Cost Optimization Model for the Multiresource Leveling Problem with Allowed Activity Splitting

Resource leveling aims at minimizing the resource usage fluctuations, which is accomplished by moving noncritical activities within their float. The project duration is fixed and is not affected by the leveling. Most of resource leveling techniques assumes that activities cannot be split. Although this assumption is valid for most construction activities, there are several activities that can be split to achieve better resource leveling. However, there is an added cost associated with splitting such as startup and restarting costs. This paper presents an optimization model for resource leveling that allows activity splitting and minimizes its associated costs. The objective is to level resources in a way that provides a tradeoff between the extra cost of acquiring and releasing resources versus the extra cost of activity splitting. The model can be used to determine at what values of the splitting cost, the preemption of an activity is recommended. One example problem is solved at the end of the paper in order to illustrate the proposed model.     

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.     

Binary Resource Leveling Model: Activity Splitting Allowed

The resource leveling problem is common and has been studied numerous times. In these studies and the resulting solutions, there exists a common element, which is once an activity is started, it cannot be stopped and restarted again. That is, it cannot be split. In many instances in actual construction, there exist activities that can be stopped and restarted. However, not all activities have this characteristic. This paper presents a linear program binary variable model to level resources that permits selected activities to stop and restart. This splitting of activities results in improvement to the leveling solution that is traditionally achieved when splitting is not permitted. Examples are presented that illustrate the improvement in the solution obtained from the proposed model compared to models that do not allow splitting and compares the result to that obtained using commercially available software. The results are beneficial to construction professionals who may be unaware of the impacts of using activity splitting.     

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.     

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.     

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.     

Modification of Minimum Moment Approach in Resource Leveling

This paper proposes a modification to the minimum moment approach that is used for resource leveling as presented by Harris and based upon the critical path method. The proposed and the traditional methods were developed with the assumption of no activity splitting and a fixed project duration with unlimited availability of resources. The difference between these methods is in the criteria of selecting the activity that has to be shifted from its original position to a better position. This is judged by the change in the statical moment of the resource histogram before and after such movement. In the proposed method, and for the activities that lie at the same sequence step, the activity that is to be shifted first is selected based upon both the value of its free float (S) and the value of its resource rate (R). In this way, the calculation of the improvement factor is needed only to determine the extent to which an activity is to be shifted. On the other hand, using the traditional method, the activity with the maximum improvement factor found for each possible day of shifting is selected first. The process is then repeated for all remaining activities using the updated histogram resulting from the shifted activity. The proposed method significantly reduces the calculations so that the number of iterations in each sequence step is equal to the number of its noncritical activities (n) as compared to (n!) in the traditional method. In addition, the calculation process using the proposed method is easier—especially for manual computations—than the traditional one. The results were insignificantly different, and in many cases they were identical. In this paper, the traditional and the proposed methods will be presented along with an example problem that was solved using the two methods. It should be noted that neither of the two methods provides the true minimum moment.     

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.     

Permutation-Based Elitist Genetic Algorithm for Optimization of Large-Sized Resource-Constrained Project Scheduling

The resource-constrained project scheduling problem (RCPSP) has received the attention of many researchers because its general model can be used in a wide variety of construction planning and scheduling applications. The exact procedures and priority-rule-based heuristics fail to search for the optimum solution to the RCPSP of large-sized project networks in a reasonable amount of time for successful application in practice. This paper presents a permutation-based elitist genetic algorithm for solving the problem in order to fulfill the lack of an efficient optimal solution algorithm for project networks with 60 activities or more as well as to overcome the drawback of the exact solution approaches for large-sized project networks. The proposed algorithm employs the elitist strategy to preserve the best individual solution for the next generation so the improved solution can be obtained. A random number generator that provides and examines precedence feasible individuals is developed. A serial schedule generation scheme for the permutation-based decoding is applied to generate a feasible solution to the problem. Computational experiments using a set of standard test problems are presented to demonstrate the performance and accuracy of the proposed algorithm.     

Linear versus Network Scheduling: A Critical Path Comparison

Linear scheduling methods provide an alternative way of scheduling repetitive projects, to the commonly used network methods. Critical path identification is a major attribute for both methods; therefore, it is very important for practitioners to understand the function of the two methods in this area. The present paper compares the critical path of the recently developed Kallantzis-Lambropoulos repetitive project model against the network scheduling critical path method (CPM), aiming at delving into and pointing out the differences and similarities between them. Initially, the rules for transforming the linear project into an equivalent CPM network are proposed. Then, the rules are applied on a sample linear project. Due to the additional constraint for maintaining resource continuity that the linear method takes into account, the critical paths vary. The constraint is subsequently removed from selected activities and comparison is repeated; the critical paths then coincide. In order to validate the findings and ensure impartiality of results, a random linear project generator is developed. A group of twenty-five random linear projects and their equivalent networks is produced. Their critical paths are analyzed, compared and classified. Conclusions support that the proposed comparison could be beneficial to users of linear scheduling methods, while the random project generator can serve other related research.     

