Time-cost Trade-off Problem Research Articles

A Constraint Programming Approach for Discrete Time–Cost Tradeoff Problems in a Time-Constrained Activity Network

The discrete time-cost tradeoff problem (DTCTP) is a well-researched topic in the field of operations research. The majority of existing DTCTP models are based on traditional activity networks, which permit the execution of an activity as soon as all its predecessors have been completed. This assumption is reasonable, but it is important to note that there are always exceptions. The main work of this study was threefold. Firstly, we expanded the analysis of the DTCTP to encompass time-constrained activity networks (DTCTPTC), which encompassed three different types of time constraints. The first constraint was the time-window constraint, which limited the time interval during which an activity could be executed. The second constraint was the time-schedule constraint, which specified the times at which an activity could begin execution. The third constraint was the time-switch constraint, which required project activities to start at specific times and remain inactive during designated time periods. Secondly, a constraint programming (CP) model was developed for the purpose of solving the DTCTPTC. The model employed interval variables to define the activity and its potential time constraints, while CP expressions were utilized to ensure the feasibility of the solution. The objective was to identify the optimal execution mode for each activity, the optimal start times for time-scheduled activities, and the optimal work/rest patterns for time-switch activities, with the aim of minimizing the total cost of the project. Finally, the efficacy of the proposed CP model was validated through two case studies based on two illustrative projects of varying sizes. The outcomes were then compared against existing algorithms. The results demonstrated that time constraints were important factors affecting schedule optimization, and the proposed CP model had the ability to solve large-scale DTCTPTC.

Optimizing Three-Dimensional Trade-Off Problem of Time–Cost–Quality over Multi-Mode Projects with Generalized Logic

Clients typically tend to aim for reasonable prices, minimum possible makespans, and the best quality for the construction projects that they engage in. Evidently, weighing the available offers and coming up with an optimal decision can pose challenges for the decision makers. In this regard, the generation of a tool that helps decision makers strike a proper balance among the conflicting project objectives (i.e., time, cost, and quality) is imperative. To this end, this study proposes a method which assists in the selection of the best compromise choices among the options available for each of the project activities. In addition to the time and cost, the proposed method is designed to bring the quality aspect into the equation as well. To quantify the quality, a value referring to the weighted importance and performance of each activity is used. The proposed method is based on a modified multi-objective genetic algorithm (GA) that incorporates the domination concept for the selection of the best solutions out of the potential candidates. The GA-based method is capable of handling an unlimited number of precedence relationships for each activity, and above all, it is able to capture and unravel any type of logical relationship. This very feature significantly improves the practical relevance of this research, as the parallelization of activities is a common practice in real-life projects. Planners benefit from the various types of relationships (i.e., Start to Start, Start to Finish, Finish to Start, and Finish to Finish), and the concept of lag time frequently introduces parallelization into the network. Overlapped activities, in turn, help reduce the unwanted idle times and speed up the project significantly. Accordingly, in order to demonstrate the application and effectiveness of the proposed model, it has been used in the solution of four time–cost–quality (TCQ) trade-off problems, three of which are generated within the context of this paper. The practiced instances include a small benchmark TCQT problem with 18 activities taken from the literature in addition to more complex 29- and 63-activity TCQTPs produced herein based on benchmark time–cost trade-off problems. The performance of the presented approach is ultimately examined over a large-scale, real-case construction project with over four hundred activities and generalized logic in an unprecedented attempt to validate a model in the realm of TCQTPs. The successful results of the experiments reveal the effectiveness of the proposed model and corroborate the feasibility of its application by the planners amidst arduous decision-making processes.

