Mode Choice in a Hub-and-Spoke Network: A Zero-One Linear Programming Approach

While research has tackled the hub-and-spoke network design problem, that research has overlooked the air-truck modal integration issue which is a common feature of real express delivery systems. This paper devises integer linear programs to represent the mode and route assignment aspects of the operational problem. The model is solved under four different levels of delivery schedule, and the results show that as the promised delivery schedule is relaxed, not only does the use of truck routes become more desirable, but also interesting adjustments in mode and hub assignment occur. Consider the case of hubs in Los Angeles and Dayton. As the time constraints are relaxed, cities such as Minneapolis and New Orleans originally linked by air to Los Angeles, switch to Dayton because cheaper truck routes become feasible.     

Classical Central Places as Protected Thresholds

Previous research efforts demonstrate the use of location covering in the spatial structuring of central places within a single-good context. In a multilevel context, this paper similarly develops a mathematical programming approach to the siting of central places based on the “protection” of inner (or threshold) markets. The objective function maximizes both market coverage of demand and market overlap, subject to an upper bound on market overlap; this allows the formation of different market structures consistent with the various K-valued central place systems of Christaller and Lösch. Siting examples serve to illustrate the working of the protected threshold model in isotropic settings. Furthermore, ways in which the present model might be extended for other situations are examined.     

DO METROPOLITAN AREAS MEAN ANYTHING? A RESEARCH NOTE*

This note analyzes whether central cities and suburbs of a metropolitan area relate to each other in a meaningful way. Specifically, it analyzes whether there is a factor specific to the metropolitan area in central-city and suburban growth once national and regional factors have been taken into account. Data are analyzed for growth of metropolitan areas from 1960 to 1980.