Time-cost Trade-off Problem Research Articles

An Overview of the Time-Cost Trade-off Problems of Project Planning

In project management there are two main operation problems like scheduling and cost optimization. These are correlated with each other and have good mathematical proved solutions for the basics. In case of applying arbitrary calendars generates such effects in scheduling which make the time -cost trade-o problem unusable. The aim of this paper is to point out these effects and give an advance to find a new way to the problem.

Managing risk-adjusted resource allocation for project time-cost tradeoffs

In the traditional project crashing problem (also known as the time-cost tradeoff problem) associated with a project network, the decision variables are assumed to be continuous, representing the amount of reduction in the duration of the tasks in the project, and the objective is to find the least expensive set of time reductions (“crashing” times) to complete the project within a given time limit (to avoid penalties). We will study a variant of this problem with a combinatorial probabilistic version, where the objective is to find the set of “crashing” choices that minimizes the time reduction cost and the expected penalty risk from tardiness. We show this problem is NP-hard, so we propose efficient heuristics that can provide approximate solutions to this problem. We also extend this problem so that resource assignments can be adjusted following project status reviews several times before reaching the project deadline.

<b>The Optimization of the Time-Cost Tradeoff Problem in Projects with Conditional Activities Using of the Multi-Objective Charged System Search Algorithm (SMOCSS)</b>

Abstract The appropriate planning and scheduling for reaching the project goals in the most economical way is the very basic issue of the project management. As in each project, the project manager must determine the required activities for the implementation of the project and select the best option in the implementation of each of the activities, in a way that the least final cost and time of the project is achieved. Considering the number of activities and selecting options for each of the activities, usually the selection has not one unique solution, but it consists of a set of solutions that are not preferred to each other and are known as Pareto solutions. On the other hand, in some actual projects, there are activities that their implementation options depend on the implementation of the prerequisite activity and are not applicable using all the implementation options, and even in some cases the implementation or the non-implementation of some activities are also dependent on the prerequisite activity implementation. These projects can be introduced as conditional projects. Much researchs have been conducted for acquiring Pareto solution set, using different methods and algorithms, but in all the done tasks the time-cost optimization of conditional projects is not considered. Thus, in the present study the concept of conditional network is defined along with some practical examples, then an appropriate way to illustrate these networks and suitable time-cost formulation of these are presented. Finally, for some instances of conditional activity networks, conditional project time-cost optimization conducted multi-objectively using known meta-heuristic algorithms such as multi-objective genetic algorithm, multi-objective particle swarm algorithm and multi-objective charged system search algorithm.

A Hybrid Method Based on Fuzzy AHP and VIKOR for the Discrete Time-Cost-Quality Trade-off Problem

Time, cost and quality are considered as the main components in managing each project. Previous researches have mainly focused on the time-cost trade-off problems. Recently quality is considered as the most important factor in projecti?½s success, which is influenced by time acceleration that is the less time is spent the more success is gained. In time-cost-quality trade-off problems, each activity can be done in various execution modes and determination of these execution modes is seen as to minimize the project time and cost and maximize its quality .In this paper, three integer programming models are provided and one of the main objectives is optimized in each model by assigning the proper bound to other objectives. Following the non-dominated solutions obtained by solving models, and by means of hybrid approach of Fuzzy AHP strategy and VIKOR method regarded as multi-criteria decision making methods, the best possible alternative (from among non-dominated solutions) has been suggested.Fuzzy AHP method has been used to determine the importance rate of each objective. In this method linguistic variables were used which take us closer to reality. At the end, with applying these weights in VIKOR method, the best possible alternatives (among non-dominated solutions) were found. Using this hybrid approach can help managers, to a great extent, in selecting the appropriate solution so that maximum desirability is obtained due to the importance rate of the objective functions from the viewpoint of decision maker.

Application of Multi-technique in Project Planning to Solve Time-cost Trade-off Problem

One of the most important problems in project management is the time-cost trade-off problem (TCTP) that must be taken into consideration during project planning and control process through the use of suitable planning techniques. This study presented a model aims to solve (TCTP) using crashing as a traditional project planning technique and concurrency technique with activities partitioning in addition to new suggested technique that mixes between the two techniques and named as Concurrency-with Partitioning and Crashing Technique (CPCT). The model focuses on minimizing project time and cost and it is applied on an adopted case study. The results show that the suggested (CPCT) produces the best results for the two objectives compared to other applied techniques.

