Relative Average Deviation as Measure of Robustness in the Stochastic Project Scheduling Problem

Main Article Content


Néstor Raúl Ortiz-Pimiento, M.Sc.
Francisco Javier Díaz-Serna, Ph. D.


In the Project Scheduling Problem (PSP), the solution robustness can be understood as the capacity that a baseline has to support the disruptions generated by unplanned events (risks). A robust baseline of the project can be obtained from redundancy based methods, which are considered proactive methods to solve the stochastic project scheduling problem.  In this research, three redundancy based methods are evaluated and their performance is compared in terms of robustness. These methods add extra time to the original activities duration in order to face the eventualities that may appear during the project execution. In this article a new indicator to analyze the solution robustness to the Project Scheduling Problem with random duration of activities is proposed. This indicator called Relative Average Deviation (RAD) is defined as the margin of deviation of the activities’ start times in relation to their durations. The RAD is based in a traditional concept that seeks to minimize the value of the differences between the planned start times and the real executed start times. The planned start times were obtained from the project baseline generated by each redundancy based method and the real executed start times were obtained from a simulation process based on Monte Carlo technique. The new indicator was used to evaluate the robustness of three baselines generated by different methods but applied to the same case study. Finally, the results suggest that the Relative Average Deviation (RAD) facilitates the interpretation of the robustness concept because it focuses on analyzing the deviation margin associated with an activity.


Article Details


Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

All articles included in the Revista Facultad de Ingeniería are published under the Creative Commons (BY) license.

Authors must complete, sign, and submit the Review and Publication Authorization Form of the manuscript provided by the Journal; this form should contain all the originality and copyright information of the manuscript.

The authors who publish in this Journal accept the following conditions:

a. The authors retain the copyright and transfer the right of the first publication to the journal, with the work registered under the Creative Commons attribution license, which allows third parties to use what is published as long as they mention the authorship of the work and the first publication in this Journal.

b. Authors can make other independent and additional contractual agreements for the non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly indicate that the work It was first published in this Journal.

c. Authors are allowed and recommended to publish their work on the Internet (for example on institutional or personal pages) before and during the process.
review and publication, as it can lead to productive exchanges and a greater and faster dissemination of published work.

d. The Journal authorizes the total or partial reproduction of the content of the publication, as long as the source is cited, that is, the name of the Journal, name of the author (s), year, volume, publication number and pages of the article.

e. The ideas and statements issued by the authors are their responsibility and in no case bind the Journal.


[1] D. G. Malcolm, J. H. Roseboom, C. E. Clark, and W. Fazar, “Application of a Technique for Research and Development Program Evaluation,” Operations Research, vol. 7 (5). pp. 646-669, 1959.

[2] P. Pontrandolfo, “Project Duration in Stochastic Networks by the PERT-Path Technique,” Int. J. Proj. Manag., vol. 18, pp. 215-222, 2000.

[3] D.-E. Lee, “Probability of Project Completion Using Stochastic Project Scheduling Simulation,” J. Constr. Eng. Manag., vol. 131 (3), pp. 310-318, 2005.

[4] E. M. Goldratt, Critical Chain. Great Barrington MA: The North River Press Publishing Corporation, 1997.

[5] S. Van de Vonder, E. Demeulemeester, W. Herroelen, and R. Leus, “The Use of Buffers in Project Management: The Trade-off between Stability and Makespan,” Int. J. Prod. Econ., vol. 97, pp. 227–240, 2005.

[6] K. Rezaie, B. Manouchehrabadi, and S. N. Shirkouhi, “Duration Estimation, a New Approach in Critical Chain Scheduling,” in Proceedings-2009 3rd Asia International Conference on Modelling and Simulation, 2009, pp. 481-484.

[7] L. Bie, N. Cui, and X. Zhang, “Buffer Sizing Approach with Dependence Assumption between Activities in Critical Chain Scheduling,” in POMS 22nd Annual Conference, 2011.

[8] H. Ke, and B. Liu, “Project Scheduling Problem with Stochastic Activity Duration Times,” Appl. Math. Comput., vol. 168 (1), pp. 342-353, 2005.

[9] H. Ke, W. Ma, and X. Chen, “Modeling Stochastic Project Time-Cost Trade-Offs with Time-Dependent Activity Durations,” Appl. Math. Comput., vol. 218 (18), pp. 9462–9469, 2012.

[10] W. J. Gutjahr, C. Strauss, and E. Wagner, “A Stochastic Branch and Bound Approach to Activity Crashing in Project Management,” INFORMS J. Comput., vol. 12 (2), pp. 125-135, 2000.

[11] P. Jaskowski, and S. Biruk, “The Method for Improving Stability of Construction Project Schedules through Buffer Allocation,” Technol. Econ. Dev. Econ., vol. 17 (3), pp. 429-444, 2011.

[12] L. Valadares Tavares, J. A. Antunes Ferreira, and J. Silva Coelho, “On the Optimal Management of Project Risk,” Eur. J. Oper. Res., vol. 107 (2), pp. 451-469, 1998.

[13] H. Mizuyama, “A Time Quality Tradeoff Problem of a Project with Nonstandardized Activities,” in 36th International Conference on Computers and Industrial Engineering, ICC and IE, 2006, pp. 3039-3049.

