Optimal design of a two-level transportation network with a different unit cost for each secondary link

The objective of this paper is to further develop Singhal's framework for designing a two-level hierarchical transportation network consisting of a trunk or primary link and several feeder or secondary links. Secondary links are perpendicular lines from each of the given points and the primary link is a straight line or curve connecting the feet of two extreme perpendicular lines. The problem and the associated strategic and operational considerations such as cost, time, feasibility, and preferred regions for the primary Link in the context of rural highway planning are discussed. Two-level networks are also common in electricity transmission, pipelines, and telecommunication design. The core of the framework is a model for finding the path of a primary link such that a weighted sum of the lengths of the perpendicular lines from each point to a linear primary link and the distance between the feet of the two extreme perpendicular lines is minimized. The analysis shows that for almost every problem there exists a wide range of solutions for which the total cost is only slightly higher than that of the optimal solution. This offers considerable flexibility to the decison maker. These solutions can be evaluated in view of the border objectives and constraints that are not included in the model. The use of computer graphics and the option of a nonlinear or piecewise linear primary link are also discussed.