Optimizing time and cost in construction projects with a hybridized multi-verse optimizer and opposition-based learning

PurposeFor successful management of construction projects, a precise analysis of the balance between time and cost is imperative to attain the most effective results. The aim of this study is to present an innovative approach tailored to tackle the challenges posed by time-cost trade-off (TCTO) problems. This objective is achieved through the integration of the multi-verse optimizer (MVO) with opposition-based learning (OBL), thereby introducing a groundbreaking methodology in the field.Design/methodology/approachThe paper aims to develop a new hybrid meta-heuristic algorithm. This is achieved by integrating the MVO with OBL, thereby forming the iMVO algorithm. The integration enhances the optimization capabilities of the algorithm, notably in terms of exploration and exploitation. Consequently, this results in expedited convergence and yields more accurate solutions. The efficacy of the iMVO algorithm will be evaluated through its application to four different TCTO problems. These problems vary in scale – small, medium and large – and include real-life case studies that possess complex relationships.FindingsThe efficacy of the proposed methodology is evaluated by examining TCTO problems, encompassing 18, 29, 69 and 290 activities, respectively. Results indicate that the iMVO provides competitive solutions for TCTO problems in construction projects. It is observed that the algorithm surpasses previous algorithms in terms of both mean deviation percentage (MD) and average running time (ART).Originality/valueThis research represents a significant advancement in the field of meta-heuristic algorithms, particularly in their application to managing TCTO in construction projects. It is noteworthy for being among the few studies that integrate the MVO with OBL for the management of TCTO in construction projects characterized by complex relationships.

An optimization model for energy project scheduling problem with cost-risk-quality-social consideration trade-off under uncertainty: A real-world application

To complete a successful energy project, all aspects and criteria which can influence the project should be considered. Classic time-cost trade-off (TCT) is used when the completion time of project is not acceptable for customers or top managers. This paper proposes a new cost-risk-quality-social consideration trade-off (CRQST) model for energy projects in a time-constrained problem for achieving specified due date under uncertainty. Moreover, a new comprehensive definition of risk criterion is proposed, and a novel approach for the quality criterion of project based on the dependence of the quality of activities with each other is presented. The internal and external environment of the energy project are considered simultaneously and a new criterion in TCT problem, called social consideration criterion, is introduced. A developed fuzzy augmented ε-constraint method is introduced for the presented multi-objective model to generate Pareto-optimal solutions. To depict the accuracy of results, the proposed model is solved by goal attainment method, and the results of two methods are compared. As a case study, a real oil and gas project is presented, and results show that the proposed method enables managers to effectively handle construction projects in real-world uncertain environments.

Solution of discrete time–cost trade-off problem with adaptive search domain

PurposeExact solution of time–cost trade-off problem (TCTP) by the state-of-the-art meta-heuristic algorithms can be obtained for small- and medium-scale problems, while satisfactory results cannot be obtained for large construction projects. In this study, a hybrid heuristic meta-heuristic algorithm that adapts the search domain is developed to solve the large-scale discrete TCTP more efficiently.Design/methodology/approachMinimum cost slope–based heuristic network analysis algorithm (NAA), which eliminates the unfeasible search domain, is embedded into differential evolution meta-heuristic algorithm. Heuristic NAA narrows the search domain at the initial phase of the optimization. Moreover, activities with float durations higher than the predetermined threshold value are eliminated and then the meta-heuristic algorithm starts and searches the global optimum through the narrowed search space. However, narrowing the search space may increase the probability of obtaining a local optimum. Therefore, adaptive search domain approach is employed to make reintroduction of the eliminated activities to the design variable set possible, which reduces the possibility of converging into local minima.FindingsThe developed algorithm is compared with plain meta-heuristic algorithm with two separate analyses. In the first analysis, both algorithms have the same computational demand, and in the latter analysis, the meta-heuristic algorithm has fivefold computational demand. The tests on case study problems reveal that the developed algorithm presents lower total project costs according to the dependent t-test for paired samples with α = 0.0005.Research limitations/implicationsIn this study, TCTP is solved without considering quality or restrictions on the resources.Originality/valueThe proposed method enables to adapt the number of parameters, that is, the search domain and provides the opportunity of obtaining significant improvements on the meta-heuristic algorithms for other engineering optimization problems, which is the theoretical contribution of this study. The proposed approach reduces the total construction cost of the large-scale projects, which can be the practical benefit of this study.

