An outer-approximation algorithm for a class of mixed-integer nonlinear programs
Mathematical Programming: Series A and B
Nonlinear time/cost tradeoff models in project management
Computers and Industrial Engineering
Project time-cost analysis under generalised precedence relations
Advances in Engineering Software - Special issue on engineering computational technology
Advances in Engineering Software - Special issue on design optimization
Ant system: optimization by a colony of cooperating agents
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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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.