the passenger line planning is a process of strategic long-term decision-making problem in the field of railway passenger planning. a line is a route between starting point and destination with certain stops, which has a certain frequency of train schedule. a new solution based on decomposition algorithm has been proposed in this paper, which is defined in a master problem and two sub problems....

Transportation Problem is an important problem which has been widely studied in Operations Research domain. It has been often used to simulate different real life problems. In particular, application of this Problem in NP-Hard Problems has a remarkable significance. In this Paper, we present the closed, bounded and non–empty feasible region of the transportation problem using fuzzy trapezoidal ...

We study a variant of the classical transportation problem in which suppliers with limited capacities have a choice of which demands (markets) to satisfy. We refer to this problem as the transportation problem with market choice (TPMC). While the classical transportation problem is known to be strongly polynomial-time solvable, we show that its market choice counterpart is strongly NP-complete....