Solving Time-Cost Tradeoff Problem with Resource Constraint Using Fuzzy Mathematical Model

Scheduling considered being one of the most fundamental and essential bases of the project management. Several methods are used for project scheduling such as CPM, PERT and GERT. Since too many uncertainties are involved in methods for estimating the duration and cost of activities, these methods lack the capability of modeling practical projects. Although schedules can be developed for construction projects at early stage, there is always a possibility for unexpected material or technical shortages during construction stage. The objective of this research is to build a fuzzy mathematical model including time cost tradeoff and resource constraints analysis to be applied concurrently. The proposed model has been formulated using fuzzy theory combining CPM computations, time-cost trade off analysis and resource constraint. MATLAB software has been adopted to perform ranking process, for each case, that facilitates obtaining the optimum solution. This research infers that it is possible to perform time-cost trade off analysis with resource restriction simultaneously, which ensures achieving scheduling optimum solution reducing the effort and the time when performing these techniques in succession using traditional methods.

Modified Streamlined Optimization Algorithm for Time–Cost Tradeoff Problems of Complex Large-Scale Construction Projects

Modified Streamlined Optimization Algorithm for Time–Cost Tradeoff Problems of Complex Large-Scale Construction Projects

Optimizing of Discrete Time-cost Trade-off Problem in Construction Projects Using Advanced Jaya Algorithm

This paper proposes a novel algorithm to optimize the discrete time-cost trade-off problem (DTCTP) in construction projects. As DTCTP is assumed NP-hard, the new metaheuristic models are investigated to contribute for decision-making of project managers. DTCTP can be modelled as multi-mode to represent real-life problems more practical. According to the model, the project activities have at least two or more durations and cost alternative modes. For solving this problem effectively, a novel optimization metaheuristic method named Advanced Jaya Algorithm (A-JA) is proposed, which is generated from Jaya Algorithm (JA). The benchmark function tests are applied to verify the model with other well-known metaheuristic methods. The key weakness of the base algorithm JA is that, it has unstable solution accuracy and low likelihood of escaping local optimums. According to the results, A-JA considerably improves these areas. Two case studies of DTCTP are carried out after verification to demonstrate the effectiveness and efficiency of the proposed algorithm in comparison with JA and three well-known methods. The results of A-JA are found to be more powerful than the base algorithm JA and the benchmark algorithms. The proposed method achieves the Pareto fronts to help decision makers to make trade-off between the objectives and choose the optimum solution considering on their preference.

Simplified Solution of Time-Cost Trade-off Problem for Building Constructions by Linear Scheduling

Time-cost trade-off is an important optimization problem for contractors, because its optimum solution minimizes the total project cost. Formation of the time-cost trade-off problem causes an important workload, since the problem requires preparation of different construction cost and duration alternatives of the activities. Previous studies focused on the optimum solution of the problem and ignored the difficulties of the preparation of the different construction alternatives for the activities, which is a very difficult task for contractors. In this study, the creation of construction alternatives consisting of different time and cost values is automated. Quantity take-off of construction items is computed by user-defined dimensions of structural elements. Workmanship and material requirements are computed by pre-defined job descriptions and quantity take-off values. Different construction alternatives are formed by assigning different crew sizes and the corresponding construction durations are computed by estimating the job efficiency of the crew by regression models derived from the literature. Precedence relationships of the main construction items are pre-defined and the construction schedule is formed by a line of balance in terms of work days. The problem is optimized by a genetic algorithm the parameters of which are fine-tuned by experimental design. The developed approach is implemented on a spreadsheet application and the total optimization process including data entry is completed in one and a half hour on a desktop computer with i5 CPU. This study contributes to relevant literature by proposing a systematic approach for the formation of construction alternatives of the time-cost trade-off problem. The proposed approach can be beneficial for contractors and project managers to form and solve the time-cost trade-off problem with minimum endeavor and cost. KEYWORDS: Time-cost trade-off, Genetic algorithm, Line of balance, Optimization, Experimental design.

