نویسندگان
1 دانشکده فنی و مهندسی، گروه مهندسی صنایع، دانشگاه خوارزمی، تهران
2 دانشکده مهندسی صنایع و سیستمهای مدیریت، دانشگاه صنعتی امیرکبیر، تهران
چکیده
در این مقاله، مسئله انتخاب و زمانبندی پروژه چندحالتی با منابع محدود با در نظر گرفتن امکان سرمایهگذاری مجدد عواید پروژه در افق زمانی انعطافپذیر مورد بررسی قرار گرفته است. بر این اساس، سازوکار مسئله مذکور بهگونهای است که از بین پروژههای پیشنهادی، تعدادی انتخاب و فعالیتهای آنها با توجه به روابط پیشنیازی و محدودیت منابع تجدیدپذیر زمانبندی میشود. در این مسئله به مقایسه سود حاصل از انتخاب سبد پروژه و زمانبندی و اجرای فعالیتهای آنها بین دو حالتی که افق زمانی ثابت و یا منعطف باشد، پرداخته شده است. به همین منظور حدود تلرانس بالا و پایینی برای افق زمانی از پیش تعیین شده در نظر گرفته شده است. در صورت تجاوز از افق زمانی مذکور، هزینهای بهعنوان جریمه در نظر گرفته خواهد شد و هدف تعیین افق زمانی مطلوب است. یک مدل برنامهریزی عدد صحیح مختلط برای این مسأله پیشنهاد شده است و جهت حل آن در ابعاد کوچک و بزرگ از نرمافزار گمز و حلگر سیپلکس و ترکیبی از یک الگوریتم ابتکاری پیشنهادی، الگوریتم ژنتیک و جست و جوی محلی استفاده شده است. سپس نتایج حاصل از آنها با یکدیگر مورد مقایسه قرار گرفته است. نتایج عددی نشان میدهند که الگوریتم پیشنهادی عملکرد قابل قبولی از منظر کیفیت جواب و زمان حل داشته و همچنین در نظر گرفتن افق زمانی انعطافپذیر میتواند افزایش عایدی قابل توجهی را نسبت به عدم در نظر گرفتن آن داشته باشد.
کلیدواژهها
عنوان مقاله [English]
Multi-mode Resource Constrained Project Selection and Scheduling Considering the Reinvestment Strategy in a Flexible Time Horizon
نویسندگان [English]
- S. Moomivand 1
- H. Davari-Ardakani 1
- H. Mosadegh 2
- M. Abouei Ardakan 1
1
2
چکیده [English]
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.
کلیدواژهها [English]
- Multi-mode project selection and scheduling
- Resource constraints
- Flexible time horizon
- Reinvestment strategy
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.
)