Optimization of Resource Allocation and Leveling Using Genetic Algorithms

Resource allocation and leveling are among the top challenges in project management. Due to the complexity of projects, resource allocation and leveling have been dealt with as two distinct subproblems solved mainly using heuristic procedures that cannot guarantee optimum solutions. In this paper, improvements are proposed to resource allocation and leveling heuristics, and the Genetic Algorithms (GAs) technique is used to search for near-optimum solution, considering both aspects simultaneously. In the improved heuristics, random priorities are introduced into selected tasks and their impact on the schedule is monitored. The GA procedure then searches for an optimum set of tasks' priorities that produces shorter project duration and better-leveled resource profiles. One major advantage of the procedure is its simple applicability within commercial project management software systems to improve their performance. With a widely used system as an example, a macro program is written to automate the GA procedure. A case study is presented and several experiments conducted to demonstrate the multiobjective benefit of the procedure and outline future extensions.     

Neurofuzzy Genetic System for Selection of Construction Project Managers

Choosing a project manager for a construction project—particularly, large projects—is a critical project decision. The selection process involves different criteria and should be in accordance with company policies and project specifications. Traditionally, potential candidates are interviewed and the most qualified are selected in compliance with company priorities and project conditions. Precise computing models that could take various candidates’ information into consideration and then pinpoint the most qualified person with a high degree of accuracy would be beneficial. On the basis of the opinions of experienced construction company managers, this paper, through presenting a fuzzy system, identifies the important criteria in selecting a project manager. The proposed fuzzy system is based on IF-THEN rules; a genetic algorithm improves the overall accuracy as well as the functions used by the fuzzy system to make initial estimates of the cluster centers for fuzzy c-means clustering. Moreover, a back-propagation neutral network method was used to train the system. The optimal measures of the inference parameters were identified by calculating the system’s output error and propagating this error within the system. After specifying the system parameters, the membership function parameters—which by means of clustering and projection were approximated—were tuned with the genetic algorithm. Results from this system in selecting project managers show its high capability in making high-quality personnel predictions.     

Precedence-Preserving GAs Operators for Scheduling Problems with Activities’ Start Times Encoding

Precedence-preserving crossover and mutation operators for scheduling problems with activities’ start times encoding are proposed and employed in this paper. The objective is to tackle the incapability of the genetic algorithms (GAs) operators to preserve the precedence relationships among activities and generate feasible solutions in scheduling problems. The proposed operators employ an embedded precedence-preserving algorithm that determines the activities’ forward free float and backward free float and utilize them in randomly selected backward and forward paths, respectively. The proposed operators were evaluated using finance-based scheduling problems for large-scale projects of 120 repetitive activities. Moreover, the proposed operators were validated by comparing the results with the optimum results of a resource-constrained scheduling problem reported in the literature. The results exhibited the robustness of the proposed operators to reduce the computational costs. In addition, the results demonstrated the high potential and effectiveness of the proposed operators to capture the optimal solutions of the problems considered.     

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.     

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.     

Network Creation and Development for Repetitive-Unit Projects

Network scheduling is typically performed in three phases—network creation, analysis, and development. Although the critical path method (CPM) constitutes a well-established logic in network analysis, human intuition and experience are required for the creation and development of the network. Because of this, a variety of alternative CPM networks can be created in scheduling the same project. The use of the most desirable network can lead to a considerable reduction in the duration of the projects. This can be achieved by accurately identifying activities and linking them in an appropriate manner. Many researchers insisted that network scheduling lacks efficiency in scheduling repetitive-unit projects. Because of this, many scheduling methods have been developed to model such types of projects. However, most are not network based and require a large amount of input data, although most leading scheduling software remains network based and field engineers desire networklike forms of the schedule. In an effort to overcome this limitation, this paper presents a procedure for creating and developing networks for repetitive-unit projects. This network-based model incorporates a two-dimensional arrangement of activities, resource-space coordinates, for ease in creating a network and optimizes the activity linkage, thus resulting in the most desirable results. The model is applied to a typical repetitive-unit project to illustrate the use and capabilities of the model. The model can serve as an aid for inexperienced schedulers in creating a network as well as its optimization. An experienced scheduler can also check the desirability of his or her own created network via the use of this model.     

Resource Scheduling Using Neural Dynamics Model of Adeli and Park

This paper presents a mathematical model for resource scheduling considering project scheduling characteristics generally ignored in prior research, including precedence relationships, multiple crew-strategies, and time cost trade-off. Previous resource scheduling formulations have traditionally focused on project duration minimization. The proposed model considers the total project cost minimization. Furthermore, resource leveling and resource-constrained scheduling have traditionally been solved independently. In the new formulation, resource leveling and resource-constrained scheduling are performed simultaneously. The proposed model is solved using the patented neural dynamics model of Adeli and Park. A case study is presented to demonstrate the performance of the method under various resource availability profiles.     

Developing a Complexity Measure for Project Schedules

Several factors contribute to the complexity of project schedules, including the number of activities, the level of detail, and the shape of the project network. This paper presents a measure that assesses the complexity of project schedules in terms of the connectivity of the activities. Unlike similar complexity measures, the proposed complexity measure does not consider redundant relationships in the project’s schedule. In addition, the measure is expressed as a percentage and therefore has the advantage of being intuitively understand by project managers. The measure considers the degree of interrelationships between the activities in the project’s schedule. The measure has been implemented in a computerized tool to help managers assess the complexity of their projects. The tool is developed as an add-in to popular commercial scheduling software like MS Project.     

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.     

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.