Network Design with Fixed and Variable Cost Elements

A route selection algorithm is presented far designing transportation networks. The algorithm balances fixed construction costs and variable user costs in a network having a fixed set of nodes and a known demand, for internode service. The problem solved is a special case of the fixed-cost, multicommodity transshipment problem in which each commodity has a single, unique source node. The route selection algorithm alternatively applies link elimination and link insertion criteria that converge to a local optimum. Upper and lower bounds on the fixed and variable portions of the globally optimum solution are determined and the sensitivity of the solution is estimated. Unique rules are formulated for identifying links that must or must not appear in the globally optimum solution. The solution procedure has been coded for a digital computer and demonstrated using a representation of Minneapolis-St. Paul having 68 nodes and 476 potential oneway links.