Network Flow Models: Use in Rural Freight Transportation Analysis and a Comparison with Linear Programming

The logistical efficiency and viability of the algorithms in comparison with linear programrural transportation system is a growing conming for solution of models with a network cern of agricultural producers, transportation structure. Fuller et al. [4] used a network flow regulators, and policy makers. Railroad facility model in combination with implicit enumeralimitations, abandonment of railroad track, tion for a plant location problem involving deterioration of the rural road system, and fixed charges. Their approach involved partial changing transportation rate structures are enumeration in conjunction with a network examples of issues for which solutions and flow algorithm which was found to be more efevaluations are required' [14, 15]. To plan and ficient for the solution of network structured evaluate transportation alternatives, decision subproblems than linear programming codes. makers need a research tool with an ability to Wright and Meyer [16] employed a network answer numerous "what if" types of quesmodel to analyze development of a Brazilian tions. Often the model must include a spatial rail corridor and indicated superiority of and/or temporal dimension, in addition to network flows models to linear programming microscopic detail of the transportation and for transportation planning. Although marketing system. Therefore, large models are network flow models appear to be superior for needed and efficiency of computer solution certain types of problems, no systematic procedures becomes a relevant consideration.2 analysis has been attempted to identify these The flexibility of the research tool to include situations. necessary system realism may also become an The objective of this article is to illustrate important concern, and compare network flow and linear programLinear programming has been used successming models for the solution of network strucfully by applied economists to solve a variety tured problems representative of rural freight of models which include a spatial and/or transportation systems.8 In particular, the purtemporal dimension. Many of these models poses of this article are to (1) demonstrate the have what is termed a network structure, the potential use of network flow models in rural type of structure characteristic of the transtransportation research and (2) compare linear portation and transshipment models. Pubprogramming and network flow models with lished works by Fedeler and Heady [3], Leath respect to computer solution efficiency and and Martin [11], Holroyd [6], and King and flexibility to incorporate alternative transporLogan [8] are examples from an extensive list tation system features. The comparative of research products in which linear programanalysis is carried out on a linear minimumming is used to solve models with a network cost capacitated transshipment model structure. Recently, several articles have alrepresentative of a rural freight transportation luded to the superiority of network flow system. Transportation system models often