Authors
Abstract
In this paper, a multi-mode resource constrained project selection and scheduling problem is investigated considering the reinvestment strategy in a flexible time horizon. Among a set of available projects, a number of projects are selected and scheduled regarding the constraints on renewable resources and precedence relations. The benefits of project portfolio selection and scheduling are compared in both fixed and flexible time horizons. For this purpose, upper and lower tolerance limits are considered for the predetermined time horizon. If the schedule exceeds the time horizon, a penalty cost will be charged. The objective is to determine the optimal time horizon. A mixed-integer linear programming model is proposed for this problem, and solved by GAMS software/CPLEX solver and also a combination of a proposed heuristic algorithm, Genetic Algorithm, and a local search method. Numerical results show that the proposed approach has an acceptable performance in terms of the quality of the solution and the running time. Also, dealing with the problem in a flexible time horizon is more profitable compared to a fixed time horizon.
Keywords
1. Cooper, R., Edgett, S., and Kleinschmidt, E., “Portfolio Management for New Product Development: Results of an Industry Practices Study”, R&D Management, Vol. 31, No. 4, pp. 361-380, 2001.
2. Markowitz, H., “Portfolio Selection”, The Journal of Finance, Vol. 7, No. 1, pp. 77-91, 1952.
3. Gutjahr, W. J., and Reiter, P., “Bi-objective Project Portfolio Selection and Staff Assignment Under Uncertainty”, Optimization, Vol. 59, No. 3, pp. 417-445, 2010.
4. Najafzad, H., Davari-Ardakani, H., and Nemati-Lafmejani, R., “Multi-skill Project Scheduling Problem Under Time-of-Use Electricity Tariffs and Shift Differential Payments”, Energy, Vol. 168, pp. 619-636, 2019.
5. Belenky, A. S., “A Boolean Programming Problem of Choosing an Optimal Portfolio of Projects and Optimal Schedules for Them by Reinvesting within the Portfolio the Profit From Project Implementation”, Applied Mathematics Letters, Vol. 25, No. 10, pp. 1279-1284., 2012.
6. Jafarzadeh, M., Tareghian, H. R., Rahbarnia, F., and Ghanbari, R., “Optimal Selection of project Portfolios Using Reinvestment Strategy within a Flexible Time Horizon”, European Journal of Operational Research, Vol. 243, No. 2, pp. 658-664, 2015.
7. Liu, Y. J., and Zhang, W. G., “Flexible Time Horizon Project Portfolio Optimization with Consumption and Risk Control”, Applied Soft Computing, Vol. 76 , pp. 282-293, 2019.
8. Huang, X., Zhao, T., and Kudratova, S. , “Uncertain Mean-Variance and Mean-Semivariance Models for Optimal Project Selection and Scheduling”, Knowledge-Based Systems, Vol. 93, pp. 1-11, 2016.
9. Bhattacharyya, R., Kumar, P., and Kar, S., “Fuzzy R&D Portfolio Selection of Interdependent Projects”, Computers & Mathematics with Applications, Vol. 62, No. 10, pp. 3857-3870, 2011.
10. Khalili-Damghani, K., Tavana, M., Abtahi, A. R., and Arteaga, F. J. S., “Solving Multi-Mode Time–Cost–Quality Trade-off Problems Under Generalized Precedence Relations”, Optimization Methods and Software, Vol. 30, No. 5, pp. 965-1001, 2015.
11. Cheng, J., Fowler, J., Kemp, K., and Mason, S., “Multi-Mode Resource-Constrained Project Scheduling Problems with Non-Preemptive Activity Splitting”, Computers & Operations Research, Vol. 53, pp. 275-287, 2015.
12. Maghsoudlou, H. R., Afshar-Nadjafi, B., and Akhavan Niaki, S. T., “A Multi-Objective Invasive Weeds Optimization Algorithm for Solving Multi-Skill Multi-Mode Resource Constrained Project Scheduling Problem”, Computers & Chemical Engineering, Vol. 88, pp. 157-169, 2016.