DEVELOPING NEW CHARGED SYSTEM SEARCH-BASED ALGORITHM: APPLICATION IN THE TIME-COST TRADE-OFF PROBLEMS

The trade-off between the total cost and project duration is one of the most important parameters of construction project planning. There are various methods to optimize time-cost trade-off problems. Mathematical programming models as one type of them cannot solve large and complex networks effectively. On the other hand, although the meta-heuristics algorithms in many cases can find a complete set of solutions but to optimize the time-cost trade-off problems in very massive construction projects they need to spend a lot of time, so existence a powerful algorithm with higher convergence rate is necessary. In this paper new procedures MAWA-CSS and SMOCSS are introduced to generalize the well-known CSS algorithm for solving TCTP optimization problem and all multi-objective optimization problems in discrete and continuous search space. The overall structure of SMOCSS algorithm is similar to the MOPSO and to determine the Charge magnitude of particles a new simple method is introduced. The proposed method is examined for different test functions and the results are compared to the results of two well-known multi- objective algorithms (NSGA-II and MOPSO). In addition, two example of time-cost optimization problem (Feng and Zheng network with 18 and 7 activities respectively) are used to evaluate the performance of the proposed algorithms. The results indicate that the SMOCSS algorithm has the ability to find out the optimal solution and define the Pareto front as well in reasonable time. Hence the proposed approach in this paper is much adaptive and suitable for tackling TCTP, which is useful and beneficial for decision-making on the trade-off between project duration and total cost.

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...

Some Special Cases of a Continuous Time-Cost Tradeoff Problem with Multiple Milestones under a Chain Precedence Graph

We consider a time-cost tradeoff problem with multiple milestones under a chain precedence graph. In the problem, some penalty occurs unless a milestone is completed before its appointed date. This can be avoided through compressing the processing time of the jobs with additional costs. We describe the compression cost as the convex or the concave function. The objective is to minimize the sum of the total penalty cost and the total compression cost. It has been known that the problems with the concave and the convex cost functions for the compression are NP-hard and polynomially solvable, respectively. Thus, we consider the special cases such that the cost functions or maximal compression amounts of each job are identical. When the cost functions are convex, we show that the problem with the identical costs functions can be solved in strongly polynomial time. When the cost functions are concave, we show that the problem remains NP-hard even if the cost functions are identical, and develop the strongly polynomial approach for the case with the identical maximal compression amounts.

Direct Solution of Time–Cost Tradeoff Problem with Fuzzy Decision Variables

ABSTRACTProject time–cost tradeoff problem is concerned with shortening project duration time with minimum cost. Due to uncertain environment conditions, such as inflation, climate changes, space congestion, productivity level, lack of accurate data, etc., there can be uncertainty in the parameters. The uncertainty in the parameters can be modeled using fuzzy set theory. In this study, a fuzzy time–cost tradeoff problem with fuzzy normal and crash durations, and fuzzy duration of activities and occurrence time of events is handled. The fuzzy time–cost tradeoff problem is solved directly by making use of a fuzzy ranking method and the tabu search (TS) algorithm.

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.

Optimizing time–cost trade-offs in product development projects with a multi-objective evolutionary algorithm

Time–cost trade-offs arise when organizations seek the fastest product development (PD) process subject to a predefined budget, or the lowest-cost PD process within a given project deadline. Most of the engineering and project management literature has addressed this trade-off problem solely in terms of crashing—options to trade cost for time at the individual activity level—and using acyclical networks. Previously (Meier et al. in IEEE Trans Eng Manag 62(2):237–255, 2015), we presented a rich model of the iterative (cyclical) PD process that accounts for crashing, overlapping, and stochastic activity durations and iterations. In this paper, we (1) propose an optimization strategy for the model based on a multi-objective evolutionary algorithm, called e-MOEA, which identifies the Pareto set of best time–cost trade-off solutions, and (2) demonstrate the approach using an automotive case study. We find that, in addition to crashing, activity overlapping, process architecture, and work policy provide further managerial levers for addressing the time–cost trade-off problem. In particular, managerial work policies guide process cost and duration into particular subsets of the Pareto-optimal solutions. No work policy appeared to be superior to the others in both the cost and duration dimensions; instead, a time–cost trade-off arises due to the choice of work policy. We conclude that it is essential for managers to consider all of the key factors in combination when planning and executing PD projects.