Solving large-scale discrete time–cost trade-off problem using hybrid multi-verse optimizer model

The analysis of the relationship between time and cost is a crucial aspect of construction project management. Various optimization techniques have been developed to solve time–cost trade-off problems. A hybrid multi-verse optimizer model (hDMVO) is introduced in this study, which combines the multi-verse optimizer (MVO) and the sine cosine algorithm (SCA) to address the discrete time–cost trade-off problem (DTCTP). The algorithm's optimality is evaluated by using 23 well-known benchmark test functions. The results demonstrate that hDMVO is competitive with MVO, SCA, the dragonfly algorithm and ant lion optimization. The performance of hDMVO is evaluated using four benchmark test problems of DTCTP, including two medium-scale instances (63 activities) and two large-scale instances (630 activities). The results indicate that hDMVO can provide superior solutions in the time–cost optimization of large-scale and complex projects compared to previous algorithms.

Multi-objective time–cost trade-off optimization for the construction scheduling with Rao algorithms

Determining the time and cost of activities is one of the most important stages of construction project planning. Measures taken to shorten the time, such as the need for more or more qualified employees, equipment and machinery, increase project direct cost. The process of deciding which option to use in activities with more than one time–cost option has revealed the time–cost trade-off problem which is discrete optimization. Within the scope of this study, the non-dominant sorting (NDS) method is integrated into the Rao-1 and Rao-2 algorithms and applied to small and medium-scale problems. The numerical results show that the NDS-Rao-2 algorithm has found a better result with a significant number of function evaluations compared to algorithms such as PSO, ACO, GA and TLBO used in previous studies. In addition, the NDS-based Rao-2 algorithm not only find optimal /near results, but also suggest more than one pareto result to the decision maker for time–cost trade-off problem. For this reason, the developed multi-objective Rao-2 algorithm can be considered as a very good alternative for time–cost trade-off problems which are combinatorial problems.

The time-cost trade-off problem and its extensions: A state-of-the-art survey and outlook

The time-cost optimization is amongst the most critical fields, which has an extensive range of implementation in project scheduling. Achieving a satisfactory balance between these factors can lead to an efficient construction project by reducing both the length of the project and costs at the same time. An effective balance can be achieved using various methods, depending on the situation. This study aims to incorporate the various algorithms used in the last 15 years to reach a satisfying balance between time and cost, including meta-heuristics, heuristics, and exact algorithms. A comprehensive view of the problems associated with time-cost optimization will be provided throughout this review to assist new and challenging researchers who are interested in this type of research. For this purpose, we have reviewed some objective functions and uncertainty techniques that could be employed in time-cost balancing problems. The literature review tables contain a variety of columns, including uncertainties such as fuzzy, probabilistic, interval, robust, and objective functions, along with cost and time, for the investigation of various types of balance issues. In the conclusion of this article, we will show the results of our literature review table using different types of graphic diagrams. For each main column of the table, we will show various types of diagrams to make the results easier to understand.

Time-Cost Tradeoff and Resource-Scheduling Problems in Construction: A State-of-the-Art Review

Time-Cost Tradeoff and Resource-Scheduling Problems in Construction: A State-of-the-Art Review

A new qualitative and quantitative analytical approach for risk management in energy project time-cost trade-off problem under interval type-2 fuzzy uncertainty: A case study in the gas industry

This paper proposes a novel risk management approach to develop a Time-Cost Trade-off (TCT) mathematical model under fuzzy uncertainty. In this paper, firstly, a Linear Assignment Method (LAM) is proposed to rank the activities of a project according to their encountering risks when the activities are crashed. Secondly, activities are grouped into different classes in accordance with their risk level so as to concentrate on high-risk activities. Then, a new fuzzy TCT mathematical model considering the risk criterion is presented. In the next step, a quantitative analysis of risks is proposed by Primavera Risk Analysis. Ultimately, risk response strategies are presented, and the results are meticulously scrutinized. Due to more precision in considering uncertainty and advantages of interval type-2 fuzzy set (IT2FS), this fuzzy set is applied throughout the whole methodology. An actual project of a company in the gas industry is adopted to examine the method efficiency.

