A type-2 fuzzy optimization model for project portfolio selection and scheduling incorporating project interdependency and splitting
Abstract
This paper presents a new optimization model and a new interval type-2 fuzzy solution approach for project portfolio selection and scheduling (PPSS) problem, in which split of projects and re-execution are allowable. Afterward, the approach is realized as a multi-objective optimization that maximizes total benefits of projects concerning economic concepts by considering the interest rate and time value of money and minimizes the tardiness value and total number of interruptions of chosen projects. Besides, budget and resources limitation, newfound relations are proposed to consider dependency relationships via a synergy among projects to solve PPSS problem hiring interval type-2 fuzzy sets. For validation of the model, numerical instances are provided and solved by a new extended procedure based on fuzzy optimistic and pessimistic viewpoints regarding several situations. In the end, their results are studied. The results show that it is more beneficial when projects are allowed to be split.
Keyword : project portfolio selection and scheduling, interdependent project, project splitting, interval type-2 fuzzy sets
How to Cite
Zolfaghari, S., Mousavi, S. M., & Antuchevičienė, J. (2021). A type-2 fuzzy optimization model for project portfolio selection and scheduling incorporating project interdependency and splitting. Technological and Economic Development of Economy, 27(2), 493-510. https://doi.org/10.3846/tede.2021.14652
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Egri, P., & Kis, T. (2020). Allocating raw materials to competing projects. Computers & Industrial Engineering, 143, 106386. https://doi.org/10.1016/j.cie.2020.106386
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Haghighi, M. H., Mousavi, S. M., Antucheviciene, J., & Mohagheghi, V. (2019b). A new analytical methodology to handle time-cost trade-off problem with considering quality loss cost under intervalvalued fuzzy uncertainty, Technological and Economic Development of Economy, 25(2), 277–299. https://doi.org/10.3846/tede.2019.8422
Hall, N. G., Long, D. Z., Qi, J., & Sim, M. (2015). Managing underperformance risk in project portfolio selection. Operations Research, 63(3), 660–675. https://doi.org/10.1287/opre.2015.1382
Huang, X., & Zhao, T. (2014). Project selection and scheduling with uncertain net income and investment cost. Applied Mathematics and Computation, 247, 61–71. https://doi.org/10.1016/j.amc.2014.08.082
Javanmard, M., & Nehi, H. M. (2019). A solving method for fuzzy linear programming problem with interval Type-2 fuzzy numbers. International Journal of Fuzzy Systems, 21(3), 882–891. https://doi.org/10.1007/s40815-018-0591-3
Kundu, P., Majumder, S., Kar, S., & Maiti, M. (2019). A method to solve linear programming problem with interval type-2 fuzzy parameters. Fuzzy Optimization and Decision Making, 18(1), 103–130. https://doi.org/10.1007/s10700-018-9287-2
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Li, X., Fang, S. C., Tian, Y., & Guo, X. (2015). Expanded model of the project portfolio selection problem with divisibility, time profile factors and cardinality constraints. Journal of the Operational Research Society, 66(7), 1132–1139. https://doi.org/10.1057/jors.2014.75
Liao, S. H., & Ho, S. H. (2010). Investment project valuation based on a fuzzy binomial approach. Information Sciences, 180(11), 2124–2133. https://doi.org/10.1016/j.ins.2010.02.012
Liesiö, J., Mild, P., & Salo, A. (2008). Robust portfolio modeling with incomplete cost information and project interdependencies. European Journal of Operational Research, 190(3), 679–695. https://doi.org/10.1016/j.ejor.2007.06.049
Liu, S. S., & Wang, C. J. (2011). Optimizing project selection and scheduling problems with timedependent resource constraints. Automation in Construction, 20(8), 1110–1119. https://doi.org/10.1016/j.autcon.2011.04.012
Mendel, J. M., John, R. I., & Liu, F. (2006). Interval type-2 fuzzy logic systems made simple. IEEE Transactions on Fuzzy Systems, 14(6), 808–821. https://doi.org/10.1109/TFUZZ.2006.879986