13. Toffolo, T. A. M., Santos. H. G., Carvalho, M. A. M. and Soares, J. A., “An Integer Programming Approach to the Multimode Resource-Constrained Multiproject Scheduling Problem”, Journal of Scheduling, Vol. 19, No. 3, pp. 295-307, 2016.
14. Delgoshaei, A., Al-Mudhafar, A., and Ariffin, M. K. A., “Developing a New Method for Modifying Over-Allocated Multi-Mode Resource Constraint Schedules in the Presence of Preemptive Resources”, Decision Science Letters, Vol. 5, No. 4, pp. 499-518, 2016.
15. Naber, A. and Kolisch, R., “MIP Models for Resource-Constrained Project Scheduling with Flexible Resource Profiles”, European Journal of Operational Research, Vol. 239, No. 2, pp. 335-348, 2014.
16. Schnabel, A., Kellenbrink, C., and Helber, S., “Profit-Oriented Scheduling of Resource-Constrained Projects with Flexible Capacity Constraints”, Business Research, Vol. 11, No. 2, pp. 329-356, 2018.
17. Chen, A., Liang, Y., and Padilla, J., “An Experimental Reactive Scheduling Framework for the Multi-Mode Resource Constrained Project Scheduling Problem”, in Proceedings of the International Multi Conference of Engineers and Computer Scientists, 2017.
18. Tao, S., and Dong, Z. S., “Multi-Mode Resource-Constrained Project Scheduling Problem with Alternative Project Structures”, Computers & Industrial Engineering, Vol. 125, pp. 333-347, 2018.
19. Javanmard, S., Afshar-Nadjafi, B., and Niaki, S.T.A., “Preemptive Multi-Skilled Resource Investment Project Scheduling Problem: Mathematical Modelling and Solution Approaches”, Computers & Chemical Engineering, Vol. 96, pp. 55-68, 2017.
20. Zamani, R., “An Effective Mirror-Based Genetic Algorithm for Scheduling Multi-Mode Resource Constrained Projects”, Computers & Industrial Engineering, Vol. 127, pp. 914-924, 2019.
21. Nemati-Lafmejani, R., Davari-Ardakani, H., and Najafzad, H., “Multi-Mode Resource Constrained Project Scheduling And Contractor Selection: Mathematical Formulation and Metaheuristic Algorithms”, Applied Soft Computing, Vol. 81, 2019, In press.
22. .Lin, J., Zhu, L., and Gao, K., “A Genetic Programming Hyper-Heuristic Approach for the Multi-Skill Resource Constrained Project Scheduling Problem”, Expert Systems with Applications, Vol. 140, 2020, In press.
2. Markowitz, H., “Portfolio Selection”, The Journal of Finance, Vol. 7, No. 1, pp. 77-91, 1952.
3. Gutjahr, W. J., and Reiter, P., “Bi-objective Project Portfolio Selection and Staff Assignment Under Uncertainty”, Optimization, Vol. 59, No. 3, pp. 417-445, 2010.
4. Najafzad, H., Davari-Ardakani, H., and Nemati-Lafmejani, R., “Multi-skill Project Scheduling Problem Under Time-of-Use Electricity Tariffs and Shift Differential Payments”, Energy, Vol. 168, pp. 619-636, 2019.
5. Belenky, A. S., “A Boolean Programming Problem of Choosing an Optimal Portfolio of Projects and Optimal Schedules for Them by Reinvesting within the Portfolio the Profit From Project Implementation”, Applied Mathematics Letters, Vol. 25, No. 10, pp. 1279-1284., 2012.
6. Jafarzadeh, M., Tareghian, H. R., Rahbarnia, F., and Ghanbari, R., “Optimal Selection of project Portfolios Using Reinvestment Strategy within a Flexible Time Horizon”, European Journal of Operational Research, Vol. 243, No. 2, pp. 658-664, 2015.
7. Liu, Y. J., and Zhang, W. G., “Flexible Time Horizon Project Portfolio Optimization with Consumption and Risk Control”, Applied Soft Computing, Vol. 76 , pp. 282-293, 2019.