[14] G. Mitchell, and T. Klastorin, “An Effective Methodology for the Stochastic Project Compression Problem,” IIE Trans., vol. 39 (10), pp. 957-969, 2007.

[15] S. Creemers, R. Leus, and M. Lambrecht, “Scheduling Markovian PERT Networks to Maximize the Net Present Value,” Oper. Res. Lett., vol. 38 (1), pp. 51-56, 2010.

[16] D. Kong, L. Liu, R. Miao, and L. Yin, “Risk Prediction of Project Scheduling Based Cloud Model,” in IEEE International Conference on Service Operations and Logistics, and Informatics, 2008, pp. 2553-2557.

[17] S. Biruk, and P. Jaskowski, “Simulation Modelling Construction Project with Repetitive Tasks Using Petri Nets Theory,” J. Bus. Econ. Manag., vol. 9 (3), pp. 219-226, 2008.

[18] I. Bendavid, and B. Golany, “Setting Gates for Activities in the Stochastic Project Scheduling Problem through the Cross Entropy Methodology,” Ann. Oper. Res., vol. 189 (1), pp. 25-42, 2011.

[19] I. Bendavid, and B. Golany, “Predetermined Intervals for Start Times of Activities in the Stochastic Project Scheduling Problem,” Ann. Oper. Res., vol. 186 (1), pp. 429-442, 2011.

[20] M. Mohammadi, M. Sayed, and M. Mohammad, “Scheduling New Product Development Projects Using Simulation-Based Dependency Structure Matrix,” Int. J. logisctics Syst. Manag., vol. 19 (3), pp. 311-328, 2014.

[21] J. Zhang, X. Song, H. Chen, and R. S. Shi, “Determination of Critical Chain Project Buffer Based on Information Flow Interactions,” J. Oper. Res. Soc., pp. 1-12, 2016.

[22] E. D. Gálvez, S. F. Capuz-Rizo, and J. B. Ordieres, “A Method for Identification of Critical Scheduling Decisions,” J. Mod. Proj. Manag., vol. 5 (1), pp. 46-61, 2017.

[23] M. Brčić, D. Kalpic, and K. Fertalj, “Resource Constrained Project Scheduling under Uncertainty: A Survey,” in 23rd Central European Conference on Information and Intelligent Systems, pp. 401-409, 2012.

[24] S. Rostami, S. Creemers, and R. Leus, “New Strategies for Stochastic Resource-Constrained Project Scheduling,” J. Sched., vol. 20 (1), pp. 1-17, 2017.

[25] W. Herroelen, and R. Leus, “The Construction of Stable Project Baseline Schedules,” Eur. J. Oper. Res., vol. 156 (3), pp. 550-565, 2004.

[26] V. J. Leon, S. D. Wu, and R. H. Storer, “Robustness Measures and Robust Scheduling for Job Shops,” IIE Trans. Institute Ind. Eng., vol. 26 (5), pp. 32-43, 1994.

[27] H. Chtourou, and M. Haouari, “A Two-Stage-Priority-Rule-Based Algorithm for Robust Resource-Constrained Project Scheduling,” Comput. Ind. Eng., vol. 55 (1), pp. 183-194, 2008.

[28] O. Hazir, M. Haouari, and E. Erel, “Robust Scheduling and Robustness Measures for the Discrete Time/Cost Trade-Off Problem,” Eur. J. Oper. Res., vol. 207 (2), pp. 633-643, 2010.

[29] M. A. Khemakhem, and H. Chtourou, “Efficient Robustness Measures for the Resource-Constrained Project Scheduling Problem,” Int. J. Ind. Syst. Eng., vol. 14 (2), p. 245, 2013.

[30] R. Kolisch, and A. Sprecher, “PSPLIB - A Project Scheduling Problem Library,” Eur. J. Oper. Res., vol. 96 (1), pp. 205-216, 1996.

[31] J. Xiong, J. Liu, Y. Chen, and H. A. Abbass, “A Knowledge-Based Evolutionary Multiobjective Approach for Stochastic Extended Resource Investment Project Scheduling Problems,” IEEE Trans. Evol. Comput., vol. 18 (5), pp. 742-763, 2014.

[32] Ö. Ökmen, and A. Özta, “Judgmental Risk Analysis Process Development in Construction Projects,” vol. 40, pp. 1244-1254, 2005.

[33] A. Zafra-Cabeza, M. A. Ridao, and E. F. Camacho, “Using a Risk-Based Approach to Project Scheduling: A Case Illustration from Semiconductor Manufacturing,” Eur. J. Oper. Res., vol. 190 (3), pp. 708-723, 2008.

[34] S. Mansoorzadeh, S. M. Yusof, S. Mansoorzadeh, and H. Zeynal, “A Comprehensive and Practical Framework for Reliable Scheduling in Project Management,” Adv. Mater. Res., vol. 903, pp. 378-383, 2014.

[35] J. Zhang, R. Shi, and E. Díaz, “Dynamic Monitoring and Control of Software Project Effort Based on an Effort Buffer,” J. Oper. Res. Soc., vol. 66 (9), pp. 1555-1565, 2015.

[36] M. M. Cervantes, F. Barber-Sanchís, and A. Lova-Ruiz, Nuevos métodos metaheurísticos para la asignación eficiente, optimizada y robusta de recursos limitados. Valencia: Universidad Politécnica de Valencia, 2010.


Download data is not yet available.