Mirnezami, S. A., Mousavi, S. M., & Mohagheghi, V. (2020). A new interval type-2 fuzzy approach for multi-scenario project cash flow assessment based on alternative queuing method and dependency structure matrix with a case study. Engineering Applications of Artificial Intelligence, 95, 103815. https://doi.org/10.1016/j.engappai.2020.103815
Mohagheghi, V., Mousavi, S. M., Antuchevičienė, J., & Dorfeshan, Y. (2019). Sustainable infrastructure project selection by a new group decision-making framework introducing MORAS method in an interval type 2 fuzzy environment. International Journal of Strategic Property Management, 23(6), 390–404. https://doi.org/10.3846/ijspm.2019.10536
Mohagheghi, V., Mousavi, S. M., & Vahdani, B. (2015). A new optimization model for project portfolio selection under interval-valued fuzzy environment. Arabian Journal for Science and Engineering, 40(11), 3351–3361. https://doi.org/10.1007/s13369-015-1779-6
Mohagheghi, V., Mousavi, S. M., Mojtahedi, M., & Newton, S. (2020). Evaluating large, high-technology project portfolios using a novel interval-valued Pythagorean fuzzy set framework: An automated crane project case study. Expert Systems with Applications, 162, 113–117. https://doi.org/10.1016/j.eswa.2019.113007
Nowak, M., & Trzaskalik, T. (2021). A trade-off multiobjective dynamic programming procedure and its application to project portfolio selection. Annals of Operations Research. https://doi.org/10.1007/s10479-020-03907-y
Peng, X., & Huang, H. (2020). Fuzzy decision making method based on CoCoSo with critic for financial risk evaluation. Technological and Economic Development of Economys. https://doi.org/10.3846/tede.2020.11920
Rahman, H. F., Chakrabortty, R. K., & Ryan, M. J. (2020). Memetic algorithm for solving resource constrained project scheduling problems. Automation in Construction, 111, 103052. https://doi.org/10.1016/j.autcon.2019.103052
Relich, M. (2021). A Decision Support System for Portfolio Management of NPD Projects. In decision support for product development (pp. 81–94). Springer, Cham. https://doi.org/10.1007/978-3-030-43897-5_4
Salehi, K. (2018). Fuzzy multi-objective project selection problem using additive weighted fuzzy programming. Industrial Engineering Frontiers, 1(1), 1–15.
Santhanam, R., & Kyparisis, G. J. (1996). A decision model for interdependent information system project selection. European Journal of Operational Research, 89(2), 380–399. https://doi.org/10.1016/0377-2217(94)00257-6
Selim, H., & Ozkarahan, I. (2008). A supply chain distribution network design model: an interactive fuzzy goal programming-based solution approach. The International Journal of Advanced Manufacturing Technology, 36(3–4), 401–418. https://doi.org/10.1007/s00170-006-0842-6
Shafahi, A., & Haghani, A. (2013, February). A linearization approach for project selection with interdependencies in resource costs. In ICORES (pp. 230–235). https://doi.org/10.5220/0004214402300235
Tao, X., & Schonfeld, P. (2006). Selection and scheduling of interdependent transportation projects with island models. Transportation Research Record, 1981(1), 133–141. https://doi.org/10.1177/0361198106198100120
Tofighian, A. A., & Naderi, B. (2015). Modeling and solving the project selection and scheduling. Computers & Industrial Engineering, 83, 30–38. https://doi.org/10.1016/j.cie.2015.01.012
Wang, J., & Hwang, W. L. (2007). A fuzzy set approach for R&D portfolio selection using a real options valuation model. Omega, 35(3), 247–257. https://doi.org/10.1016/j.omega.2005.06.002
Watermeyer, K., & Zimmermann, J. (2020). A branch-and-bound procedure for the resource-constrained project scheduling problem with partially renewable resources and general temporal constraints. OR Spectrum, 42(2), 427–460. https://doi.org/10.1007/s00291-020-00583-z
Zhang, X., Hipel, K. W., & Tan, Y. (2019). Project portfolio selection and scheduling under a fuzzy environment. Memetic Computing, 11(4), 391–406. https://doi.org/10.1007/s12293-019-00282-5
Bhattacharyya, R., Kumar, P., & Kar, S. (2011). Fuzzy R&D portfolio selection of interdependent projects. Computers & Mathematics with Applications, 62(10), 3857–3870. https://doi.org/10.1016/j.camwa.2011.09.036
Chen, J., & Askin, R. G. (2009). Project selection, scheduling and resource allocation with time dependent returns. European Journal of Operational Research, 193(1), 23–34. https://doi.org/10.1016/j.ejor.2007.10.040