A polynomial time repeated cuts algorithm for the time cost tradeoff problem: The linear and convex crashing cost deadline problem

The time cost tradeoff problem in project management, TCTP, is to achieve a given deadline on the project completion time by expediting the normal durations of activities at the cheapest cost possible. The linear TCTP, in which the expediting costs of each activity are linear, as a function of the number of time periods reduced, can be solved using linear programming. We present here an algorithm that solves the linear or convex costs TCTP that runs in polynomial time and calls only for a minimum s,t-cut routine at each iteration. This repeated cuts algorithm is related to the non-polynomial time algorithm by Phillips and Dessouky (1977), the PD-algorithm. The PD-algorithm reduces the project duration, at each iteration, by one time unit, at a minimum cost. The choice of the activities to expedite, in order to reduce the project duration by one unit, is determined by a solution to a minimum s,t-cut in a respective graph.We present here previously unknown properties of the PD-algorithm, and a new concept of cut-decomposition. These properties are used in devising the repeated cuts algorithm based on scaling. The repeated cuts algorithm solves in polynomial time, the linear as well as the convex TCTP. The algorithm solves the TCTP problem in polynomial time even when the durations and/or the target deadline are not necessarily integers.

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...

Min-Max Regret Version of the Linear Time–Cost Tradeoff Problem with Multiple Milestones and Completely Ordered Jobs

We consider a linear time–cost tradeoff problem with multiple milestones and uncertain processing times such that all jobs are completely ordered. The performance measure is expressed as the sum of total weighted number of tardy jobs and total crashing cost. The processing times uncertainty is described through two types of scenarios: discrete and interval scenarios. The objective is to minimize maximum deviation from optimality over all scenarios. For the discrete scenario case, we prove its NP-hardness, develop a pseudo-polynomial time approach, and present a polynomially solvable case. Finally, we show that the interval scenario case is also NP-hard.

A multi-objective resource-constrained optimization of time-cost trade-off problems in scheduling project

This paper presents a multi-objective resource-constrained project scheduling problem with positive and negative cash flows. The net present value (NPV) maximization and making span minimization are this study objectives. And since this problem is considered as complex optimization in NP-Hard context, we present a mathematical model for the given problem and solve three evolutionary algorithms; NSGA-II, MOSA and MOPSO are applied to find the set of Pareto solutions for this multi-objective scheduling problem. In order to show performance of the algorithms, different metrics are applied and comparisons between the two algorithms are also considered. The computational results for a set of test problems taken from the project scheduling problem Bandar Abbas Gas condensate Refinery project and library are presented and discussed. Finally, the computational results illustrate the superior performance of the NSGA-II, MOSA and MOPSO algorithm with regard to the proposed metrics. In order to solve proposed method from NSGA-II algorithm, the results are compared with GAMS software in some problems. The proposed method is a Converge to the optimum and efficient solution algorithm.

Effects of Project Uncertainties on Nonlinear Time-Cost Tradeoff Profile

This study presents the effects of project uncertainties on nonlinear time-cost tradeoff (TCT) profile of real life engineering projects by the fusion of fuzzy logic and artificial neural network (ANN) models with hybrid meta-heuristic (HMH) technique, abridged as Fuzzy-ANN-HMH. Nonlinear time-cost relationship of project activities is dealt with ANN models. ANN models are then integrated with HMH technique to search for Pareto-optimal nonlinear TCT profile. HMH technique incorporates simulated annealing in the selection process of multiobjective genetic algorithm. Moreover, in real life engineering projects, uncertainties like management experience, labor skills, and weather conditions are commonly involved, which affect the duration and cost of the project activities. Fuzzy-ANN-HMH analyses responsiveness of nonlinear TCT profile with respect to these uncertainties. A comparison of Fuzzy-ANN-HMH is made with another method in literature to solve nonlinear TCT problem and the superiority of Fuzzy-ANN-HMH is demonstrated by results. The study gives project planners to carry out the best plan that optimizes time and cost to complete a project under uncertain environment.

MULTI-OBJECTIVE TIME-COST OPTIMIZATION USING COBB-DOUGLAS PRODUCTION FUNCTION AND HYBRID GENETIC ALGORITHM

Existing research on construction time-cost tradeoff issues rarely explore the origin of the crashing cost. Crashing cost function was either assumed without much justification, or came from historical data of some real pro­jects. As a result the conclusions of the papers can hardly be used to guide allocations of labor and equipment resources respectively. The authors believe Cobb-Douglas function provides a much-needed piece to modeling the cost functions in the construction time-cost tradeoff problem during the crashing process. We believe this new perspective fills a gap of existing time-cost tradeoff research by considering project duration, labor and equipment cost as parameters of the Cobb- Douglas production function. A case study was presented to show how the proposed framework works. Our conclusion is that introducing Cobb-Douglas function into time-cost tradeoff problem provides us extra capacity to further identify the optimal allocations of labor and equipment resources during crashing.