A fuzzy set-based decision making tool for the transportation network synchronous digital hierarchy planning

This work presents a mathematical formulation of the optimal p-hub allocation and routing problem in designing Transportation Network (TN) in Synchronous Digital Hierarchy (SDH) using the Fuzzy Set (FS) theory. The objective is to maximize the satisfaction level of attending the TN demanded flow through its configuration while obeying all operational conditions. The multicommodity flow of TN–SDH problem is modeled with fuzzy objective and fuzzy constraints. Linear membership functions of the FS are modeled and a Fuzzy Mixed Integer Linear Programming problem is formulated. The solution space in this case is defined as the intersection of the FS describing the constraints and the objective function. The optimal solution is the one with the maximum value for the satisfaction parameters.