Non-dominated NSGA-II genetic algorithm for schedule acceleration considering the discrete time-cost compensation problem (DTCTP) in a construction project

Sometimes after scheduling a project, it is necessary to shorten its duration. There are many factors that force to crash the duration. Some reasons may be saving costs, early commissioning or avoiding potential risks. In this case, it is necessary to allocate more resources to activities to shorten their duration while trying to invest as little money as possible. The time–cost tradeoff problem is one important problem in project scheduling. In this study the time–cost tradeoff problem is aborded considering a discrete approach and it is solved using a non-dominated genetic algorithm. The application in a construction project identified a Pareto front that managers could use for decision making. Managers were able to analyze different scenarios to meet delivery date, costs, and scope.

A comparative study of modeling and solution approaches for the multi-mode resource-constrained discrete time–cost trade-off problem: Case study of an ERP implementation project

Most knowledge-intensive industries, especially companies developing software engineering projects such as Enterprise Resource Planning (ERP) implementation projects, generally necessitate finding the optimal trade-off between the project duration and total usage cost of the renewable resource costs (e.g., human resource expertise costs). Therefore, the MRC-DTCTP, which integrates classical multi-mode resource-constrained project scheduling (MRCPSP) and discrete time–cost trade-off problems (DTCTP), can be seen as a more applicable problem since it better reflects the objectives and requirements of today’s real-life software project applications. The MRC-DTCTP is a much more complex variant of the MRCPSP since it aims to minimize total direct/indirect costs of the resources simultaneously under a pre-specified project deadline. Based on this motivation, a new explicit integer-linear programming (ILP) model of the MRC-DTCTP was first developed based on the implicit non-linear programming model of Wuliang and Chengen (2009). Due to its NP-hard nature, we also proposed a constraint programming (CP) model that includes several search strategies to solve large-sized problem instances within reasonable computation time. In addition, a genetic algorithm (GA) approach in combination with a Modified Serial Schedule Generation scheme (SSGS) is implemented to make further comparisons on several benchmark instances, which are generated based on the existing MRCPSP data sets taken from the project scheduling problem library (PSPLIB) by considering additional problem characteristics. A comprehensive experimental study has shown that the proposed CP model and GA approach can provide superior results in shorter run times for large-sized benchmark instances. Finally, an international Enterprise Resource Planning (ERP) Software Company’s real-life application is presented. The ERP projects generally necessitate finding the optimal trade-off between project makespan and human resource costs, making the MRC-DTCTP much more difficult than classical MRCPSPs & DTCTPs. For further analysis, time–cost trade-off curves under different human resource availabilities and project deadlines are drawn to provide managerial insights to ERP project managers.

On the Application of a Lexicographic Method to Fuzzy Linear Programming Problems

The literature on fuzzy variable linear programming (FVLP) and fuzzy number linear programming (FNLP) is prolific in terms of the number of available solution methods. In FVLP problems, only the decision variables and right-hand side values of the constraints are fuzzy numbers. In FNLP problems, except forthe decision variables, all parameters are fuzzy numbers. A widespread approach for solving problemsin FVLP and FNLP is to use linear ranking functions in order to transform the fuzzy problems into conventional ones. Previous studies have shown that linear ranking functions do not guarantee uniqueness of the optimal fuzzy objective values. In this paper, we use a lexicographic method to find unique optimal fuzzy objective values of such problems and compare the results with those obtained via linear ranking function approaches. The paper also discusses applications of the lexicographic method in diet and time–cost trade-off problems in fuzzy environments.

