Mixed-Integer Nonlinear Programming Model for Nonlinear Discrete Optimization of Project Schedules under Restricted Costs
Publication: Journal of Construction Engineering and Management
Volume 142, Issue 3
Abstract
This paper presents the mixed-integer nonlinear programming (MINLP) model for nonlinear discrete optimization of project schedules under restricted costs. The proposed model includes cost-objective function, generalized precedence relationship constraints, project duration restraints, logical conditions, and cost restrictions. The MINLP model allows inclusion of a wide variety of nonlinear expressions and provides the exact optimal output data for construction project management, such as a Gantt chart, histogram, and S-curve of total project cost. The novelty of the contribution is that the planner is now enabled to perform the exact optimal scheduling of project activities simultaneously with scheduling of nonlinearly restricted total project cost at each discrete working time unit. At this point, the restrictions can be set on increments and cumulative values of total project cost. A set of application examples is shown in this paper to demonstrate the advantages of the proposed model.
Get full access to this article
View all available purchase options and get full access to this article.
References
Adeli, H., and Karim, A. (1997). “Scheduling/cost optimization and neural dynamics model for construction.” J. Constr. Eng. Manage., 450–458.
Al Haj, R., and El-Sayegh, S. (2015). “Time-cost optimization model considering float-consumption impact.” J. Constr. Eng. Manage., 04015001.
Brooke, A., Kendrick, D., Meeraus, A., and Raman, R. (2014). GAMS—A user’s guide, GAMS Development, Washington, DC.
Cheng, Y. M., Yu, C. H., and Wang, H. T. (2011). “Short-interval dynamic forecasting for actual S-curve in the construction phase.” J. Constr. Eng. Manage., 933–941.
CPLEX 12.4 [Computer software]. GAMS Development Corporation, Washington, DC.
De, P., Dunne, E. J., Ghosh, J. B., and Wells, C. E. (1995). “The discrete time-cost tradeoff problem revisited.” Eur. J. Oper. Res., 81(2), 225–238.
Demeulemeester, E., De Reyck, B., Foubert, B., Herroelen, W., and Vanhoucke, M. (1998). “New computational results on the discrete time/cost trade-off problem in project networks.” J. Oper. Res. Soc., 49(11), 1153–1163.
Drud, A. S. (1994). “CONOPT—A large-scale GRG code.” ORSA J. Comput., 6(2), 207–216.
Eshtehardian, E., Afshar, A., and Abbasnia, R. (2009). “Fuzzy-based MOGA approach to stochastic time-cost trade-off problem.” Autom. Constr., 18(5), 692–701.
Ezeldin, A. S., and Soliman, A. (2009). “Hybrid time-cost optimization of nonserial repetitive construction projects.” J. Constr. Eng. Manage., 42–55.
Falk, J., and Horowitz, J. L. (1972). “Critical path problems with concave cost-time curves.” Manage. Sci., 19(4), 446–455.
FIDIC (Fédération Internationale des Ingénieours-Conseils). (1999). “Conditions of contract for EPC/Turnkey projects: General conditions, guidance for the preparation of particular conditions, forms of letter of tender, contract agreement and dispute adjudication agreement.” Geneva.
Fulkerson, D. (1961). “A network flow computation for project cost curves.” Manage. Sci., 7(2), 167–178.
GAMS. (2015). “General algebraic modelling system.” Washington, DC, 〈http://www.gams.com〉 (Apr. 12, 2015).
Geem, Z. W. (2010). “Multiobjective optimization of time-cost trade-off using harmony search.” J. Constr. Eng. Manage., 711–716.
Hazir, Ö., Erel, E., and Günalay, Y. (2011). “Robust optimization models for the discrete time/cost trade-off problem.” Int. J. Prod. Econ., 130(1), 87–95.
Hazir, Ö., Haouari, M., and Erel, E. (2010). “Robust scheduling and robustness measures for the discrete time/cost trade-off problem.” Eur. J. Oper. Res., 207(2), 633–643.
He, Z., Wang, N., Jia, T., and Xu, Y. (2009). “Simulated annealing and tabu search for multi-mode project payment scheduling.” Eur. J. Oper. Res., 198(3), 688–696.
Kalhor, E., Khanzadi, M., Eshtehardian, E., and Afshar, A. (2011). “Stochastic time-cost optimization using non-dominated archiving ant colony approach.” Autom. Constr., 20(8), 1193–1203.
Klanšek, U. (2014). “Solving the nonlinear discrete transportation problem by MINLP optimization.” Transport, 29(1), 1–11.
Klanšek, U., and Pšunder, M. (2010). “Cost optimization of time schedules for project management.” Ekon. Istraz., 23(4), 22–36.
Klanšek, U., and Pšunder, M. (2012). “MINLP optimization model for the nonlinear discrete time-cost trade-off problem.” Adv. Eng. Software, 48(1), 6–16.
Lastusilta, T. (2011). “GAMS MINLP solver comparisons and some improvements to the AlphaECP algorithm.” Process Design and Systems Engineering Laboratory, Dept. of Chemical Engineering, Division for Natural Sciences and Technology, Åbo Akademi Univ., Åbo, Finland.
Lucko, G. (2011). “Optimizing cash flows for linear schedules modeled with singularity functions by simulated annealing.” J. Constr. Eng. Manage., 523–535.
Manesi, W., Golzarpoor, B., and Hegazy, T. (2013). “Fast and near-optimum schedule optimization for large-scale projects.” J. Constr. Eng. Manage., 1117–1124.
Moder, J. J., Phillips, C. R., and Davis, E. W. (1995). Project management with CPM, PERT and precedence diagramming, Blitz, Middleton, WI.
Mokhtari, H., Aghaie, A., Rahimi, J., and Mozdgir, A. (2010). “Project time-cost trade-off scheduling: A hybrid optimization approach.” Int. J. Adv. Manuf. Technol., 50(5-8), 811–822.
Moussourakis, J., and Haksever, C. (2004). “Flexible model for time/cost tradeoff problem.” J. Constr. Eng. Manage., 307–314.
Nearchou, A. C. (2010). “Scheduling with controllable processing times and compression costs using population-based heuristics.” Int. J. Prod. Res., 48(23), 7043–7062.
Posebne Gradbene Uzance (Special Construction Practice Code). (1977). “Uradni list SFRJ [Official Gazette of SFRY].”, Ljubljana, Republic of Slovenia (in Slovenian).
Sakellaropoulos, S., and Chassiakos, A. P. (2004). “Project time-cost analysis under generalised precedence relations.” Adv. Eng Software, 35(10–11), 715–724.
Sonmez, R., and Bettemir, Ö. H. (2012). “A hybrid genetic algorithm for the discrete time-cost trade-off problem.” Exp. Syst. Appl., 39(13), 11428–11434.
Vanhoucke, M. (2005). “New computational results for the discrete time/cost trade-off problem with time-switch constraints.” Eur. J. Oper. Res., 165(2), 359–374.
Westerlund, T., and Pörn, R. (2002). “Solving pseudo-convex mixed integer optimization problems by cutting plane techniques.” Optim. Eng., 3(3), 253–280.
Yang, I. T. (2007). “Using elitist particle swarm optimization to facilitate bicriterion time-cost trade-off analysis.” J. Constr. Eng. Manage., 498–505.
Information & Authors
Information
Published In
Journal of Construction Engineering and Management
Volume 142 • Issue 3 • March 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Feb 12, 2015
Accepted: Aug 19, 2015
Published online: Oct 22, 2015
Published in print: Mar 1, 2016
Discussion open until: Mar 22, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.