In this paper, we consider the Minimum Maximal Network Flow Problem (MMNFP), i.e., minimizing the flow value, minimizing the total time among the maximal flow with time-windows, which is a combinatorial optimization and an NP-hard problem. We propose a new version of a MMNFP, this version is a Minimum Maximal Network Fuzzy Flow Problem with Fuzzy Time-Windows (MMNFFPFTW). After a mathematical modeling problem, we introduce some formulations of the problem and one of them is minimization of the concave function over a fuzzy convex set. The problem can also be cast into a difference of the convex (nonconvex) functions programming. We propose a new algorithm of the MMNFFPFTW.
In this paper, we consider the Minimum Maximal Network Flow Problem (MMNFP), i.e., minimizing the flow value, minimizing the total time among the maximal flow with time-windows, which is a combinatorial optimization and an NP-hard problem. We propose a new version of a MMNFP, this version is a Minimum Maximal Network Fuzzy Flow Problem with Fuzzy Time-Windows (MMNFFPFTW). After a mathematical modeling problem, we introduce some formulations of the problem and one of them is minimization of the concave function over a fuzzy convex set. The problem can also be cast into a difference of the convex (nonconvex) functions programming. We propose a new algorithm of the MMNFFPFTW.