Damghani, K. K., Sadi-Nezhad, S., & Aryanezhad, M. B. (2011). A modular Decision Support System for optimum investment selection in presence of uncertainty: Combination of fuzzy mathematical programming and fuzzy rule based system. Expert Systems with Applications, 38(1), 824–834. https://doi.org/10.1016/j.eswa.2010.07.040
Dash, B., Narendran, T. T., & Gajanand, M. S. (2016). A model for new product introduction under resource constraints and product interdependence. International Journal of Operational Research, 26(4), pp.473-508. https://doi.org/10.1504/IJOR.2016.077685
Dixit, V. and Tiwari, M.K., 2020. Project portfolio selection and scheduling optimization based on risk measure: a conditional value at risk approach. Annals of Operations Research, 285(1–2), 9–33. https://doi.org/10.1007/s10479-019-03214-1
Dorfeshan, Y., Mousavi, S. M., Vahdani, B., & Siadat, A. (2019). Determining project characteristics and critical path by a new approach based on modified NWRT method and risk assessment under an interval type-2 fuzzy environment. Scientia Iranica, 26(4), 2579–2600. https://doi.org/10.24200/sci.2018.50091.1503
Egri, P., & Kis, T. (2020). Allocating raw materials to competing projects. Computers & Industrial Engineering, 143, 106386. https://doi.org/10.1016/j.cie.2020.106386
Eshghi, A., Mousavi, S. M., & Mohagheghi, V. (2019). A new interval type-2 fuzzy approach for analyzing and monitoring the performance of megaprojects based on earned value analysis (with a case study). Neural Computing and Applications, 31(9), 5109–5133. https://doi.org/10.1007/s00521-018-04002-x
Fox, G. E., Baker, N. R., & Bryant, J. L. (1984). Economic models for R and D project selection in the presence of project interactions. Management Science, 30(7), 890–902. https://doi.org/10.1287/mnsc.30.7.890
Haghighi, M. H., Mousavi, S. M., & Mohagheghi, V. (2019a). A new soft computing model based on linear assignment and linear programming technique for multidimensional analysis of preference with interval type-2 fuzzy sets. Applied Soft Computing, 77, 780–796. https://doi.org/10.1016/j.asoc.2019.01.048
Haghighi, M. H., Mousavi, S. M., Antucheviciene, J., & Mohagheghi, V. (2019b). A new analytical methodology to handle time-cost trade-off problem with considering quality loss cost under intervalvalued fuzzy uncertainty, Technological and Economic Development of Economy, 25(2), 277–299. https://doi.org/10.3846/tede.2019.8422
Hall, N. G., Long, D. Z., Qi, J., & Sim, M. (2015). Managing underperformance risk in project portfolio selection. Operations Research, 63(3), 660–675. https://doi.org/10.1287/opre.2015.1382
Huang, X., & Zhao, T. (2014). Project selection and scheduling with uncertain net income and investment cost. Applied Mathematics and Computation, 247, 61–71. https://doi.org/10.1016/j.amc.2014.08.082
Javanmard, M., & Nehi, H. M. (2019). A solving method for fuzzy linear programming problem with interval Type-2 fuzzy numbers. International Journal of Fuzzy Systems, 21(3), 882–891. https://doi.org/10.1007/s40815-018-0591-3
Kundu, P., Majumder, S., Kar, S., & Maiti, M. (2019). A method to solve linear programming problem with interval type-2 fuzzy parameters. Fuzzy Optimization and Decision Making, 18(1), 103–130. https://doi.org/10.1007/s10700-018-9287-2
Li, X., Fang, S. C., Guo, X., Deng, Z., & Qi, J. (2016). An extended model for project portfolio selection with project divisibility and interdependency. Journal of Systems Science and Systems Engineering, 25(1), 119–138. https://doi.org/10.1007/s11518-015-5281-1
Li, X., Fang, S. C., Tian, Y., & Guo, X. (2015). Expanded model of the project portfolio selection problem with divisibility, time profile factors and cardinality constraints. Journal of the Operational Research Society, 66(7), 1132–1139. https://doi.org/10.1057/jors.2014.75
Liao, S. H., & Ho, S. H. (2010). Investment project valuation based on a fuzzy binomial approach. Information Sciences, 180(11), 2124–2133. https://doi.org/10.1016/j.ins.2010.02.012
Liesiö, J., Mild, P., & Salo, A. (2008). Robust portfolio modeling with incomplete cost information and project interdependencies. European Journal of Operational Research, 190(3), 679–695. https://doi.org/10.1016/j.ejor.2007.06.049
