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: | Dial Robert B. |
Keywords: | programming: linear |
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.