Modeling Decisions for Project Scheduling Optimization Problem Based on Type-2 Fuzzy Numbers
This paper examines type-2 fuzzy numbers implementation to resource-constrained scheduling problem (RCSP) for agriculture production system based on expert parameter estimations. Some critical parameters in production system are usually treated as uncertain variables due to environmental changes that influence agriculture process. Implementation of type-2 fuzzy sets (T2FSs) can handle uncertain data when estimating variables for solving decision-making problems. The paper focuses on estimation procedure of uncertain variables in scheduling that reflect level of preference or attitude of decision-maker towards imprecise concepts, relations between variables. Special profiles for activity performance allow to consider uncertainty in time variables, expert estimations, flexibilities in scheduling, resource levelling problem and combinatorial nature of solution methodology. An example of activities for agriculture production system is introduced. Heuristic decision algorithm based on enumeration tree and partial schedules is developed. It can handle both resource-constrained optimization problem under uncertain variables and activity profile switching. As initial activity profile we consider expert decision about best activity execution profile on each level of enumeration tree.
KeywordsType-2 fuzzy number Fuzzy graph Combinatorial optimization Scheduling
This work has been supported by the Ministry of Education and Science of the Russian Federation under Project “Methods and means of decision making on base of dynamic geographic information models” (Project part, State task 2.918.2017).
- 2.Brentrup, F., Küsters, J., Lammela, J., Barraclough, P., Kuhlmann, H.: Environmental impact assessment of agricultural production systems using the life cycle assessment (LCA) methodology II. The application to N fertilizer use in winter wheat production systems. Eur. J. Agron. 20, 265–279 (2004)CrossRefGoogle Scholar
- 3.Billaut, J.-C., Moukrim, A., Sanlaville, E.: Flexibility and Robustness in Scheduling. Control Systems, Robotics and Manufacturing Series. Willey-ISTE, Hoboken (2013)Google Scholar
- 6.Knyazeva, M., Bozhenyuk, A., Rozenberg, I.: Scheduling alternatives with respect to fuzzy and preference modeling on time parameters. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K.T., Krawczak, M. (eds.) IWIFSGN/EUSFLAT - 2017. AISC, vol. 642, pp. 358–369. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-66824-6_32CrossRefGoogle Scholar
- 16.Majumdar, P.: Neutrosophic sets and its applications to decision making. In: Acharjya, D., Dehuri, S., Sanyal, S. (eds.) Computational Intelligence for Big Data Analysis. Adaptation, Learning, and Optimization, vol. 19, pp. 97–115. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-16598-1_4CrossRefGoogle Scholar
- 20.Herroelen, W., De Reyck, B., Demeulemeester, E.: Resource-constrained project scheduling: notation, classification, modes and methods by Brucker et al. Eur. J. Oper. Res. 128(3), 221–230 (2000)Google Scholar