Liu, S. S., & Wang, C. J. (2011). Optimizing project selection and scheduling problems with timedependent resource constraints. Automation in Construction, 20(8), 1110–1119. https://doi.org/10.1016/j.autcon.2011.04.012
Mendel, J. M., John, R. I., & Liu, F. (2006). Interval type-2 fuzzy logic systems made simple. IEEE Transactions on Fuzzy Systems, 14(6), 808–821. https://doi.org/10.1109/TFUZZ.2006.879986
Mirnezami, S. A., Mousavi, S. M., & Mohagheghi, V. (2020). A new interval type-2 fuzzy approach for multi-scenario project cash flow assessment based on alternative queuing method and dependency structure matrix with a case study. Engineering Applications of Artificial Intelligence, 95, 103815. https://doi.org/10.1016/j.engappai.2020.103815
Mohagheghi, V., Mousavi, S. M., Antuchevičienė, J., & Dorfeshan, Y. (2019). Sustainable infrastructure project selection by a new group decision-making framework introducing MORAS method in an interval type 2 fuzzy environment. International Journal of Strategic Property Management, 23(6), 390–404. https://doi.org/10.3846/ijspm.2019.10536
Mohagheghi, V., Mousavi, S. M., & Vahdani, B. (2015). A new optimization model for project portfolio selection under interval-valued fuzzy environment. Arabian Journal for Science and Engineering, 40(11), 3351–3361. https://doi.org/10.1007/s13369-015-1779-6
Mohagheghi, V., Mousavi, S. M., Mojtahedi, M., & Newton, S. (2020). Evaluating large, high-technology project portfolios using a novel interval-valued Pythagorean fuzzy set framework: An automated crane project case study. Expert Systems with Applications, 162, 113–117. https://doi.org/10.1016/j.eswa.2019.113007
Nowak, M., & Trzaskalik, T. (2021). A trade-off multiobjective dynamic programming procedure and its application to project portfolio selection. Annals of Operations Research. https://doi.org/10.1007/s10479-020-03907-y
Peng, X., & Huang, H. (2020). Fuzzy decision making method based on CoCoSo with critic for financial risk evaluation. Technological and Economic Development of Economys. https://doi.org/10.3846/tede.2020.11920
Rahman, H. F., Chakrabortty, R. K., & Ryan, M. J. (2020). Memetic algorithm for solving resource constrained project scheduling problems. Automation in Construction, 111, 103052. https://doi.org/10.1016/j.autcon.2019.103052
Relich, M. (2021). A Decision Support System for Portfolio Management of NPD Projects. In decision support for product development (pp. 81–94). Springer, Cham. https://doi.org/10.1007/978-3-030-43897-5_4
Salehi, K. (2018). Fuzzy multi-objective project selection problem using additive weighted fuzzy programming. Industrial Engineering Frontiers, 1(1), 1–15.
Santhanam, R., & Kyparisis, G. J. (1996). A decision model for interdependent information system project selection. European Journal of Operational Research, 89(2), 380–399. https://doi.org/10.1016/0377-2217(94)00257-6
Selim, H., & Ozkarahan, I. (2008). A supply chain distribution network design model: an interactive fuzzy goal programming-based solution approach. The International Journal of Advanced Manufacturing Technology, 36(3–4), 401–418. https://doi.org/10.1007/s00170-006-0842-6
Shafahi, A., & Haghani, A. (2013, February). A linearization approach for project selection with interdependencies in resource costs. In ICORES (pp. 230–235). https://doi.org/10.5220/0004214402300235
Tao, X., & Schonfeld, P. (2006). Selection and scheduling of interdependent transportation projects with island models. Transportation Research Record, 1981(1), 133–141. https://doi.org/10.1177/0361198106198100120
Tofighian, A. A., & Naderi, B. (2015). Modeling and solving the project selection and scheduling. Computers & Industrial Engineering, 83, 30–38. https://doi.org/10.1016/j.cie.2015.01.012
Wang, J., & Hwang, W. L. (2007). A fuzzy set approach for R&D portfolio selection using a real options valuation model. Omega, 35(3), 247–257. https://doi.org/10.1016/j.omega.2005.06.002
Watermeyer, K., & Zimmermann, J. (2020). A branch-and-bound procedure for the resource-constrained project scheduling problem with partially renewable resources and general temporal constraints. OR Spectrum, 42(2), 427–460. https://doi.org/10.1007/s00291-020-00583-z
Zhang, X., Hipel, K. W., & Tan, Y. (2019). Project portfolio selection and scheduling under a fuzzy environment. Memetic Computing, 11(4), 391–406. https://doi.org/10.1007/s12293-019-00282-5