Discrete Time-cost Tradeoff 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.

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.

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.

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.

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.

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.

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.

Activity Uncrashing Heuristic with Noncritical Activity Rescheduling Method for the Discrete Time-Cost Trade-Off Problem

AbstractDespite intensive research efforts that have been devoted to discrete time-cost optimization of construction projects, the current methods have very limited capabilities for solving the pro...

Preprocessing the Discrete Time-Cost Tradeoff Problem with Generalized Precedence Relations

This study investigates the deadline of the discrete time-cost tradeoff problem (DTCTP-D) with generalized precedence relations (GPRs). This problem requires modes to be assigned to the activities of a project such that the total cost is minimized and the total completion time and the precedence constraints are satisfied. Anomalies under GPRs are irreconcilable with many current theories and methods. We propose a preprocessing technology, an equivalent simplification approach, which is an effective method for solving large-scale complex problems. We first study a way to deal with the anomalies under GPRs, such as the reduce (increase) in project completion as a consequence of prolonging (shortening) an activity, and discover relationships between time floats and path lengths. Then, based on the theories, we transform the simplification into a time float problem and design a polynomial algorithm. We perform the simplification and improve the efficiency of the solution by deleting redundant calculation objects.

A heuristic procedure for solving discrete time-cost tradeoff problems in repetitive projects

This paper studies a discrete time-cost tradeoff problem in repetitive projects, in which each activity has several alternative modes and must be scheduled in sequence from the first unit to the last unit. The objective is to minimize the total project cost consisting of direct costs and idle costs of all activities while meeting a pre-specified deadline. A heuristic procedure based on the linear programing relaxation is presented to solve this problem with the goal of finding high-quality solutions for medium-or large-size problems within a short period of time. Computational experiments are conducted to verify the effectiveness of the proposed procedure.

A Data Envelopment Analysis Method for Finding Robust and Cost-Efficient Schedules in Multimode Projects

The execution of industrial projects is subject to uncertainties that cause deviations from the designated project schedules. Therefore, it is desired to generate robust schedules in the sense of being insensitive to project disruptions, such as deviations in activity durations. Beyond that, efficient schedules that offer high robustness at a low cost are preferred. This paper focuses on the discrete time-cost tradeoff problem and develops a new method for identifying and ranking efficient schedules. First, a large schedule pool with robust schedules is generated. Efficient schedules are then identified and ranked by applying data envelopment analysis (DEA) with a particular super-efficiency model. An extensive evaluation based on a project testbed and an example construction project shows that the proposed method finds and ranks efficient schedules, that can be suitably presented to a project manager for decision support .

Bi-Objective Scheduling Optimization for Discrete Time/Cost Trade-Off in Projects

In sustainable project management, time and cost are two critical factors affecting the success of a project. Time/cost trade-offs in projects accelerate the execution of some activities by increasing the amount of non-renewable resources committed to them and therefore shorten the project duration. The discrete time/cost trade-off problem (DTCTP) has been extensively studied during the past 20 years. However, due to its complexity, the DTCTP—especially the DTCTP curve problem (DTCTP-C)—has only been solved for relatively small instances. To the best of our knowledge, there is no computational performance analysis for solving the DTCTP-C on large project instances with up to 500 activities. This paper aims to fill this gap. We present two bi-objective heuristic algorithms for the DTCTP-C where both project duration and cost are minimized. The objective is to obtain a good appropriate efficient set for the large-scale instances. The first algorithm is based on the non-dominated sorting genetic algorithm II (NSGA-II) and uses a specially designed critical path-based crossover operator. The second algorithm is a steepest descent heuristic which generates efficient solutions by iteratively solving the DTCTP with different deadlines. Computational experiments are conducted to validate the proposed algorithms on a large set of randomly generated problem instances.

A Study on Complexity and Uncertainty Perception and Solution Strategies for the Time/Cost Trade-Off Problem

In this article, the Discrete Time/Cost Tradeoff Problem (DTCTP) is revisited in light of a student experiment. Two solution strategies are distilled from the data of 444 participants and are structured by means of five building blocks: focus, activity criticality, ranking, intensity, and action. The impact of complexity and uncertainty on the cost objective is quantified in a large computational experiment. Specific attention is allocated to the influence of the actual and perceived complexity and uncertainty and the cost repercussions when reality and perception do not coincide.

Network analysis algorithm for the solution of discrete time-cost trade-off problem

Optimum solution of time-cost trade-off problem has significant importance since it provides the highest profit opportunity. For this reason, exact, heuristic, and meta-heuristic algorithms are adapted to obtain the optimum or near-optimum solution. However, heuristic algorithms may not always converge into the global optimum, while meta-heuristic algorithms require significant computation to converge into global optimum and exact methods are complex for construction planners to implement. Therefore, minimum cost-slope based fast converging network analysis algorithm, which provides optimum or near-optimum solutions, is proposed for discrete time-cost trade-off problem. The algorithm searches the global optimum through the feasible crashing options. Number of feasible crashing options increase tremendously in large projects. Therefore, an elimination algorithm is embedded to reduce the number of crashing options. The crashing option with the lowest unit crashing cost is executed and global optimum is searched by stepwise crashing. Tests on 18 and 63-Activity projects revealed that the network analysis algorithm converges to optimum or near-optimum solution by only one percent of the computational demand of meta-heuristic algorithms. Consequently, the proposed heuristic algorithm is a convenient optimization method for the solution of time-cost trade-off problem.

