Acta Geographica Sinica ›› 2007, Vol. 62 ›› Issue (8): 840-848.doi: 10.11821/xb200708006

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Linking the Doubly Constr ained Gr avity Model and the Tr anspor tation Model for Tr ip Distr ibutions: A New Approach

LIANG Jinshe1, HE Canfei2, ZHANG Hua1   

  1. 1. School of Geography, Beijing Normal University, Beijing 100875, China;
    2. Department of Urban and Regional Planning, Peking University, Beijing 100871, China
  • Received:2007-01-18 Revised:2007-04-29 Online:2007-08-25 Published:2007-08-25
  • Supported by:

    National Natural Science Foundation of China, No.40635026


The premise condition of doubly constrained gravity model is the same as that of transportation model in linear programming, but the results derived from the models are diverse because of the different behavior assumptions of travelers. It has been proved by Evans that the parameter β in doubly constrained gravity model represents the relative importance of total transportation costs and the possibility of the trip distribution. Based on dual programming of transportation problem and uncertain utility method put forward by Beckmannn & Wallance and Golob & Beckmannn, this study establishes the relationship between doubly constrained gravity model and transportation model. This paper discovers that the parameter " in doubly constrained gravity model goes to positive-infinity and the total transportation costs of trip distribution derived from doubly constrained gravity model meet minimum level as the standard deviation of probability density distribution function for traveler's utility goes to zero. This paper points further out that the balance factors in doubly constrained gravity model reflect market adjustment of the price for travel ends services and the consumer surplus of travelers. Using this method, trip distribution on airlines between seven cities in China in 2003 is simulated. The result also indicates that the difference of travel ends and consumer preferences, substitution of transportation tools, and variety of travel purposes may lead to simulation error and the error can be reduced by transportation cost parameter adjustment.

Key words: transportation model, doubly constrained gravity model, dual programming, balance factor, transportation cost adjustment