Approximating the discrete time-cost tradeoff problem with bounded depth

We revisit the deadline version of the discrete time-cost tradeoff problem for the special case of bounded depth. Such instances occur for example in VLSI design. The depth of an instance is the number of jobs in a longest chain and is denoted by d. We prove new upper and lower bounds on the approximability. First we observe that the problem can be regarded as a special case of finding a minimum-weight vertex cover in a d-partite hypergraph. Next, we study the natural LP relaxation, which can be solved in polynomial time for fixed d and—for time-cost tradeoff instances—up to an arbitrarily small error in general. Improving on prior work of Lovász and of Aharoni, Holzman and Krivelevich, we describe a deterministic algorithm with approximation ratio slightly less than frac{d}{2} for minimum-weight vertex cover in d-partite hypergraphs for fixed d and given d-partition. This is tight and yields also a frac{d}{2}-approximation algorithm for general time-cost tradeoff instances, even if d is not fixed. We also study the inapproximability and show that no better approximation ratio than frac{d+2}{4} is possible, assuming the Unique Games Conjecture and text {P}ne text {NP}. This strengthens a result of Svensson [21], who showed that under the same assumptions no constant-factor approximation algorithm exists for general time-cost tradeoff instances (of unbounded depth). Previously, only APX-hardness was known for bounded depth.

Time-Cost Trade-Off problem in project management: A proposed constructive algorithm

Time and cost are two remarkable elements prescriptive of success in project management. The anticipated project length may go over the desired period in many projects. Therefore, it becomes vital to shorten the critical path in order to finish the project by the goal date. Time-cost trade-off (TCT) in project network, the reduction in time with a minimum cost of project activities, has increased efficiency of the project. To shorten a project duration activity crashing, which includes allocating additional resources to an activity with the objective of diminishing its duration, is the most commonly employed compression technique. The objective of an optimum solution of time-cost trade-off is to provide maximum profit opportunity with a minimum time. There are many algorithms (heuristic, meta-heuristic and exact) established in this regard. In this paper a constructive algorithm is proposed and implemented with a fairy application example to acquire optimum solution or close-optimum solution of TCT problems. IIUC Business Review Vol. 10, Dec. 2021 pp. 115-128

Simulation-Optimization for the Planning of Off-Site Construction Projects: A Comparative Study of Recent Swarm Intelligence Metaheuristics

Off-site construction is a modern construction method that brings many sustainability merits to the built environment. However, the sub-optimal planning decisions (e.g., resource allocation, logistics and overtime planning decisions) of off-site construction projects can easily wipe away their sustainability merits. Therefore, simulation modelling—an efficient tool to consider the complexity and uncertainty of these projects—is integrated with metaheuristics, developing a simulation-optimization model to find the best possible planning decisions. Recent swarm intelligence metaheuristics have been used to solve various complex optimization problems. However, their potential for solving the simulation-optimization problems of construction projects has not been investigated. This research contributes by investigating the status-quo of simulation-optimization models in the construction field and comparing the performance of five recent swarm intelligence metaheuristics to solve the stochastic time–cost trade-off problem with the aid of parallel computing and a variance reduction technique to reduce the computation time. These five metaheuristics include the firefly algorithm, grey wolf optimization, the whale optimization algorithm, the salp swarm algorithm, and one improved version of the well-known bat algorithm. The literature analysis of the simulation-optimization models in the construction field shows that: (1) discrete-event simulation is the most-used simulation method in these models, (2) most studies applied genetic algorithms, and (3) very few studies used computation time reduction techniques, although the simulation-optimization models are computationally expensive. The five selected swarm intelligence metaheuristics were applied to a case study of a bridge deck construction project using the off-site construction method. The results further show that grey wolf optimization and the improved bat algorithm are superior to the firefly, whale optimization, and salp swarm algorithms in terms of the obtained solutions’ quality and convergence behaviour. Finally, the use of parallel computing and a variance reduction technique reduces the average computation time of the simulation-optimization models by about 87.0%. This study is a step towards the optimum planning of off-site construction projects in order to maintain their sustainability advantages.