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We develop a discrete-time approximation technique dealing with the time-cost trade-off problem in PERT networks. It is assumed that the activity durations are independent random variables with generalized Erlang distributions, in which the mean duration of each activity is a non-increasing function of the amount of resource allocated to it. It is...
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Citations
... The optimal solution of the nonlinear discrete TCTP has received a substantial attention among the researchers and various techniques have been proposed in literature, e.g. genetic algorithms [7÷12], simulated annealing [13,14], tabu search [14,15], neural networks [16], ant colony optimization [17÷20], particle swarm optimization [21], differential evolution [22], harmony search [23] mixedinteger linear programming [24÷28] and hybrid methods, such as genetic algorithm and simulated annealing [28], genetic algorithm and dynamic programming [29], cutting plane method and Monte Carlo simulation [30], etc. ...
Optimal project scheduling under nonconvex time-cost relations represents a challenging problem in construction management. The nonconvex time-cost relations may appear in a construction project when several different duration options are available for its activities due to alternative technological processes enabled for their realization or wide accessibility of production resources. The source of nonconvexity of the project scheduling optimization problem can also be the project penalty- or bonus-duration relations arranged within the construction contract. The aim of this paper is to present the mixed-integer nonlinear programming (MINLP) based optimal time scheduling of construction projects under nonconvex costs. For this purpose, the MINLP model was developed and applied. A numerical example from literature and an example of construction project time-cost trade-off analysis under practical nonconvex penalty function are given in the paper to demonstrate advantages of MINLP optimization. The example from literature first presented the capability of the MINLP approach to obtain the optimal solution for difficult, highly combinatorial nonconvex discrete project scheduling problem. Thereupon, the following example revealed that the optimal project time-cost curve may take very nonuniform shape on account of discrete nature of activity direct cost options and nonconvex relation between project duration and total cost. In this way, the presented study intends to provide practitioners with new information from the field of optimization techniques for project scheduling as well as an alternative view on performance of total cost when project duration is changed.
... For instance, Feng et al. (1997), Li et al. (1999), Hegazy (1999), Leu and Yang (1999) and Senouci and Eldin (2004) proposed the models for optimization of the project schedules using the genetic algorithms (GA). Shtub et al. (1996) and Azaron et al. (2007) developed the simulated annealing (SA) optimization model formulations. Gagnon et al. (2002) proposed the tabu search (TS) optimization model to minimize the cost of the project. ...
The paper presents the cost optimization of the time schedules for project management. The nonlinear programming (NLP) model for the cost optimization of the time schedules under the generalized precedence relations between the project activities was developed and applied. The existing NLP optimization models have focused on the cost optimal solution of the project scheduling problems which include simplifying assumptions regarding the precedence relationships among the project activities. In this way, this research work aims to propose the NLP optimization model for making optimal time-cost decisions applicable to actual projects in project management. The generalized reduced-gradient method was used for the NLP optimization. The obtained results include the minimum total cost project schedules and the optimal project time-cost curves. The proposed optimization approach enables the insight into the interdependence between the project duration and the total project cost. The decision-maker can more effectively estimate the effect of the project deadline on a total project cost before the submission of a tender. An application example and an example of the time-cost trade-off analysis are presented in the paper to demonstrate the advantages of the proposed approach.
Due to the cyclical nature of commodity prices, the profitability of mining projects relies on proper timing. To ensure optimal profits, mines should be brought online at the time, which maximizes the potential value of the asset. In this paper, a coking coal mine construction case is used to demonstrate the effectiveness of scheduling large-scale construction projects with uncertain durations under price cyclicality. Project parameters are obtained stochastically via Monte Carlo sampling, allowing for the influence of uncertainty to be quantified. The critical path method and linear programming are employed to analyze the results and to optimize the construction process, ensuring the maximum value of the mining project. The parameters are repeatedly sampled to obtain distributions of possible project outcomes, allowing for risk and sensitivity quantification. The optimal schedule for construction was determined to be 247 weeks, with a most likely value of $813 million.
The paper presents the cost optimization of the time schedules for project management. The nonlinear programming (NLP) model for the cost optimization of the time schedules under the generalized precedence relations between the project activities was developed and applied. The existing NLP optimization models have focused on the cost optimal solution of the project scheduling problems which include simplifying assumptions regarding the precedence relationships among the project activities. In this way, this research work aims to propose the NLP optimization model for making optimal time-cost decisions applicable to actual projects in project management. The generalized reduced-gradient method was used for the NLP optimization. The obtained results include the minimum total cost project schedules and the optimal project time-cost curves. The proposed optimization approach enables the insight into the interdependence between the project duration and the total project cost. The decision-maker can more effectively estimate the effect of the project deadline on a total project cost before the submission of a tender. An application example and an example of the time-cost trade-off analysis are presented in the paper to demonstrate the advantages of the proposed approach.
This paper presents the mixed-integer nonlinear programming (MINLP) optimization model for the nonlinear discrete time–cost trade-off problem (NDTCTP). The nonlinear total project cost objective function of the proposed MINLP optimization model is subjected to a rigorous system of generalized precedence relationship constraints between project activities, project duration constraints, logical constraints, and a budget constraint. By means of the proposed MINLP optimization model, one can obtain the minimum total project cost, the project schedule with the optimal discrete start times and the optimal discrete durations of the activities, as well as the optimal time–cost curves of the project. The proposed model yields the exact optimum solution of the NDTCTP. Solving the NDTCTP, using the proposed MINLP model, avoids the need for (piece-wise) linear approximation of the nonlinear expressions. The MINLP model handles the discrete variables explicitly and requires no rounding of the continuous solution into an integer solution. The applicability of the proposed optimization model is not limited to weakly NDTCTPs. A numerical example from the literature and an example of the project time–cost trade-off analysis are presented at the end of the paper in order to show the advantages of the proposed model.
