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.     

Construction Project Scheduling with Time, Cost, and Material Restrictions Using Fuzzy Mathematical Models and Critical Path Method

This article evaluates the viability of using fuzzy mathematical models for determining construction schedules and for evaluating the contingencies created by schedule compression and delays due to unforeseen material shortages. Networks were analyzed using three methods: manual critical path method scheduling calculations, Primavera Project Management software (P5), and mathematical models using the Optimization Programming Language software. Fuzzy mathematical models that allow the multiobjective optimization of project schedules considering constraints such as time, cost, and unexpected materials shortages were used to verify commonly used methodologies for finding the minimum completion time for projects. The research also used a heuristic procedure for material allocation and sensitivity analysis to test five cases of material shortage, which increase the cost of construction and delay the completion time of projects. From the results obtained during the research investigation, it was determined that it is not just whether there is a shortage of a material but rather the way materials are allocated to different activities that affect project durations. It is important to give higher priority to activities that have minimum float values, instead of merely allocating materials to activities that are immediately ready to start.     

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.     

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.     

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.     

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.     

Challenges in Line-of-Balance Scheduling

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

Work Continuity Constraints in Project Scheduling

Repetitive projects involve the repetition of activities along the stages of the project. Since the resources required to perform these activities move from one stage to the other, a main objective of scheduling these projects is to maintain the continuity of work of these resources so as to minimize the idle time of resources. This requirement, often referred to as work continuity constraints, involves a tradeoff between total project duration and the resource idle time. The contribution of this paper is threefold. First, we provide an extensive literature summary of the topic under study. Although most research papers deal with the scheduling of construction projects, we show that this can be extended to many other environments. Second, we propose an exact search procedure for scheduling repetitive projects with work continuity constraints. This algorithm iteratively shifts repeating activities further in time in order to decrease the resource idle time. We have embedded this recursive search procedure in a horizon-varying algorithm in order to detect the complete tradeoff profile between resource idle time and project duration. The procedure has been coded in Visual C++ and has been validated on a randomly generated problem set. Finally, we illustrate the concepts on three examples. First, the use of our new algorithm is illustrated on a small fictive problem example from literature. In a second example, we show that work continuity constraints involve a tradeoff between total project duration and the resource idle time. A last example describes the scheduling of a well-known real-life project that aims at the construction of a tunnel at the Westerschelde in The Netherlands.     

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.     

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.     

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.     

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.     

Algorithm for Determining Controlling Path Considering Resource Continuity

Scheduling of construction projects that have multiple units, wherein activities repeat from one unit to another, always represent a major challenge to project managers. These projects require schedules that ensure the uninterrupted usage of resources from an activity in one unit to the similar activity in the next unit and maintaining logic constraints at the same time. The scheduling method presented in this paper considers both logic and resource continuity constraints. The method utilizes the critical path method network of a single unit. Start-to-start and finish-to-finish relationships are used. Constant activity production rate is assumed. The proposed approach determines the controlling path (logically and resource critical units) in a simplified way. To automate the proposed algorithm, a macroprogram has been written on commercial scheduling software. Details of the model development and implementation are described, and an example application is presented to validate the proposed approach. The advantages, limitations, and future extensions of the proposed approach are then discussed.     

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.     

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.     

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.     

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.     

Probabilistic Optimal-Cost Scheduling

During the planning and execution of construction projects, it often becomes necessary to shorten the duration of the project. A widely used technique for reducing the duration of a project is commonly referred to as least-cost scheduling. This procedure is based on deterministically arriving at the shortest project duration for the minimum cost possible. There is, however, one major problem with the typical application of this technique. It does not address the variability inherent in the duration and cost of the project activities. Thus, the resulting compressed schedule value cannot be applied with any stated level of statistical confidence. This paper presents a new procedure that addresses some of the major shortcomings of least-cost scheduling. It does so by accounting for the variability inherent in the duration and cost of the scheduled activities by simultaneously applying range estimating and probabilistic scheduling to the historical data. The resulting data set is then analyzed to provide a compressed schedule duration and cost estimate that have a higher overall confidence of being achieved.     

Time-Cost-Quality Trade-Off Analysis for Highway Construction

Many departments of transportation have recently started to utilize innovative contracting methods that provide new incentives for improving construction quality. These emerging contracts place an increasing pressure on decision makers in the construction industry to search for an optimal resource utilization plan that minimizes construction cost and time while maximizing its quality. This paper presents a multiobjective optimization model that supports decision makers in performing this challenging task. The model is designed to transform the traditional two-dimensional time-cost tradeoff analysis to an advanced three-dimensional time-cost-quality trade-off analysis. The model is developed as a multiobjective genetic algorithm to provide the capability of quantifying and considering quality in construction optimization. An application example is analyzed to illustrate the use of the model and demonstrate its capabilities in generating and visualizing optimal tradeoffs among construction time, cost, and quality.