of all possible constellations. Neither is suited for a fully integrated model that dynamically links schedules with their cash flows for optimization. Therefore, singularity functions, whose components define ranges of behavior between cutoffs, are used to flexibly yet accurately model cash flow profiles and their various payment terms. The new approach augments construction project management toward an integrated planning model and is validated with an example from the literature. Optimization with a simulated annealing algorithm shifts activity positions in a randomized but directed search for maximizing profits.     

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.     

Flexible Model for Time/Cost Tradeoff Problem

This paper presents a flexible mixed integer-programming model for the solution of the time/cost tradeoff problem encountered in project management. Whereas it is commonly assumed that the time/cost function is linear, the model presented in this paper makes minimal assumptions and accommodates any type of cost function that is linear, piecewise linear or discrete. The model can be used for answering various “what if” questions that may be very helpful to a project manager in making rational decisions. The basic model minimizes the total cost which is the sum of direct and indirect costs, subject to a project deadline constraint. A simple modification in the model changes the focus from minimizing total cost to minimizing project completion time subject to a resource constraint. The models of this paper can be set up and run very easily on commercially available optimization packages with an integer-programming module. These models provide a viable alternative to more specialized algorithms developed for the time/cost tradeoff problem simply because a typical project manager may not have the necessary skills or resources to implement specialized algorithms.     

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 Buyout

Buyout is the transitional time between the preconstruction and the construction phases of a project. It is during buyout that purchase orders and subcontracts are issued. Most of the literature in construction addresses either estimating or project management but ignores the buyout time frame. This paper addresses how the buyout process attempts to reduce the ambiguities that occur during the transition from the preconstruction to the construction phase.     

Electimize: New Evolutionary Algorithm for Optimization with Application in Construction Engineering

In nonlinear construction optimization problems, the capability of current optimization algorithms to find an optimal solution is usually limited by their inability to evaluate the effects of changing the value of each decision variable on reaching the optimal solution. This paper presents fundamental research aimed at developing a novel evolutionary optimization algorithm, named Electimize, that mimics the behavior of electrons flowing, through electric circuit branches with the least electric resistance. In the proposed algorithm, solutions are represented by electric wires and are evaluated on two levels: a global level, using the objective function, and a local level, evaluating the potential of each generated value for every decision variable. The paper presents (1) the research philosophy and scope, (2) the research methodology, and (3) the development of the algorithm. The proposed algorithm has been validated and applied successfully to an NP-hard cash flow optimization problem. The algorithm was able to find a better optimal solution and identified ten alternative optimal solutions for the same problem. This should prove useful in enhancing the optimization of complex large-scale problems.     

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.     

Optimization Model for Aggregate Blending

An optimization model of aggregate blending is presented that considers gradation, cost, and design requirements and is applicable to the blending of any number of aggregates. The model is formulated as a quadratic programming problem that minimizes the mean deviation from midpoint specification limits, subject to constraints on the preceding requirements. The model is applied to a numerical aggregate blending problem. Sensitivity analysis is performed to show how the model can also be used to minimize cost or to provide a trade‐off between mean deviation and cost. Extensions of the model to accommodate special practical cases are examined.     

Applying an Ant Colony Optimization Algorithm-Based Multiobjective Approach for Time–Cost Trade-Off

The time–cost trade-off is one of the most crucial aspects of construction project planning, which in fact is a combinatorial optimization problem. This technical note employed an evolutionary algorithm—ant colony optimization (ACO) algorithm to deal with the time–cost trade-off problems. Combining with the modified adaptive weight approach, the ACO algorithm can find out the optimal solutions, and define the Pareto front as well. The development of the ACO-based multiobjective approach in this technical note provides an attractive alternative to solving construction time–cost optimization.     

Chance-Constrained Time–Cost Tradeoff Analysis Considering Funding Variability

This paper proposes a chance-constrained programming model to incorporate the variability of funding, which is quantified by the coefficient of variation. The proposed model formulates financial feasibility as a stochastic constraint, transforms it into a deterministic equivalent at a prespecified confidence level, and solves the system by means of classical optimization techniques. The time–cost curve generated by the proposed model serves as a foundation for optimizing total project cost. To demonstrate the uniqueness of the proposed model, it is compared to previous approaches through a small building example.     

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.     

Application of a SOM-Based Optimization Algorithm in Minimizing Construction Time for Secant Pile Wall

Construction time matters for activities where rental equipment must be used. The building of a secant pile wall requires the rental of equipment and finding the optimal sequence to minimize the construction time is one way to lower construction costs. In this study we develop an effective and efficient optimization algorithm, which we call self-organizing feature map (SOM)-based optimization (SOMO), to minimize the construction time. The algorithm is applied to a case study to obtain the optimal sequences for both primary and secondary bored piles for a secant pile wall. The new SOMO algorithm is developed based on the ability of the human brain to produce topologically ordered mapping, so as to exploit better solutions via updating the weighting vectors of the neurons in a self-organizing topological way that occurs in the evolution of the feature map for optimization. Given detailed building time of the 16 activities of each bored pile, we find that 143.92 h or 27.21% of the original construction can be saved. The optimal sequences for both primary and secondary bored piles are also determined. The practicability of the SOMO algorithm is substantiated.     

Dynamic Programming Approach to Optimization of Site Remediation

Environmental restoration is a matter of national concern. Decades of abuse by industry, agriculture, and the military have caused devastating contamination of the earth, air, and water. The Department of Energy alone will spend hundreds of billions of dollars on containment and restoration. It is imperative that restoration costs are minimized. Every dollar spent on restoration is a dollar that will not go toward research, a dollar that will not go to upgrade our nation’s infrastructure. The work presented here uses cost as a decision variable in restoration projects. Contaminated sites frequently vary from one point to another in type and level of contamination. In addition, a single piece of property may contain several distinct contaminated areas, each of which has characteristics unlike any of the other areas. Thus one should look at optimizing the selection of remediation technologies to address the variation. A methodology has been developed that will optimize the selection of remediation technologies based on cost. This methodology uses geostatistics and dynamic programming to break a site into discrete cells and then select the optimal sequence of remediation technologies.     

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.     

Dynamic Site Layout Planning Using Approximate Dynamic Programming

Dynamic site layout planning requires identifying and updating the positions of all temporary construction facilities such as offices, storage areas, and workshops over the entire project duration. Existing models do not guarantee global optimal solutions because they focus on optimizing the planning and layout of successive construction stages in a chronological order, without considering the future implications of layout decisions made in early stages. This paper presents the development of an approximate dynamic programming model that is capable of searching for and identifying global optimal dynamic site layout plans. The model applies the concepts of approximate dynamic programming to estimate the future effects of layout decisions in early stages on future decisions in later stages. The model is developed in three main phases: (1) formulating the decision variables, geometric constraints, and objective function of the dynamic site layout planning problem; (2) modeling the problem using approximate dynamic programming; and (3) implementing and evaluating the performance of the model. An evaluation example is analyzed to illustrate the use of the model and demonstrate its capabilities in generating global optimal solution for dynamic site layout planning of construction projects.