Application of Fuzzy Sets to Aggregate Production Planning With Multiproducts and Multitime Periods
The objective of this study is to develop a fuzzy mathematical programming method to solve aggregate production planning (APP) decision problems that involve multiproducts and multitime periods in a fuzzy environment. The fuzzy APP model that is developed here attempts to minimize total cost with respect to inventory carrying levels, available labor levels, machine capacity and warehouse space, and the constraint of available budget. The proposed APP method evaluates monetary interest of related operating cost categories and provides greater computational efficiency and flexibility by adopting triangular fuzzy numbers and piecewise linear membership functions to represent both imprecise data and fuzzy goals. The actual performance of an industrial company was used to demonstrate the feasibility of applying the proposed method to real-world APP decisions. The proposed method yields an efficient solution and presents overall decision-maker satisfaction with the given goal values. This paper also presents several significant management implications that are related to the practical application of the proposed method.
- "In this study, fuzzy model for production planning is considered, which is also extensively used in the literature. Liang et al. (2011), for instance, developed a fuzzy mathematical programming method to solve aggregate production planning decision problems that involve multi products and multi time periods in a fuzzy environment. The study evaluates monetary interest of related operating cost categories and provides greater computational efficiency and flexibility by adopting triangular fuzzy numbers and piecewise linear membership functions to represent both imprecise data and fuzzy goals. "
[Show abstract] [Hide abstract] ABSTRACT: We combine the concepts of gradual numbers and Kaucher arithmetic on extended intervals to define extended gradual interval (EGI) arithmetic in which subtraction and division operators are the inverse operators of addition and multiplication, respectively. Use of the proposed EGI operators can lead to non-monotonic gradual intervals that are not fuzzy subsets and cannot be represented by fuzzy intervals. In this context and when fuzzy representation results are desired, an approximation strategy is proposed to determine the nearest fuzzy interval of the non-monotonic gradual interval obtained. This approximation is viewed as an interval regression problem according to an optimization procedure. The EGI operators are applied to the common fuzzy weighted average (FWA) leading to a gradual weighted average (GWA).0Comments 2Citations
- "More complicated and realistic cases must be further tested. For example, the proposed operators may be used in the context of sensitivity analysis , solving of uncertain linear and nonlinear systems , uncertain aggregation operators , solving of optimization problems , solving of multiple-criteria decision-making problems [13,35,47,48], inverse control design [5,6,10], determination of cluster centers for linguistic fuzzy C-means , and aggregation of Sugeno-like rule consequents . Table A.1 Interpretation of the indicator Ξ (λ). "
- [Show abstract] [Hide abstract] ABSTRACT: Recently, gradual numbers have been introduced as a means of extending standard interval computation methods to fuzzy and gradual intervals. However, it is well known that the practical use of standard interval arithmetic operators, just like their fuzzy extension, gives results that are more imprecise than necessary and, in some cases, even counterintuitive. In this paper, we combine the concepts of gradual numbers and Kaucher arithmetic on extended intervals to define extended gradual interval arithmetic, where subtraction and division operators are, respectively, the inverse operators of the addition and the multiplication. They are applied to the inversion of a linear regressive model and to a control problem that is based on the inversion of a linear model.0Comments 3Citations