8. Huang, X., Zhao, T., and Kudratova, S. , “Uncertain Mean-Variance and Mean-Semivariance Models for Optimal Project Selection and Scheduling”, Knowledge-Based Systems, Vol. 93, pp. 1-11, 2016.
9. Bhattacharyya, R., Kumar, P., and Kar, S., “Fuzzy R&D Portfolio Selection of Interdependent Projects”, Computers & Mathematics with Applications, Vol. 62, No. 10, pp. 3857-3870, 2011.
10. Khalili-Damghani, K., Tavana, M., Abtahi, A. R., and Arteaga, F. J. S., “Solving Multi-Mode Time–Cost–Quality Trade-off Problems Under Generalized Precedence Relations”, Optimization Methods and Software, Vol. 30, No. 5, pp. 965-1001, 2015.
11. Cheng, J., Fowler, J., Kemp, K., and Mason, S., “Multi-Mode Resource-Constrained Project Scheduling Problems with Non-Preemptive Activity Splitting”, Computers & Operations Research, Vol. 53, pp. 275-287, 2015.
12. Maghsoudlou, H. R., Afshar-Nadjafi, B., and Akhavan Niaki, S. T., “A Multi-Objective Invasive Weeds Optimization Algorithm for Solving Multi-Skill Multi-Mode Resource Constrained Project Scheduling Problem”, Computers & Chemical Engineering, Vol. 88, pp. 157-169, 2016.
13. Toffolo, T. A. M., Santos. H. G., Carvalho, M. A. M. and Soares, J. A., “An Integer Programming Approach to the Multimode Resource-Constrained Multiproject Scheduling Problem”, Journal of Scheduling, Vol. 19, No. 3, pp. 295-307, 2016.
14. Delgoshaei, A., Al-Mudhafar, A., and Ariffin, M. K. A., “Developing a New Method for Modifying Over-Allocated Multi-Mode Resource Constraint Schedules in the Presence of Preemptive Resources”, Decision Science Letters, Vol. 5, No. 4, pp. 499-518, 2016.
15. Naber, A. and Kolisch, R., “MIP Models for Resource-Constrained Project Scheduling with Flexible Resource Profiles”, European Journal of Operational Research, Vol. 239, No. 2, pp. 335-348, 2014.
16. Schnabel, A., Kellenbrink, C., and Helber, S., “Profit-Oriented Scheduling of Resource-Constrained Projects with Flexible Capacity Constraints”, Business Research, Vol. 11, No. 2, pp. 329-356, 2018.
17. Chen, A., Liang, Y., and Padilla, J., “An Experimental Reactive Scheduling Framework for the Multi-Mode Resource Constrained Project Scheduling Problem”, in Proceedings of the International Multi Conference of Engineers and Computer Scientists, 2017.
18. Tao, S., and Dong, Z. S., “Multi-Mode Resource-Constrained Project Scheduling Problem with Alternative Project Structures”, Computers & Industrial Engineering, Vol. 125, pp. 333-347, 2018.
19. Javanmard, S., Afshar-Nadjafi, B., and Niaki, S.T.A., “Preemptive Multi-Skilled Resource Investment Project Scheduling Problem: Mathematical Modelling and Solution Approaches”, Computers & Chemical Engineering, Vol. 96, pp. 55-68, 2017.
20. Zamani, R., “An Effective Mirror-Based Genetic Algorithm for Scheduling Multi-Mode Resource Constrained Projects”, Computers & Industrial Engineering, Vol. 127, pp. 914-924, 2019.
21. Nemati-Lafmejani, R., Davari-Ardakani, H., and Najafzad, H., “Multi-Mode Resource Constrained Project Scheduling And Contractor Selection: Mathematical Formulation and Metaheuristic Algorithms”, Applied Soft Computing, Vol. 81, 2019, In press.
22. .Lin, J., Zhu, L., and Gao, K., “A Genetic Programming Hyper-Heuristic Approach for the Multi-Skill Resource Constrained Project Scheduling Problem”, Expert Systems with Applications, Vol. 140, 2020, In press.
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