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On the Role of Congestion in Transportation Problems
Author(s) -
Prager William
Publication year - 1955
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19550350606
Subject(s) - product (mathematics) , production (economics) , consumption (sociology) , computer science , operations research , transport engineering , economics , microeconomics , mathematics , engineering , social science , geometry , sociology
In discussing the most efficient manner of distributing a product from several sources to numerous locations, Hitchcock [1] assumed that the specific transportation cost for a given shipping route was independent of the amount shipped over this route. In the present paper the problem is discussed under the assumption that the specific shipping cost for a route increases linearly with the amount shipped over this route. It is shown that the optimal shipping program then is unique and that it can be discussed either in terms of flows along the routes or in terms of accounting princes at the centers of production and consumption. A maximum principle is established for the accounting prices, which leads to a maximum characterization of the cost of the optimal program.