Minimal-revenue congestion pricing Part II: An efficient algorithm for the general case

Minimal-revenue congestion pricing Part II: An efficient algorithm for the general case

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Article ID: iaor20012843
Country: United Kingdom
Volume: 34B
Issue: 8
Start Page Number: 645
End Page Number: 665
Publication Date: Nov 2000
Journal: Transportation Research. Part B: Methodological
Authors:
Keywords: programming: linear
Abstract:

The second of a two-part series, this paper derives an efficient solution to the minimal-revenue tolls problem. As introduced in Part I, this problem can be defined as follows: Assuming each trip uses only a path whose generalized cost is smallest, find a set of arc tolls that simultaneously minimizes both average travel time and out-of-pocket cost. As a point of departure, this paper first re-solves the single-origin problem of Part I, modeling it as a linear program. Then with a change of variable, it transforms the LP's dual into a simple longest-path problem on an acyclic network. The multiple-origin problem – where one toll for each arc applies to all origins – solves analogously. In this case, however, the dual becomes an elementary linear multi-commodity max-cost flow problem with an easy bundling constraint and infinite arc capacities. After a minor reformulation that simplifies the model's input to better accommodate output from common traffic assignment software, a solution algorithm is exemplified with a numerical example.

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