Pareto Front Particle Swarm Optimizer for Discrete Time-Cost Trade-Off Problem

AbstractIntensive heuristic and metaheuristic research efforts have focused on the Pareto front optimization of discrete time-cost trade-off problem (DTCTP). However, very little success has been a...

Multi-objective optimization of discrete time–cost tradeoff problem in project networks using non-dominated sorting genetic algorithm

The time–cost tradeoff problem is one of the most important and applicable problems in project scheduling area. There are many factors that force the mangers to crash the time. This factor could be early utilization, early commissioning and operation, improving the project cash flow, avoiding unfavorable weather conditions, compensating the delays, and so on. Since there is a need to allocate extra resources to short the finishing time of project and the project managers are intended to spend the lowest possible amount of money and achieve the maximum crashing time, as a result, both direct and indirect costs will be influenced in the project, and here, we are facing into the time value of money. It means that when we crash the starting activities in a project, the extra investment will be tied in until the end date of the project; however, when we crash the final activities, the extra investment will be tied in for a much shorter period. This study is presenting a two-objective mathematical model for balancing compressing the project time with activities delay to prepare a suitable tool for decision makers caught in available facilities and due to the time of projects. Also drawing the scheduling problem to real world conditions by considering nonlinear objective function and the time value of money are considered. The presented problem was solved using NSGA-II, and the effect of time compressing reports on the non-dominant set.

Genetic Algorithm–Based Method for the Deadline Problem in Repetitive Construction Projects Considering Soft Logic

AbstractThe discrete time-cost trade-off problem (DTCTP) is a multiobjective problem usually encountered in practical projects. Current optimization methods for this problem in repetitive construction projects often assume that there is only one work sequence between units. In practice, however, the work sequence is not necessarily unchangeable. Scheduling with variable work sequences is known as the soft logic method. This study develops a mathematical model considering soft logic to address the DTCTP in repetitive construction projects. The objective is to select a set of activity modes, start times, and work sequences between units such that the total cost is minimized while meeting a given deadline. A targeted genetic algorithm is also presented, in which only the activity modes and work sequences between units are encoded, and suitable start times of all subactivities are then determined using a linear programming approach. Two example projects are analyzed, and their computation results support that...

Discrete particle swarm optimization method for the large-scale discrete time–cost trade-off problem

Despite many research studies have concentrated on designing heuristic and meta-heuristic methods for the discrete time–cost trade-off problem (DTCTP), very little success has been achieved in solving large-scale instances. This paper presents a discrete particle swarm optimization (DPSO) to achieve an effective method for the large-scale DTCTP. The proposed DPSO is based on the novel principles for representation, initialization and position-updating of the particles, and brings several benefits for solving the DTCTP, such as an adequate representation of the discrete search space, and enhanced optimization capabilities due to improved quality of the initial swarm. The computational experiment results reveal that the new method outperforms the state-of-the-art methods, both in terms of the solution quality and computation time, especially for medium and large-scale problems. High quality solutions with minor deviations from the global optima are achieved within seconds, for the first time for instances including up to 630 activities. The main contribution of the proposed particle swarm optimization method is that it provides high quality solutions for the time–cost optimization of large size projects within seconds, and enables optimal planning of real-life-size projects.

Critical Sequence Crashing Heuristic for Resource-Constrained Discrete Time–Cost Trade-Off Problem

AbstractDespite the importance of project deadlines and resource constraints in construction scheduling, very little success has been achieved in solving the resource-constrained discrete time–cost...

A trade-off between time and cost in scheduling repetitive construction projects

The discrete time/cost trade-off problem (DTCTP) is commonly encountered in repetitive project scheduling. The current models for this problem assume that logical sequences of activities cannot be changed in different units. However, logical sequences are often changed to shorten the project time and minimize project total cost in many practical situations. This characteristic of repetitive activities is referred to as the soft logic. This paper presents a mixed integer nonlinear programming model that combines the general DTCTP and the concept of soft logic. The execution modes of an activity in different units are also considered. The DTCTP is known to be strongly NP-hard, and the introduction of soft logic makes it even more complex. A genetic algorithm (GA) is proposed to resolve the problem. The effectiveness of the proposed GA is verified using the example of a bridge construction project presented in the previous literature. The model proposed in this paper provides more flexibility to reduce the total cost and time of a repetitive project for the planners.