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The combined distribution and stochastic assignment problem.

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Title: The combined distribution and stochastic assignment problem.
Authors: Lundgren, Jan T.1 jalun@mai.liu.se, Patriksson, Michael2 mipat@math.chalmers.se
Source: Annals of Operations Research. 1998, Vol. 82 Issue 1-4, p309-329. 21p. 1 Chart.
Subjects: Assignment problems (Programming), Nonlinear assignment problems, Air travel, Economic equilibrium, Algorithms, Commercial aeronautics, Economics
Abstract: The combined distribution and assignment problem is the problem of the simultaneous determination of the distribution of trips between origins and destinations in a transportation network and the assignment of trips to routes in each origin-destination pair. In the model most widely used, the distribution is assumed to follow a gravity model with a negative exponential deterrence function and the assignment is made according to the deterministic user equilibrium principle. In this paper, we describe an extension of this model in which the allocation of trips to routes is made according to the principle of stochastic user equilibrium. We discuss the behavioural foundations of trip assignment and combined models assuming deterministic or stochastic route choice. In particular, we describe how they can be derived using the efficiency principle from discrete choice theory; the combined distribution and stochastic assignment model is obtained as the continuous approximation of the discrete problem of finding the most probable flow pattern under the assumption of efficient trip making behaviour. We outline an algorithm for the solution of the model which is based on route (column) generation, disaggregate simplicial decomposition, and partial linearization. [ABSTRACT FROM AUTHOR]
Copyright of Annals of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22Annals+of+Operations+Research%22">Annals of Operations Research</searchLink>. 1998, Vol. 82 Issue 1-4, p309-329. 21p. 1 Chart.
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  Data: <searchLink fieldCode="DE" term="%22Assignment+problems+%28Programming%29%22">Assignment problems (Programming)</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+assignment+problems%22">Nonlinear assignment problems</searchLink><br /><searchLink fieldCode="DE" term="%22Air+travel%22">Air travel</searchLink><br /><searchLink fieldCode="DE" term="%22Economic+equilibrium%22">Economic equilibrium</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Commercial+aeronautics%22">Commercial aeronautics</searchLink><br /><searchLink fieldCode="DE" term="%22Economics%22">Economics</searchLink>
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  Data: The combined distribution and assignment problem is the problem of the simultaneous determination of the distribution of trips between origins and destinations in a transportation network and the assignment of trips to routes in each origin-destination pair. In the model most widely used, the distribution is assumed to follow a gravity model with a negative exponential deterrence function and the assignment is made according to the deterministic user equilibrium principle. In this paper, we describe an extension of this model in which the allocation of trips to routes is made according to the principle of stochastic user equilibrium. We discuss the behavioural foundations of trip assignment and combined models assuming deterministic or stochastic route choice. In particular, we describe how they can be derived using the efficiency principle from discrete choice theory; the combined distribution and stochastic assignment model is obtained as the continuous approximation of the discrete problem of finding the most probable flow pattern under the assumption of efficient trip making behaviour. We outline an algorithm for the solution of the model which is based on route (column) generation, disaggregate simplicial decomposition, and partial linearization. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Annals of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1023/A:1018970905404
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        Text: English
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        PageCount: 21
        StartPage: 309
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      – SubjectFull: Assignment problems (Programming)
        Type: general
      – SubjectFull: Nonlinear assignment problems
        Type: general
      – SubjectFull: Air travel
        Type: general
      – SubjectFull: Economic equilibrium
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      – SubjectFull: Algorithms
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      – SubjectFull: Commercial aeronautics
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      – SubjectFull: Economics
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              Text: 1998
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